Re: [fricas-devel] Re: Debian package on github?
Hi Ralf In principle, in *every* linux distribution one can: 1) install the powerful nix package manager (This in general is easily done manually, but in Debian >= bulleyes official packages are available, see [1]) 2) use nix to install and regularly update fricas (1.3.7 is available in nixpkgs stable [2]). The simple file default.nix controls the compilation on nix side: it shows that sbcl is used [3]. Notes: - in "nix on Debian" setup the nix packages are stored in a folder different from standard Debian's one. - the fricas nix package has currently not a fully fledged maintainer and, in case of delay, one should ask for updates to the nix newsgroup. - jfricas is not in nix, so one should use also pythonic package managers. I planned to use this method but then I went for direct compilation (thanks to your kind help). Cheers riccardo REFS: * [1] https://packages.debian.org/bullseye/nix-setup-systemd * [2] https://search.nixos.org/packages?channel=21.11&from=0&size=50&sort=relevance&type=packages&query=fricas * [3] https://github.com/NixOS/nixpkgs/blob/nixos-21.11/pkgs/applications/science/math/fricas/default.nix#L15 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/45d6b689-f967-392c-dbf9-73f6c4594581%40gmail.com.
[fricas-devel] Mathcad 6.0 relies on Fricas
Hello, just for your info (and maybe for the website): it seems that Mathcad Prime 6.0 Symbolic Engine uses FriCAS as symbolic engine. https://community.ptc.com/t5/PTC-Mathcad/Mathcad-Prime-6-0-Symbolic-Engine-based-on-Axiom-Fricas/m-p/629190 best regards Riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/3a709e7b-3a24-da66-0625-87724af0d691%40gmail.com.
Re: Re: [fricas-devel] book.pdf for fricas 1.3.5 ?
Thanks for the updated docs Ralf! riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/b56ba1cc-5352-0f9e-663e-39d3d795fbdb%40gmail.com. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] book.pdf for fricas 1.3.5 ?
Hi to all! If I understand correctly, the current version of book.pdf in fricas.github.io is not in sync with patches in the docs introduced in 1.3.5 . Are there any problems in this sense? riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/6b68f904-ee9f-bfc5-ea20-ccbeef242e17%40gmail.com. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] strange sum error
Reproduced in 1.3.4 ric PS btw thanks Waldek and you all for 1.3.5 FriCAS Computer Algebra System Version: FriCAS 1.3.4 Timestamp: Wed Jun 27 13:40:07 CEST 2018 - Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave FriCAS and return to shell. - Type: Void (1) -> sum(sum(a^k, a=1..k), k=1..n) - log(%C) >> Error detected within library code: Hidden constant detected (1) -> sum(sum(a^k, a=1..k), k=1..10) - log(%C) >> Error detected within library code: Hidden constant detected (1) -> sum(a^k, a=1..k) k ──┐k (1) > a ──┘ a = 1 Type: Expression(Integer) (2) -> f(k)==sum(a^k, a=1..k) Type: Void (3) -> sum(f(k), k=1..n) Compiling function f with type Variable(k) -> Expression(Integer) - log(%C) >> Error detected within library code: Hidden constant detected (3) -> f(3) Compiling function f with type PositiveInteger -> Fraction( Polynomial(Integer)) (3) 36 Type: Fraction(Polynomial(Integer)) (4) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/22fd4bb3-6551-54d0-f451-9e23e595a7ee%40gmail.com. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Re: Simple Gaussian integral fails
1) Why does not sqrt(a^2) return abs(a)?
IIUC:
When operating on a symbolic expression x in Expression R,
the operator sqrt "represents an arbitrary (but always the same through the code)
solution y of the algebraic equation y^2=x".
Even when R = Integer, there are still 2 real roots y that satisfy the equation.
Similar semantics for the n-th root nthRoot:
"an arbitrary (but always the same through the code) solution of the algebraic
equation y^n=x".
Note that sqrt(x) may not be imagined to be a set with two elements
because the (pointwise) product of two sets would be a set including also
non-diagonal products of the elements.
(IE sqrt(4)={+2,-2} ==> sqrt(4)*sqrt(4) = {(+2)*(+2),...} = {+4, -4}).
So, FriCAS deliberately tries not to make a choice of roots
and consequently sqrt has a different semantics (on expressions)
as compared to all other CAS in my knowledge.
As for the (sometimes) weird behavior of abs in FriCAS
this should be related to the fact that using a smart abs one might construct
zero divisors,
(nonzero x1,x2 such that x1 * x2 = 0). This would violate the fact that
Expression Integer
is meant to be a differential field, which is essential for the indefinite
integration algorithms.
To recover more information I advice you to track the above keywords in the
past messages:
many of your (present and future) questions have been already asked many times
in the last 10 years.
riccardo
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[fricas-devel] Re: Re: Simple Gaussian integral fails
On 11/8/18 1:05 PM, Marduk wrote: 3) How can one tell FriCAS that a>0 in the Gaussian integral? Write a=A^2 : (1) -> inf ==> %plusInfinity; integrate(exp(-A^4*x^2),x=-inf..inf) ┌───┐ \│%pi (1) ── 2 A Type: Union(f1: OrderedCompletion(Expression(Integer)),...) another sad physicist... -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] friCAS API: weird eval signature?
Hi to all. This is mainly for Ralf.
In
http://fricas.github.io/api/FunctionSpace.html#l-function-space
I read:
eval: (%, List Symbol, List NonNegativeInteger, List List % -> %) -> % if R has
Ring
eval(x, [s1, ..., sm], [n1, ..., nm], [f1, ..., fm])
replaces every si(a1, ..., an)^ni in x by fi(a1, ..., an) for any a1, …, am.
Now, if function application without parentheses is right associating (ie 'f g
x = f(g(x)')
I parse
List List % -> %
above as
( List (List %) ) -> %
or
List( List (% -> %) )
depending on the binding strength of '->'.
(Guess is the former case, ie '->' is weaker than function application.)
But in
https://github.com/hemmecke/fricas/blob/master-hemmecke/src/algebra/fspace.spad#L494
I see:
eval : (%, List SY, List N, List(List % -> %)) -> %
++ eval(x, [s1, ..., sm], [n1, ..., nm], [f1, ..., fm]) replaces
++ every \spad{si(a1, ..., an)^ni} in x by \spad{fi(a1, ..., an)}
++ for any a1, ..., am.
which seems to suggest that the correct parsing is different from the previous
two, ie:
List( List(%) -> % )
Am I missing something or there is a real problem?
Riccardo
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Re:Re: Re: [fricas-devel] weird primitive
Waldek:
Unfortunately no. You have equalty when additionaly real parts of
z1 and z2 are nonnegative. But in whole D things are "interesting".
Your claim (1) shows that principal branch creates traps that
normal users do not see. So "familiar" should be taken with
grain of salt.
Upss ... that *was* familiar some time ago... SHAME ON ME!!
DLMF [10] says that it should be correct to replace
"if z1*z2 in D" in (1)
by
"if pi< arg(z1)+arg(z2) <= pi"
Well, whatever, the point was to use (correct) identities by default
in PrincipalBranchExpression.
Waldek:
Actually, you have the some trouble with (2) as with (1).
More nonsense of mine?
I thought that (2) was OK in polar coordinates z~(r,phi)
for the "log -manifold" and with
log z(r,phi) := log r + i phi
z1*z2 := ( z1.r * z2.r, z1.phi + z2.phi )
... but maybe you mean if we work on complex patches homemorphic to C-cut.
Waldek:
Users are brainwashed to accept principal branches, but
in most applications we deal with continous functions.
That is, correct branch is one leading to continous
function. So, much of complexity (unsolvability!)
introduced by principal branches really is useless
and does not correspond to real world. Part of
branch cut complications is due to using wrong
model, that is pretending that we are working
on euclidean space when we should work with manifolds.
sounds elegant, but is that doable in a CAS?
Waldek:
Well, how you define 'x^a'? I am aware of only one FriCAS domain
which defines 'x^a' for irrational 'a' differently than via 'exp'.
The exception is SmallOrdinal and you could argue that ordinals
are in some sense "rational".
OK, so for irrational 'a' FriCAS defines
x^a := e^{a log(x)}
but does this definition hold (in FriCAS) also for rational 'a' and in
particular 'a = 1/n'?
I mean, I'm confused by my tests below
(1) -> (2^sqrt(3) = e^(sqrt(3)*log(2)))::Boolean
(1) false
Type: Boolean
(2) -> (2^(1/3) = e^(1/3*log(2)))::Boolean
(2) false
Type: Boolean
(3) -> (2^(5/3) = e^(5/3*log(2)))::Boolean
(3) false
Type: Boolean
(4) -> (1^sqrt(3) = e^(sqrt(3)*log(1)))::Boolean
(4) false
Type: Boolean
(5) -> (1^(5/3) = e^(5/3*log(1)))::Boolean
(5) true
Type: Boolean
(6) -> (1^(1/3) = e^(1/3*log(1)))::Boolean
(6) true
Type: Boolean
--- below dependent kernels on purpose,
--- why they are not simplified unsing definition of '^'?
(7) -> integrate(2^sqrt(3)-e^(sqrt(3)*log(2)),x)
┌─┐┌─┐
log(2)\│3 log(e) log(2)\│3
(7) - x %e + x %e
Type: Union(Expression(Integer),...)
(8) -> integrate(2^(5/3)-e^((5/3)*log(2)),x)
5 log(2)log(e)
──
3 3┌─┐2
(8) - x %e + 2 x \│2
Type: Union(Expression(Integer),...)
(9) -> integrate(2^(1/3)-e^((1/3)*log(2)),x)
log(2)log(e)
3 3┌─┐
(9) - x %e + x\│2
Type: Union(Expression(Integer),...)
Waldek:
You should understand that domain that you propose is quite
unlike domains already present in FriCAS. Main point is
that there are almost no absolute equalities, most things
are conditional.
Well, you over-evaluate my understanding of FriCAS global design:
I understand that one would simplify only if some conditions are met,
and that many equalities would be undecidable =
larger expressions with hidden identities
but I do not quite see why one could not recycle most of code from the current
Expression Integer, and why a "full tree representation of expressions"
would be mandatory instead of the usual rational function of kernels
representation.
Waldek:
I have some sympathy towards such domain. But implementing
it is no small task. First, it should be correct. It should
cooperate somewhat with other domains (which is tricky
because it so different from other parts of FriCAS).
And it should be reasonably efficient (naive tree-rewriting
in many cases gives exponential blowup).
"M* on FriCAS" ... the best of the two worlds in a single (open source) CAS...
appealing indeed.
Thanks for your time
riccardo
[10] https://dlmf.nist.gov/4.8.E2
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Re: Re: Re: [fricas-devel] weird primitive
PS:
* Lapsus: in 1) replace "differential algebra" by "differential field" (*-commutative,
those used by "Risch... alg"). Sorry for the confusion
* I forgot a question:
6) for which domains of a and x is true that x^a = e^{a log(x)} (in FriCAS, I
mean)? When this is (automatically) used? I will do empirical tests asap I'll
have time but a design statement is always helpful.
riccardo
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Re: Re: [fricas-devel] weird primitive
Dear Waldek
thanks for having immediately sent the *summary* of the note I've asked
... now I'm eager to read the forthcoming full note with its details ;)
Well, apart from jokes, I've not re-replied immediately because
I've spent some time digging in old mails of this list trying to grasp
the main ideas of FriCAS present and future design.
Below you'll find some thoughts/questions you might want to comment/answer.
These thoughts concern the user interface for the inverse functions, which is
a topic that periodically returns in the list.
In the past you repeatedly spoke of users with inconsistent wishes, so,
to be more "precise", let me start by setting up some "notation",
reviewing some facts I learned from the list.
I will restrict to log and sqrt for shortness and expose the various ways
such functions might be defined.
All the definitions below (apart maybe SetValuedExpression, I do not know)
should respect the property that
these functions are right-inverses under composition, ie
(sqrt(x))^2 =x exp(log(x))=x for every x in their domain D.
--- PrincipalBranchExpression ---
Let the PrincipalBranchExpression be a domain of analytic, complex valued
functions each defined by its respective ``principal branch'',
ie defined in a cut complex plane,
the cuts being arbitrarily but conventionally agreed to be as detailed
eg by Olver et al. in [2]:
sqrt, log: D -> C where D:=C -[0,-oo] (I neglect boundaries for simplicity).
For every z1,z2 in D such that z1*z2 in D we have the nice relations
sqrt(z1)*sqrt(z2)=sqrt(z1*z2) and log(z1)+log(z2)=log(z1*z2) (1)
In my knowledge this domain and (1) is well-defined mathematically
but has not a nice algebraic properties adapted to "Risch... algorithm"
and no algorithms to decide if A=0 in full generality. Too Bad.
On the other hand,
a heuristic & arbitrary "simplify" is possible,
based on pattern-matching transformations, eg
implementing a bunch of transformation rules (including (1)) and choosing
the best/shortest result based on some arbitrary expression length function.
This is the domain in which happily & daily work thousand of researchers out
there,
using Maxima, Sympy and other CAS I do not master or afford.
I guess that (1) is applied automatically by these CAS whenever its hypotheses
may be proven to be satisfied, hence the following replacements are
likely to be exploited.
sqrt(2)*sqrt(3)<~>sqrt(6) and sqrt(1-i)sqrt(1+i)<~>sqrt(2)
--- RealExpression ---
One may define a domain RealExpression of
regular functions on a real subset,
sqrt, log: D -> R where D:=(0,oo) (I neglect boundaries for simplicity).
At the price of banning some incompatible "highschool relation"
(like (-1)^(1/3)=-1)
I guess that one can consider the functions in RealExpression as appropriate
restriction of functions in PrincipalBranchExpression,
up to optimizations that exploit reality to improve the speed.
So I do not consider any more this domain.
--- AnyBranchExpression ---
Let AnyBranchExpression be the domain of analytic complex valued
functions, each well-defined on some arbitrary cut complex plane,
not necessary the ``principal branch''.
In this case a to a function with a single branch point
correspond in general a non countable
infinity of functions, think for instance
sqrt, log: D -> C where D:=C-[0,oo]*e^{i theta}
with theta in R
and also to the fact that the cut need not to be a straight line.
Now I give some possible approaches to "multi-valued" functions:
--- RiemannSurfaceExpression ---
Let RiemannSurfaceExpression be the domain of meromorphic functions
defined on Riemann surface.
sqrt, log: D -> R where D "is" {(r,phi): r in R_+ and phi in R }
for every z1,z2 in D
sqrt(z1)*sqrt(z2)=sqrt(z1*z2) and log(z1)+log(z2)=log(z1*z2) (2)
--- SetValuedExpression ---
Let SetValuedExpression be a domain of set-valued functions:
sqrt: C-{0} -> Parts(C),
x|-> { princbranchsqrt(x), -princbranchsqrt(x)}.
log: C-{0} -> Parts(C),
x|-> {princbranchlog(x)+2pi i k, with k in Z}.
I see that there are attempts to construct a mathematical theory of these
set valued functions [3]
IIUC the product in this space is defined by direct product:
f(x)*g(y) = { zf*zg with zf in f(x) and zg in g(y)}.
--- DifferentialField ---
(The following domain is quite new to me and I have much to learn,
so forgive my sloppiness)
Let DifferentialField be some *abstract* field endowed with an additive
derivative
satisfying Leibniz rule and extending the rational fild Q(x).
This is the natural framework for implementing the "Risch... algorithm"
for finding antiderivatives.
(I do not really know how should define the algebraic "functions" here.
See below.)
In this field one defines
log(x) by D(log(x))=1/x
Actually this does define log(x) "up to a constant", so I do not know if this
log(x) has something to do with the other log(x) defined in the other domains.
As an aside:
Are the elements of DifferentialField naturally isomorphic to
*concrete, numerical* functions?
I
Re: [fricas-devel] weird primitive
Hi Waldek I've done some elementary tests to try to understand how FriCAS looks at n-rooths and log, but now I am even more confused. * (1) puzzles me: from your previous answer I have understood that (...)^(1/n) with n>1 was "mostly" seen by FriCAS as a multivalued and possibly complex algebraic number. Is (1) an exception? * (3) seems to suggest that for positive integer n and positive x x^(1/n) = e^(log(x)/n), but this is violated by (7) * (6) and (8) are consistent, but how is defined x^a with a irrational and positive x? (1) -> (1 = (1)^(1/2))::Boolean (1) true Type: Boolean (2) -> (1 = e^(1/2*log(1)))::Boolean (2) true Type: Boolean (3) -> (sqrt(1) = e^(1/2*log(1)))::Boolean (3) true Type: Boolean (4) -> (1 = (1)^(sqrt(3)))::Boolean (4) false Type: Boolean (5) -> (1 = e^(sqrt(3)*log(1)))::Boolean (5) true Type: Boolean (6) -> ((1)^(sqrt(3)) = e^(sqrt(3)*log(1)))::Boolean (6) false Type: Boolean (7) -> (sqrt(2) = e^(1/2*log(2)))::Boolean (7) false Type: Boolean (8) -> (2^sqrt(2) = e^(sqrt(2)*log(2)))::Boolean (8) false Type: Boolean I guess that the present status of the code is, as usual, "quite intricated", but, if not already done, would it be possible for you to take the time (on the medium term) to write a short note or some rule of thumbs to explain to new users how FriCAS behaves in view of irrational powers, log, inverse functions, which relations are expected to hold, and how integrate and complex integrate behave in view of explicitly trascendental numbers, integration variable and external parameters, like a or a^b or log(a)? Furthermore, your view on what should be the ideal target behavior to nicely resolve these ambiguities and have a homogeneous interface would surely be a relief ... Best regards Riccardo PS Speaking of oddities, to me (11) and (12) should behave in the same way: as elements of R->R or or as complex multivalued. (9) -> sin(0) (9) 0 Type: Expression(Integer) (10) -> sinh(0) (10) 0 Type: Expression(Integer) (11) -> asin(0) (11) 0 Type: Expression(Integer) (12) -> asinh(0) (12) asinh(0) -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] question on using .fricas.input, it is not being read by Fricas
No idea what is the problem but I reproduce the issue with Nasser erfc function. The macro erfc2 is taken into account and works. ric (1) -> )system cat /home/guida/.fricas.input )set output characters default macro %SIF(e) == unparse(e::InputForm) -- SPAD Input Form erfc(x) == 1 - erf(x) macro erfc2(x) == 1 - erf(x) (1) -> erfc2(1) (1) - erf(1) + 1 Type: Expression(Integer) (2) -> erfc(1) There are no library operations named erfc Use HyperDoc Browse or issue )what op erfc to learn if there is any operation containing " erfc " in its name. Cannot find a definition or applicable library operation named erfc with argument type(s) PositiveInteger Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need. (2) -> )display op erfc erfc is not a known function. FriCAS will try to list its functions which contain erfc in their names. This is the same output you would get by issuing )what operations erfc There are no operations containing those patterns (2) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: [fricas-devel] Using aldor FFI to link mathgl
3) ~ (Naive || impudent) Funny fix! Thanks for your clarifications, Kurt. Riccardo PS ... and yes I dreamed of replace sman hyperdoc and graphics with Qt (+- mathgl) PS2: could you give a link to the asymptote wrapper? -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] weird primitive
After a rescaling of a and b, the fundamental theorem of calculus holds, uff :) But still (4) in my previous email was weird. ric (1) -> integrand:=1/(x^3*(a*9+b*x)^(1/3)) 1 (1) ─── 3 3┌─┐ x \│b x + 9 a Type: Expression(Integer) (2) -> primitive:=integrate(integrand,x) (2) 2 2 ┌─┐3┌───┐3┌─┐2 3┌───┐2 3┌─┐ - 2 b x \│3 log(\│9 a \│b x + 9 a + \│9 a \│b x + 9 a + 9 a) + 2 2 ┌─┐3┌───┐2 3┌─┐ 4 b x \│3 log(\│9 a \│b x + 9 a - 9 a) + ┌─┐3┌───┐2 3┌─┐ ┌─┐ 2 2 2 \│3 \│9 a \│b x + 9 a + 9 a\│3 12 b x atan() 27 a + ┌─┐3┌───┐3┌─┐2 (12 b x - 81 a)\│3 \│9 a \│b x + 9 a / 2 2 ┌─┐3┌───┐ 1458 a x \│3 \│9 a Type: Union(Expression(Integer),...) (3) -> shouldBeZero := D(primitive,x) - integrand (3) 0 Type: Expression(Integer) (4) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] weird primitive
Hi I was unable to get zero out of (3) , so I tried a trick in (4) (Waldek once wrote that integrate simplifies its input), but (4) is now positive for all positive a,b,x ... I'm confused... Riccardo (1) -> integrand:=1/(x^3*(a+b*x/sqrt(3))^(1/3)) 3┌─┐ \│3 (1) ─── ┌─┐ 3 3│┌─┐ x \│b x\│3 + 3 a Type: Expression(Integer) (2) -> primitive:=integrate(integrand,x) 6┌─┐2 \│3 (2) - ┌───┐2 2 3│6┌─┐3 2 x \│b x \│3 + 3 a Type: Union(Expression(Integer),...) (3) -> shouldBeZero := D(primitive,x) - integrand (3) ┌───┐2 3┌─┐6┌─┐3 3┌─┐ 3│6┌─┐3 (- 3 b x\│3 \│3 - 9 a\│3 )\│b x \│3 + 3 a + ┌─┐ 6┌─┐5 6┌─┐2 3│┌─┐ (4 b x \│3 + 9 a \│3 )\│b x\│3 + 3 a / ┌─┐ ┌───┐2 4 6┌─┐33 3│┌─┐ 3│6┌─┐3 (3 b x \│3 + 9 a x )\│b x\│3 + 3 a \│b x \│3 + 3 a Type: Expression(Integer) (4) -> shouldBeZero2:=eval(integrate(shouldBeZero,z),z=1) (4) 6┌─┐5 b \│3 ─ ┌───┐2 3 52 3 6┌─┐3 2 4 3 2 3│6┌─┐3 ((9 b x + (27 a + 18 a)b x )\│3 + 27 a b x + 81 a x )\│b x \│3 + 3 a Type: Expression(Integer) -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Fwd: [fricas-devel] Using aldor FFI to link mathgl
Dear Kurt, a lot of infos: thanks! BTW A list of all FriCAS non-core packages available on internet would be quite helpful to new users, hope Ralf one day will add it to the github site (Kurt)> May certainly compete with mathgl regarding quality ;) I do not want to enter in graphics-lib faith wars :) -- I must say I do not care the lib as far as standard features are available and layout is reasonably good. As for mathgl: I spent (and I'm spending) some hours in trying to clarify the question of angles (theta,phi) in viewport, and I rapidly realized that the C code is -- how to say that politely -- "quite intricate" (tons of global variables and includes, verbatim code repetitions, unnecessarily repeated computations of geometrical matrices, mysterious changes of signs every here and there). For instance, nowadays, each time you plot a single 3D point in view3D you compute two 4x4 matrix products (of which one involving the *identity matrix*) to recover the matrices describing the global geometry (which is shared among *all* points in a given object). So, to calm my stomach ache, I just started to think how I would replace viewmanager and hyperdoc (and maybe socket manager) if I was a programmer and to dream of a nice Qt interface (mathgl is self contained but Qt friendly). As for spad_http: I did not follow your spad_http project in the last months and now I'm really impressed by the the fact that you managed to have Jupyter working for spad and with some graphics support: bravo! On the other hand, I must say that there a few things in spad_http that disturb me :( and (for the moment) prevent me from rush and install it in my production system: basically my motivations are due to paranoia and ignorance, which may pass with time & study of your code. Let me impudently expose them: 1) I do not like the idea of having a package loader (quicklisp) that installs things in my production system (where btw?). IIUC, looking at the *.asd files, at each start of the kernel quicklisp is called to load your webSPAD server, which depends only on hunchentoot which :depends-on (:chunga, :cl-base64, :cl-fad, :cl-ppcre :flexi-streams :md5 :rfc2388 :trivial-backtrace :usocket :bordeaux-threads). In debian I have py2 and py3 packages for all the 3 needed main dependences: requests, plotly and Hunchentoot: why should I need quicklisp at all? Would not be better to keep install of dependencies as an optional command, well separated from kernel start & run? 2) (less severe, I guess) Why do you hardcode the dependence on python 2 ? On my side I have Jupyter running in python 3 (simpy is stopping support of python2 and sagemath working towards supporting py3). I do not know if I can safely install debian packages for python2-jupyter and python3-jupyter, so I would prefer to patch your code for py3. Would not be better to stay py2/py3 agnostic and possibly leave the choice to the user via configuration or environmental variable? 3) (Naive & impudent) Why did you introduce a dependence on hunchentoot and drop the original python-only Jupyter kernel wrapper or the lisp one? Zero dependencies is better than one dependency: are the latter really impossible? Riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Using aldor FFI to link mathgl
Hi Quite dreamy, I was thinking at the conceptual possibility of writing a spad wrapper for the mathgl graphics library [1]. One could make spad-system-calls (systemCommand$MoreSystemCommands) sending scripts in mgl language to the mgl interpreter [2] (in the spirit of Bill's GnuDraw) or one could try to link the shared objects from the available C interface [3]. I've seen Waldek's experimental lapack package [4]. IIUC correctly the equivalent in this case would be spad functions calling lisp function wrappers which make "alien-calls" to functions in the shared objects from C. I was wondering, waiting for a FFI for spad, would not be possible/realistic/efficient to prepare aldor wrapper functions that directly call the external C functions, then "somehow" compile these functions via FriCAS, and finally expose them? I'm sorry I'm vague but I never used aldor. Riccardo [1] http://mathgl.sourceforge.net/doc_en/MathGL-features.html#MathGL-features [2] http://mathgl.sourceforge.net/doc_en/Utilities.html#Utilities http://mathgl.sourceforge.net/doc_en/UDAV.html#UDAV [3] http://mathgl.sourceforge.net/doc_en/C-interface.html [4]http://www.math.uni.wroc.pl/~hebisch/fricas/lapack/ -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Buggy looking output form of a Type
... unevaluated concat's in (3). Riccardo (1) -> gametes:=['AB,'Ab,'aB,'ab] (1) [AB, Ab, aB, ab] Type: List(OrderedVariableList([AB,Ab,aB,ab])) (2) -> segregationRates : List SquareMatrix(4,FRAC INT) := [matrix [ [1, 1/2, 1/2, 9/20], [1/2, 0, 1/20, 0], [1/2, 1/20, 0, 0], [9/20, 0, 0, 0] ], matrix [ [0, 1/2, 0, 1/20], [1/2, 1, 9/20, 1/2], [0, 9/20, 0, 0], [1/20, 1/2, 0, 0] ], matrix [ [0, 0, 1/2, 1/20], [0, 0, 9/20, 0], [1/2, 9/20, 1, 1/2], [1/20, 0, 1/2, 0] ], matrix [ [0, 0, 0, 9/segregationRates : List SquareMatrix(4,FRAC INT) := [matrix [ [1, 1/2, 1/2, 9/20], [1/2, 0, 1/20, 0], [1/2, 1/20, 0, 0], [9/20, 0, 0, 0] ], matrix [ [0, 1/2, 0, 1/20], [1/2, 1, 9/20, 1/2], [0, 9/20, 0, 0], [1/20, 1/2, 0, 0] ], matrix [ [0, 0, 1/2, 1/20], [0, 0, 9/20, 0], [1/2, 9/20, 1, 1/2], [1/20, 0, 1/2, 0] ], matrix [ [0, 0, 0, 9/20], [0, 0, 1/20, 1/2], [0, 1/20, 0, 1/2], [9/20, 1/2, 1/2, 1] ] ] (2) ┌1 19┐ ┌11┐ ┌11┐ ┌ 9┐ │1 ─ ─ ──│ │0 ─ 0 ──│ │0 0 ─ ──│ │0 0 0 ──│ │2 2 20│ │2 20│ │2 20│ │20│ │ │ │ │ │ │ │ │ │11│ │19 1 │ │ 9│ │ 1 1 │ │─ 0 ── 0 │ │─ 1 ── ─ │ │0 0 ── 0 │ │0 0 ── ─ │ │2 20│ │2 20 2 │ │20│ │20 2 │ [│ │, │ │, │ │, │ │] │11│ │ 9│ │19 1 │ │ 1 1 │ │─ ── 0 0 │ │0 ── 0 0 │ │─ ── 1 ─ │ │0 ── 0 ─ │ │2 20│ │20│ │2 20 2 │ │20 2 │ │ │ │ │ │ │ │ │ │ 9│ │ 1 1 │ │ 1 1 │ │ 9 1 1 │ │── 0 0 0 │ │── ─ 0 0 │ │── 0 ─ 0 │ │── ─ ─ 1 │ └20┘ └20 2 ┘ └20 2 ┘ └20 2 2 ┘ Type: List(SquareMatrix(4,Fraction(Integer))) (3) -> x : ALGSC(DECIMAL, 4, gametes, segregationRates) := convert [3/10, 1/5, 1/10, 2/5] (3) 0.4ab + 0.1aB + 0.2Ab + 0.3AB Type: AlgebraGivenByStructuralConstants(DecimalExpansion,4,[AB,Ab,aB,ab],[[[1,CONCAT(0,.,5),CONCAT(0,.,5),CONCAT(0,.,CONCAT(4,5))],[CONCAT(0,.,5),0,CONCAT(0,.,CONCAT(0,5)),0],[CONCAT(0,.,5),CONCAT(0,.,CONCAT(0,5)),0,0],[CONCAT(0,.,CONCAT(4,5)),0,0,0]],[[0,CONCAT(0,.,5),0,CONCAT(0,.,CONCAT(0,5))],[CONCAT(0,.,5),1,CONCAT(0,.,CONCAT(4,5)),CONCAT(0,.,5)],[0,CONCAT(0,.,CONCAT(4,5)),0,0],[CONCAT(0,.,CONCAT(0,5)),CONCAT(0,.,5),0,0]],[[0,0,CONCAT(0,.,5),CONCAT(0,.,CONCAT(0,5))],[0,0,CONCAT(0,.,CONCAT(4,5)),0],[CONCAT(0,.,5),CONCAT(0,.,CONCAT(4,5)),1,CONCAT(0,.,5)],[CONCAT(0,.,CONCAT(0,5)),0,CONCAT(0,.,5),0]],[[0,0,0,CONCAT(0,.,CONCAT(4,5))],[0,0,CONCAT(0,.,CONCAT(0,5)),CONCAT(0,.,5)],[0,CONCAT(0,.,CONCAT(0,5)),0,CONCAT(0,.,5)],[CONCAT(0,.,CONCAT(4,5)),CONCAT(0,.,5),CONCAT(0,.,5),1]]]) (4) -> z : ALGSC(Fraction Integer, 4, gametes, segregationRates) := convert [3/10, 1/5, 1/10, 2/5] 2 1 1 3 (4) ─ ab + ── aB + ─ Ab + ── AB 5 10 5 10 Type: AlgebraGivenByStructuralConstants(Fraction(Integer),4,[AB,Ab,aB,ab],[[[1,1/2,1/2,9/20],[1/2,0,1/20,0],[1/2,1/20,0,0],[9/20,0,0,0]],[[0,1/2,0,1/20],[1/2,1,9/20,1/2],[0,9/20,0,0],[1/20,1/2,0,0]],[[0,0,1/2,1/20],[0,0,9/20,0],[1/2,9/20,1,1/2],[1/20,0,1/2,0]],[[0,0,0,9/20],[0,0,1/20,1/2],[0,1/20,0,1/2],[9/20,1/2,1/2,1]]]) (5) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Re: [fricas-devel] BUG: viewpoint$ThreeDimensionalViewport + METAPATCHES
Replies to Waldek's ones (in non-chronological order):
Sorry, not replotting is the feature. It is impossible to "undo"
spurious replot. On fast displays spurious replots merely waste
time but on slow ones can create ugly artifacts. So quality
plotting routines must give user control of replotting.
The main point of the proposal was homogeneity of user interface (UI).
Presently viewpoint(vp,1,2,3) and rotate(vp,3.14/4.0,3.14/4.0) actually redraw
so homogeneity of UI and your feature argument would imply to shut-off these
anti-feature... but mine was a weak suggestion, so it is ok to stay here.
Some unsolicited thoughts "pour parler":
I assume that guaranteeing a user-friendly and as-simple-as-possible UI is
among FriCAS mandatory targets. I hope for the survival of FriCAS that this is
the case :)
Viewport UI is not very homogeneous among 2D and 3D: many names, semantics, and
options are different.
I'm happy to see that there are other packages in development (Scene and
GnuDraw) but again new UI and, especially for Scene, new concepts and new names
(sadly violating the full-words naming convention used in Axiom/FriCAS).
Would not be useful to have a few categories that impose a minimal "2D, 3D
scientific plotting" UI that past, present, and future drawing packages must honor
(and of course extend if they wish)? This way a user might smoothly move from one package
to another, and learn the whole details of a package if more functionalities were needed.
It would encourage developers to test new ways without burdening the users.
Just as a stupid example (with no pretensions, one has to think carefully to
names, functionalities, options,)
Plot2DShowCategory():Category with
plot2DFunction
plot2DCurve
plot2DPoints
show2DPlots
Plot2DFormats ==> Union(SVG, Postscript, GnuPlot,)
Plot2DToXCategory( F:Plot2DFormats ):Category
plot2DFunctionTo
plot2DCurveTo
plot2DPointsTo
show2DPlotsTo
... analog in 3d ...
end of "pour parler".
but ATM I do not see why anybody would want such a routine.
Well, as a benchmark of FriCAS present scientific graphical capabilities I was
trying to reproduce
https://et.wikipedia.org/wiki/Fail:Gamma_abs_3D.png
with the same parameters:
ViewPoint -> {-2, -2.5, 1}
ie position (x,y,z) of an observer looking toward the object.
Probably first we need to know what those angles really mean.
Saying longitude and latitude avoids real question: what is their
role in display.
You are right. The problem is that src/graph is a jungle...
I'm wondering if the time that it would take to understand all the details of
src/graph and maintain it is not comparable to that that an experienced C/C++
programmer (which excludes me) could take to reconstruct from scratch a minimal
viewport interface (possibly with more than 9 plots allowed and vector
graphics...), maybe extracting it form an open source project, ie the Qt based
https://en.wikipedia.org/wiki/FreeMat
Anyway, at a first sight I would say that a necessary condition is the
understanding of the omnipresent global macro ROTATE and friends:
void
ROTATE(float xxR[4][4])
{
xxR[0][0]= -(cosTheta); xxR[0][1]= -(-sinTheta*cosPhi); xxR[0][2]=
-(sinTheta*sinPhi); xxR[0][3]= 0.0;
xxR[1][0]= -(sinTheta); xxR[1][1]= -(cosTheta*cosPhi); xxR[1][2]=
-(-cosTheta*sinPhi); xxR[1][3]= 0.0;
xxR[2][0]= 0.0; xxR[2][1]= -(sinPhi); xxR[2][2]= -(cosPhi);
xxR[2][3]= 0.0;
xxR[3][0]= 0.0; xxR[3][1]= 0.0; xxR[3][2]= 0.0;
xxR[3][3]= -(1.0);
}
https://github.com/fricas/fricas/blob/master/src/graph/view3D/transform3d.c#L90
The problem is that a search gives more definitions of these
sinTheta/cosTheta/...:
https://github.com/fricas/fricas/search?q=cosTheta&unscoped_q=cosTheta
I guess that the one which interest us are in
https://github.com/fricas/fricas/blob/master/src/graph/view3D/viewport3d.c
more on this later
Riccardo
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Re: [fricas-devel] Re: [fricas-devel] eigenvalues
I see, thanks both of you! @Waldek What's wrong in trying to "honestly" convert eg Expression(Integer) to a Polynomial(Expression(Integer)) or a Fraction (Polynomial(Expression(Integer)))? 1) -> Expression(Integer) has Ring (1) true Type: Boolean (2) -> Expression(Integer) has Field (2) true Type: Boolean (3) -> Expression(Integer) has PolynomialFactorizationExplicit (3) true Type: Boolean (4) -> exi:=%pi+%e^2 2 (4) %e + %pi Type: Expression(Integer) (5) -> exi::Polynomial(Expression(Integer)) Polynomial(Expression(Integer)) is not a valid type. (5) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] eigenvalues
Hi does anybody know how to compute the eigenvalues of (1) -> m:= matrix [[%p, %i *%e],[-%i*%e,%pi^2]] ┌ %p %i %e┐ (1) │ │ │2 │ └- %i %e %pi ┘ with one of friCAS eigenvalues function? Thanks in advance, Riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] zeroOf
Hi The function zeroOf(p) zeroOf(p,x), with p a polynomial at first sight seems more harmful than useful: if there are no radical solution to p=0 it should be equivalent to rootOf, which return a generic solution, while if there are radicals solution it returns one solution (which one?). What would be its use case? Is it really wise to leave it exposed? ric PS zerosOf is OK. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Re: [fricas-devel] )set message bottomup on which function signature is selected?
Ralf wrote: Obviously, for the result, it wouldn't matter. Well, maybe obvious for you ... in absence of documentation and without reading the code I can imagine at least 3 ways of coercing x^10 + y -1 to a SparseUnivariatePolynomial(Exprression(Integer)): Calling ? the variable, (x^10+ y -1)*(?^0) OR (?^10) + (y-1)*(?^0) OR (?^1)+ (x^10-1)*(?^0) ric PS now I know it is the first one... (6) -> sup 10 (6) y + x - 1 Type: SparseUnivariatePolynomial(Expression(Integer)) (7) -> coefficients sup 10 (7) [y + x - 1] Type: List(Expression(Integer)) -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] [FricasUG] Descriptions of rootOf(suv,x) and rootsOf(suv,x) seem, unhonored
Mainly Ralf ...
From
https://github.com/fricas/fricas/blob/master/src/algebra/algfunc.spad#L14
rootOf : (SparseUnivariatePolynomial %, Symbol) -> %
++ rootOf(p, y) returns y such that \spad{p(y) = 0}.
++ The object returned displays as \spad{'y}.
https://github.com/fricas/fricas/blob/master/src/algebra/algfunc.spad#L26
rootsOf : (SparseUnivariatePolynomial %, Symbol) -> List %
++ rootsOf(p, z) returns \spad{[y1, ..., yn]} such that \spad{p(yi) = 0};
++ The returned roots contain new symbols \spad{'%z0}, \spad{'%z1} ...;
++ Note: the new symbols are bound in the interpreter to the
++ respective values.
From the wordings above I would have expected see %z0, %z1,...
in (4), (5) below...
Don't you?
(1) -> suv:(SparseUnivariatePolynomial(Integer)) := x^10-1
10
(1) ? - 1
Type: SparseUnivariatePolynomial(Integer)
(2) -> rootOf(suv) -- OK
(2) %A
Type: AlgebraicNumber
(3) -> rootsOf(suv) -- OK
(3)
23 3 2
[%A, %%B1 %A, %%B1 %A, %%B1 %A, (%%B1 - %%B1 + %%B1 - 1)%A, - %A,
2 3 3 2
- %%B1 %A, - %%B1 %A, - %%B1 %A, (- %%B1 + %%B1 - %%B1 + 1)%A]
Type: List(AlgebraicNumber)
(4) -> rootOf(suv,z) -- expected %z ...
(4) %A
Type: AlgebraicNumber
(5) -> rootsOf(suv,z) -- expected %z ...
(5)
23 3 2
[%A, %%B1 %A, %%B1 %A, %%B1 %A, (%%B1 - %%B1 + %%B1 - 1)%A, - %A,
2 3 3 2
- %%B1 %A, - %%B1 %A, - %%B1 %A, (- %%B1 + %%B1 - %%B1 + 1)%A]
Type: List(AlgebraicNumber)
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[fricas-devel] )set message bottomup on which function signature is selected?
Hi! I'm using ')set message bottomup on' to understand coercitions and the selection of function signatures. (If you now a better way, please tell me). Problem: Which function is chosen when more then one choice is admissible? Eg: In the example below I understand that [1] and [2] at bottom are admissible signatures for rootsOf but I do not understand which signature is selected among the two... ?? maybe they are boldly shown by interpreter preference so, always the first, ie [1], is used ?? (1) -> pxy:=x^10+y-1 -- poly in two variables 10 (1) y + x - 1 Type: Polynomial(Integer) (2) -> )set message bottomup on (2) -> pxy%ys:=rootsOf(pxy,y) Function Selection for rootsOf Arguments: (POLY(INT), VARIABLE(y)) -> no appropriate rootsOf found in Polynomial(Integer) -> no appropriate rootsOf found in Variable(y) -> no appropriate rootsOf found in Polynomial(Integer) -> no appropriate rootsOf found in Variable(y) Modemaps from Associated Packages no modemaps Remaining General Modemaps [1] (D,Symbol) -> List(D) from D if D3 has Join(COMPAR,INTDOM) and D has ACFS(D3) [2] (SparseUnivariatePolynomial(D),Symbol) -> List(D) from D if D has ACF [1] signature: (EXPR(INT), SYMBOL) -> LIST(EXPR(INT)) implemented: slot (List $)$(Symbol) from EXPR(INT) [2] signature: (SUP(EXPR(INT)), SYMBOL) -> LIST(EXPR(INT)) implemented: slot (List $)(SparseUnivariatePolynomial $)(Symbol) from EXPR(INT) 10 (2) [- x + 1] Type: List(Expression(Integer)) Thanks in advance for any hint. ric PS Is it possible to have full names and not abbreviations is the above messages? -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Re: Re: Expressing erf as cumulative normal
IIUC there is a misprint in both previous emails: %x in the LHS of the rule should be replaced by x as in the RHS. ric (1) -> N := operator 'N (1) N Type: BasicOperator (2) -> phirule := rule erf(%x)==2*N(x*sqrt(2))-1 -- BAD ┌─┐ (2) erf(%x) == 2 N(x\│2 ) - 1 Type: RewriteRule(Integer,Integer,Expression(Integer)) (3) -> phirule(erf(y)) ┌─┐ (3) 2 N(x\│2 ) - 1 Type: Expression(Integer) (4) -> phirule := rule erf(x)==2*N(x*sqrt(2))-1 -- OK ┌─┐ (4) erf(x) == 2 N(x\│2 ) - 1 Type: RewriteRule(Integer,Integer,Expression(Integer)) (5) -> phirule(erf(y)) ┌─┐ (5) 2 N(y\│2 ) - 1 Type: Expression(Integer) -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: [fricas-devel] interesting error in integration
This is old confusion between real and complex. We create Complex(Complex(Integer)) and loose. Naive question: is it not possible/enough to define Complex(R) to be R if R = Complex (S)? -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] BUG: viewpoint$ThreeDimensionalViewport + METAPATCHES + SUGGESTED FEATURE
I'm sorry I do not yet have a developer framework setup (virtual machine, git
...) so you must content yourselves with an untested METAPATCH. ric
PROBLEM:
Crazy behavior of viewpoint function invoked by command line.
BUG:
Evident confusion among radians and degrees in the implementation of viewpoint.
CONVENTIONS:
A viewpoint is a data record inside ThreeDimensionalViewport and has type
V ==> Record( theta : SF, phi : SF, scale : SF, scaleX : SF, scaleY : SF,
scaleZ : SF, deltaX : SF, deltaY : SF )
https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L39
where, believing to the ++ descriptions, theta is the longitude and phi the
latitude (Mmmm... physicists use the opposite convention).
Conversion factors degrees to radians are defined by
degrees := pi()$F / 180.0
degreesSF := pi()$SF / 180
https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L401
From the use of the most primitive function rotate one understands that theta
and phi in V are in radians and Float
https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L801
I do not really understand the difference among the detailed actions
of rotate (line 801) and viewpint (Line 703) because depend on the server.
I *guess* that for given theta, phi they act in the same way, while viewpoint
(Line 703) updates all the fields.
It would be nice to double check these conventions but I'm unable to dive in
ViewportServer$Lisp
METAPATCHES:
1) https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L728
radian/degree mismatch: delete the two occurrences of * degreesSF below:
viewpoint (viewport : %, Theta : F, Phi : F) : Void ==
viewport.viewpoint.theta := convert(Theta)@SF * degreesSF
viewport.viewpoint.phi := convert(Phi)@SF * degreesSF
2)
https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L742
2.1: Replace 180.0 by %pi and 90.0 by %pi/2 below
2.2: The two occurrences of * degrees in rotate must be deleted.
(Modification 2.2 is superseeded by 4.2 below)
viewpoint (viewport : %, X : F, Y : F, Z : F) : Void ==
Theta : F
Phi : F
if (X = 0$F) and (Y = 0$F) then
Theta := 0$F
if (Z>=0$F) then
Phi := 0$F
else
Phi := 180.0
else
Theta := asin(Y/(R := sqrt(X*X+Y*Y)))
if (Z = 0$F) then
Phi := 90.0
else
Phi := atan(Z/R)
rotate(viewport, Theta * degrees, Phi * degrees)
2.3 The corresponding ++ description is wrong
https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L242
The corresponding ++ description is wrong:
viewpoint : (%, F, F, F)-> Void
++ viewpoint(v, rotx, roty, rotz) sets the rotation about the x-axis
++ to be \spad{rotx} radians, sets the rotation about the y-axis
++ to be \spad{roty} radians, and sets the rotation about the z-axis
++ to be \spad{rotz} radians, for the viewport v, which is of the
++ domain \spadtype{ThreeDimensionalViewport} and displays v with
++ the new view position.
If I understand correctly the new description should be
viewpoint : (%, F, F, F)-> Void
++ viewpoint(v, x, y, z) sets the viewpoint to cartesian coordinates
(x,y,z)
++ for the viewport v, which is of the
++ domain \spadtype{ThreeDimensionalViewport} and displays v with
++ the new view position.
3)
You may safely delete the lines 425 to 431 because arcsinTemp and arctanTemp
are unused.
(Can one call them from other files?)
https://github.com/fricas/fricas/blob/master/src/algebra/view3D.spad#L425
4) SUGGESTED FEATURE: let ALL viewpoint functions to force replotting the
viewport.
4.1) for the viewpoint at line 720, 724: add at the end the line
viewpoint(viewport,viewport.viewpoint)
4.2) for the viewpoint at line 732 the replotting should be forced, but to be
homogeneous I would replace
rotate(viewport, Theta, Phi)
by
viewpoint (viewport, Theta, Phi)
4.3) Delete in the ++ strings the statements
++ The new
++ dimensions are not displayed until the function
++ \spadfun{makeViewport3D} is executed again for v.
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Re: Re: [fricas-devel] Re: Error detected within library code:, index out
Hi If using A == Test(SL) with (in package PTEST): IIUC Test(SL) is a domain: is it legal in SPAD to use a domain in the LHS of a 'with' statement? (In Aldor it is not, "the LHS is an optional 'Category'-valued expression", see AldorUG sec 7.9) ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Re: Error detected within library code:, index out of range
Hi Kurt As FriCAS exercise of the day, I tried to understand the source of your bug but the best I can do is a minimal example (vaguely related to the original one) and similar errors. I do not know what mean "non extending category" and "has no ..." compilation messages but there were similar ones in the original version. Hope not increasing the confusion ric Cumulative Statistics for Constructor SIunits Time: 0.00 seconds --non extending category-- .. SIunits of cat (CATEGORY |package| (SIGNATURE |u| ((|List| (|PhysicalUnitSystem| (|::| (|construct| '|a| '|b| '|c|) (|List| (|Symbol| has no (|PhysicalUnit|)finalizing NRLIB SI Processing SIunits for Browser database: --->-->SIunits(constructor): Not documented --->-->SIunits((u ((List (PhysicalUnitSystem (:: (construct (QUOTE a) (QUOTE b) (QUOTE c)) (List (Symbol: Not documented --->-->SIunits(): Missing Description ; compiling file "/data/devel/guida/WIP/fricas_learning/SI.NRLIB/SI.lsp" (written 17 JUL 2018 04:37:23 PM): ; /data/devel/guida/WIP/fricas_learning/SI.NRLIB/SI.fasl written ; compilation finished in 0:00:00.005 SIunits is now explicitly exposed in frame frame1 SIunits will be automatically loaded when needed from /data/devel/guida/WIP/fricas_learning/SI.NRLIB/SI (1) -> )system cat PhysicalUnitsSystem.spad )abbrev category PUNIT PhysicalUnit PhysicalUnit() : Category == with coerce : % -> OutputForm )abbrev domain PUSYS PhysicalUnitSystem PhysicalUnitSystem(u:List Symbol) : Exports == Implementation where Exports == PhysicalUnit with baseUnits : () -> List % Implementation == add Rep:=FreeModule(Integer,OrderedVariableList(u)) baseUnits() == [ 0$Rep] coerce(x)== coerce(x)$Rep )abbrev package SI SIunits SIunits : Exports == Implementation where Exports == with u : () -> List(PhysicalUnitSystem(['a,'b,'c]::List(Symbol))) Implementation == PhysicalUnitSystem(['a,'b,'c]::List(Symbol)) add u() == baseUnits()$(PhysicalUnitSystem(['a,'b,'c]::List(Symbol))) (1) -> )show PUSYS PhysicalUnitSystem(u: List(Symbol)) is a domain constructor Abbreviation for PhysicalUnitSystem is PUSYS This constructor is exposed in this frame. ─── Operations baseUnits : () -> List(%) coerce : % -> OutputForm (1) -> )show SI SIunits is a package constructor Abbreviation for SIunits is SI This constructor is exposed in this frame. ─── Operations >> Error detected within library code: Improper script count in symbol (1) -> u()$SI LISP output: () >> Error detected within library code: index out of range (1) -> )show PUSYS PhysicalUnitSystem(u: List(Symbol)) is a domain constructor Abbreviation for PhysicalUnitSystem is PUSYS This constructor is exposed in this frame. ─── Operations baseUnits : () -> List(%) coerce : % -> OutputForm (1) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Re: System error: The value |RandomFloatDistributions| is not of type SEQUENCE
PS: If I compile my poor function I get "Apparent user error"... (1) -> )compile RandomGraph.spad Compiling FriCAS source code from file /data/devel/guida/WIP/fricas_learning/RandomGraph.spad using old system compiler. RANGRAPH abbreviates package RandomGraph initializing NRLIB RANGRAPH for RandomGraph compiling into NRLIB RANGRAPH compiling exported randomGraph : () -> GraphImage processing macro definition nHues ==> 27 processing macro definition nPoints ==> 100 ** comp fails at level 3 with expression: ** error in function randomGraph (SEQ (MDEF (|nHues|) (NIL) (NIL) 27) (MDEF (|nPoints|) (NIL) (NIL) 100) (DEF (|randomX|) (NIL) (NIL) | << | (|::| (((|Sel| (|RandomFloatDistributions|) |uniform|) 0 1)) (|DoubleFloat|)) | >> |) (DEF (|randomY|) (NIL) (NIL) (|::| (((|Sel| (|RandomFloatDistributions|) |uniform|) 0 1)) (|DoubleFloat|))) (DEF (|randomPoint|) (NIL) (NIL) (((|Sel| |Point| |point|) (|construct| |randomX| |randomY|)) (|DoubleFloat|))) (DEF (|randomPointColor|) (NIL) (NIL) (|dark| ((|Sel| (|Color|) |color|) (+ 1 ((|Sel| (|Integer|) |random|) |nHues|) (DEF (|randomLineColor|) (NIL) (NIL) (|dark| ((|Sel| (|Color|) |color|) (+ 1 ((|Sel| (|Integer|) |random|) |nHues|) (DEF (|randomPointSize|) (NIL) (NIL) (|::| (+ 1 ((|Sel| (|Integer|) |random|) 30)) (|PositiveInteger|))) (|:=| |gim| ((|Sel| (|GraphImage|) |graphImage|))) (REPEAT (IN |i| (SEGMENT 1 |nPoints|)) ((|Sel| (|GraphImage|) |component|) |gim| |randomPoint| |randomPointColor| |randomLineColor| |randomPointSize|)) (|exit| 1 (|return| |gim|))) ** level 3 ** $x:= (:: (((Sel (RandomFloatDistributions) uniform) (Zero) (One))) (DoubleFloat)) $m:= NIL $f:= |randomX| #) (|nPoints| #) (|nHues| #) (|randomGraph| #) ...))) >> Apparent user error: Cannot coerce (call (ELT $ 15) (call (applyFun (call (ELT $ 14) (call (CONST $ 10)) (call (CONST $ 11)) of mode (DoubleFloat) to mode (1) -> )system cat RandomGraph.spad )abbrev package RANGRAPH RandomGraph RandomGraph(): Exports == Implementation where Exports == with randomGraph: () -> GraphImage Implementation == add randomGraph() == nHues ==> 27 -- hardcoded in FriCAS :( nPoints ==> 100 randomX == ((uniform(0,1)$RandomFloatDistributions)())::DoubleFloat randomY == ((uniform(0,1)$RandomFloatDistributions)())::DoubleFloat randomPoint == point([randomX, randomY])$Point DoubleFloat randomPointColor == dark ( color(1 + (random(nHues)$Integer))$Color ) randomLineColor == dark ( color(1 + (random(nHues)$Integer))$Color ) randomPointSize == (1 + random(30)$Integer)::PositiveInteger gim := graphImage()$GraphImage for i in 1..nPoints repeat component(gim, randomPoint, randomPointColor, randomLineColor, randomPointSize)$GraphImage return gim (1) -> randomX == ((uniform(0,1)$RandomFloatDistributions)())::DoubleFloat --- this works Type: Void (2) -> randomX Compiling body of rule randomX to compute value of type DoubleFloat (2) 0.9642863855364605 Type: DoubleFloat (3) -> randomX (3) 0.03437972397951383 Type: DoubleFloat (4) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] System error: The value |RandomFloatDistributions| is not of type SEQUENCE
Hi 2 problems: 1) I can't understand why the function randomGraph defined in drawPoints2.input is not find in the same file. Same behavior with drawPoints.input which has a more functional style in the use of $. 2) Trying to debugging I've met a system error that might interest the developers... Thanks in advance for any hint! ric (1) -> )read drawPoints2.input randomGraph: () -> GraphImage Type: Void randomGraph() == nHues ==> 27 -- hardcoded in FriCAS :( nPoints ==> 100 randomX == ((uniform(0,1)$RandomFloatDistributions)())::DoubleFloat randomY == ((uniform(0,1)$RandomFloatDistributions)())::DoubleFloat randomPoint == point([randomX, randomY])$Point DoubleFloat randomPointColor == dark ( color(1 + (random(nHues)$Integer))$Color ) randomLineColor == dark ( color(1 + (random(nHues)$Integer))$Color ) randomPointSize == (1 + random(30)$Integer)::PositiveInteger gim := graphImage()$GraphImage for i in 1..nPoints repeat component(gim, randomPoint, randomPointColor, randomLineColor, randomPointSize)$GraphImage return gim Type: Void gi1:GraphImage := randomGraph() Compiled code for randomGraph has been cleared. Compiling body of rule randomX to compute value of type DoubleFloat Compiling body of rule randomY to compute value of type DoubleFloat Compiling body of rule randomPoint to compute value of type Point( DoubleFloat) Compiling body of rule randomPointColor to compute value of type Palette Compiling body of rule randomLineColor to compute value of type Palette Compiling body of rule randomPointSize to compute value of type PositiveInteger Compiling function randomGraph with type () -> GraphImage There are no library operations named randomGraph Use HyperDoc Browse or issue )what op randomGraph to learn if there is any operation containing " randomGraph " in its name. Cannot find a no-argument definition or library operation named randomGraph . (3) -> )display properties Properties of % : Value (has type Void): "()" Properties of %e : This is a system-defined macro. macro %e () == exp(1) Properties of %i : This is a system-defined macro. macro %i () == complex(0,1) Properties of %infinity : This is a system-defined macro. macro %infinity () == infinity() Properties of %minusInfinity : This is a system-defined macro. macro %minusInfinity () == minusInfinity() Properties of %pi : This is a system-defined macro. macro %pi () == pi() Properties of %plusInfinity : This is a system-defined macro. macro %plusInfinity () == plusInfinity() Properties of SF : This is a system-defined macro. macro SF () == DoubleFloat() Properties of gi1 : Declared type or mode: GraphImage Properties of randomGraph : Declared type or mode: (() -> GraphImage) This is an interpreter function. This depends on the following functions or rules: $elt GraphImage component randomPoint randomPointColor randomLineColor randomPointSize graphImage PositiveInteger random Integer color Color dark randomY randomX point DoubleFloat Point uniform RandomFloatDistributions /throwAway >> System error: The value |RandomFloatDistributions| is not of type SEQUENCE. (3) -> )clear completely All user variables and function definitions have been cleared. All )browse facility databases have been cleared. Internally cached functions and constructors have been cleared. )clear completely is finished. (1) -> )read drawPoints.input randomGraph: () -> GraphImage Type: Void randomGraph() == nHues ==> 27 -- hardcoded in FriCAS :( nPoints ==> 100 randomX == ((uniform$RandomFloatDistributions)(0,1)())::DoubleFloat randomY == ((uniform$RandomFloatDistributions)(0,1)())::DoubleFloat randomPoint == (point$Point DoubleFloat)([randomX, randomY]) randomPointColor == dark ((color$Color)(1 + (random$Integer)(nHues))) randomLineColor == dark ((color$Color)(1 + (random$Integer)(nHues))) randomPointSize == (1 + (random$Integer)(30))::PositiveInteger gim := (graphImage$GraphImage)() for i in 1..nPoints repeat (component$GraphImage)(gim, randomPoint, randomPointColor, randomLineColor, randomPointSize) return gim Type: Void gi1:GraphImage := randomGraph() Compiled code for randomGraph has been cleared. Compiling body of rule randomX to compute value of type DoubleFloat Compiling body of rule randomY to compute value of type DoubleFloat Compiling body of rule randomPoint to compute value of type Point( DoubleFloat) Compiling body of rule randomPointColor to compu
[fricas-devel] [FriCASUG +API] metapatches on 2D graphs
Mainly for Ralf ...
--
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L154
REPLACE:
\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16)}
BY:
\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16,title=="A title here")}
MOTIVATION:
A title was announced the line before.
---
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L222
REPLACE:
\psXtc{
The title may be an arbitrary string and is an
optional argument to the \spadfun{draw} command.
}{
\spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi)}
}{
BY:
\psXtc{
Note that \Language{} provides a default title based on
the first function specified in \spadfun{curve}.
The title may be an arbitrary string and is an
optional argument to the \spadfun{draw} command.
}{
\spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi, title=="A title here" )}
}{
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L263
DELETE:
Also note that \Language{} provides a default title based on
the first function specified in \spadfun{curve}.
MOTIVATION:
Sentence anticipated where it is relevant.
A title was announced the line before the first patch.
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L276
MOTIVATION:
In 276 -- 293 \spad{p(x,y)} is used instead of a mathematical polynomial p(x,y).
I would eliminate \spad and use the command appropriate for maths.
In 296--310, The mathematical notation p(x,y) of a polynomial expression
is misleading in a command reference, and leads to think to a function p is
needed.
I suggest to replace p(x,y) by p, and explain that it is an expression
of type Polynomial with variables x,y.
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L392
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L406
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L445
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L458
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L468
TODO:
Patch draw to show units when unit=... is given
MOTIVATION:
unit=-=... is used but nothing is shown in the image.
---
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug07.htex#L400
REPLACE:
Option {\tt clip} with a range sets point clipping of a graph within the
BY:
Option {\tt clip} with a range shows only points within the
MOTIVATION: 'to set point clipping' seems quite technical, plain words are
better.
---
https://github.com/fricas/fricas/blob/master/src/algebra/view2D.spad#L10
REPLACE:
++ Description: TwoDimensionalGraph creates virtual two dimensional graphs
BY:
++ Description: GraphImage creates virtual two dimensional graphs
MOTIVATION:
IIUC TwoDimensionalGraph does not exist (old name of GraphImage?)
https://github.com/search?q=TwoDimensionalGraph+repo%3Africas%2Ffricas+extension%3Aspad&type=Code&ref=advsearch
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Re: Re : [fricas-devel] [BUG]: draw option unit == [a,b] ignored
Ralf 1) Many graphs in chapter seven FriCAS UG do NOT correspond to what announced in the text (I was preparing a list of patches but you anticipated me). In 2D graphs this is due to a missing 'title=...' in the invoked command draw and also due the fact that 'unit=...' shows nothing because the system default is do not show units. This way one has to manually switch them via the control panel, as Johannes remarked, or by invoking units. This behavior is highly user-unfriendly: if a user takes the time to write unit=... in the command, that likely means that s/he wants to see them (immediately!) So, to me, the simplest & user-friendliest solution would be a patch that adds a line that shows the unit whenever the unit=... option is there (maybe by calling units, but I do not know if the viewport is available at that level). Right now I'm unable to suggest more... 2) Speaking of the wide family of draw functions, I have the impression that there is some interpreter black magics involved in how options are dealt with. The problem is that one needs functions with a variable number of formal parameters (the options). In the API I see signatures involving 'List DrawOption' : draw: (Ex, SegmentBinding Float, List DrawOption) -> TwoDimensionalViewport draw(f(x), x = a..b, [ title="bim", units=[1.0..2.0,1.0..2.0] ]) but in interpreter you invoke them WITHOUT a list of options i.e. draw(f(x), x = a..b, title="bim", units=[1.0..2.0,1.0..2.0]) This conflicts with the API, and I guess plain SPAD ... I hate exceptions! I see that there is some hardcoded code in the interpreter dealing with draw src/interp/i-funsel.boot#L300 [1] but I do not really understand if the aforementioned magic happens here. Hope that Waldek will pass and prune the un-necessary here... 3) Speaking of user-unfriendliness of draw functions, I would like to emphasize that draw for algebraic curves draw(f(x, y) = g(x, y), x, y, l) [2] introduces an exception to the usual syntax for ranges, obliging the user to use an adhoc option 'range': draw(x^2+y^2 =1, x, y, range==[0..1,0..1]) instead of the usual syntax draw(x^2+y^2 =1, x = 0..1, y=0..1) ... I hate exceptions! ric [1] https://github.com/fricas/fricas/blob/master/src/interp/i-funsel.boot#L300 [2] https://github.com/hemmecke/fricas/blob/master-hemmecke/src/algebra/draw.spad#L962 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: [fricas-devel] [BUG]: draw option unit == [a,b] ignored
[Grabmeier]> you must make sure that in the control panel you have "units on" and you [Grabmeier]> possibly have to scale the size of the window in order to have space for [Grabmeier]> tick labelling. Aha, thanks Johannes!!! Units was off: the following works (2) -> vp := draw(sin(11*x),x = 0..2*%pi,title == "Large and unit", unit==[0.2,0.2]) Compiling function %D with type DoubleFloat -> DoubleFloat Graph data being transmitted to the viewport manager... FriCAS2D data being transmitted to the viewport manager... (2) TwoDimensionalViewport: "Large and unit" Type: TwoDimensionalViewport (3) -> units(vp,1,"on") Type: Void So this is not a bug, just a missing feature: I would have expected that setting unit==... in draw would automatically trigger units(...,"on"). Cheers, riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] [BUG]: draw option unit == [a,b] ignored
Hi, IIC the user guide the draw option unit==[0.2,0.2] should add ticks to the axes x and y, but I cannot see anything. Try eg: draw(sin(11*x),x = 0..2*%pi,toScale == true,title == "Drawn to scale") draw(sin(11*x),x = 0..2*%pi,toScale == true,title == "Drawn to scale and unit", unit==[0.2,0.2]) draw(sin(11*x),x = 0..2*%pi,toScale == true,title == "Drawn to scale and unit", unit==[0.5,0.5]) draw(sin(11*x),x = 0..2*%pi,title == "Large and unit", unit==[0.2,0.2]) draw(sin(11*x),x = 0..2*%pi,title == "Large and unit", unit==[0.5,0.5]) Am I missing something important? ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Intepreter: type declaration ignored in == AND: BOOT::|sayFunctionDeps| is undefined.
Hi, thanks for the feedback. [Bill]> Although this terminology is used in a few places, "... a few places"? Well, I would say "almost everywhere": Jenks Sutor vol 0, hyperdoc, fricasUG, mathaction ... [Bill]>I do not think it [Bill]> is correct to call == delayed assignment. Rather it only represents [Bill]> kind of function definition via matching (which granted, does involve [Bill]> some form of delayed assignment). More specifically in the interpreter [Bill]> == defines a "rule". In the case of ==, : is an operator like any [Bill]> other. E.g. I see your point of view. This sheds more light also on T3(f(x)) == ... in [1] A mystery is that according to the interpreter messages there are "interpreter functions" and "interpreter rules", so one might wonder if there are different, undocumented syntaxes and semantics: (1) -> z == 1 Type: Void (2) -> x + y == 5 -x + 10 *y Type: Void (3) -> )display properties + z Properties of + : This is an interpreter function. Definition: + (x, y) == 5 - x + 10 y Properties of z : This is an interpreter rule. ... I'm starting to believe that the only way for a user to grasp how the interpreter works in many cases is to (learn boot & lisp and) read the source files ... quite time consuming task ... sigh ... I'm also disturbed by the fact that a (fool) user can happily hide a library operation like +. I would have preferred to be obliged to write something like IAmNotInsaneAndIReallyWantToRedefine(_+) before being able to redefine. [ric]> (2) -> y:Integer == 1 [Oldk1331]> This is a strange way to input in FriCAS, it actually defined a rule for ':' Well, I had the (unwise) idea of approaching FriCAS by first reading the whole AldorUG, so my test was Aldor-inspired [1] regards riccardo [1] https://www.mail-archive.com/fricas-devel@googlegroups.com/msg12354.html [2] http://www.aldor.org/docs/HTML/chap5.html#3 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Intepreter: type declaration ignored in == AND: BOOT::|sayFunctionDeps| is undefined.
Hi Command line interpreter: I realize that type declaration is ignored in delayed assignment == even for variables (see [1] for a similar behavior for functions) Same behavior from .input file. AND At the same occasion I get a weird system error in )display properties, which might interest Waldek... cheers, riccardo (1) -> x:Integer := 1 (1) 1 Type: Integer (2) -> y:Integer == 1 Type: Void (3) -> z == 1 Type: Void (4) -> [x,y,z] Compiling body of rule z to compute value of type PositiveInteger (4) [1, y, 1] Type: List(Polynomial(Integer)) (5) -> )display properties x y z Properties of x : Declared type or mode: Integer Value (has type Integer): 1 Properties of y : none Properties of z : This is an interpreter rule. >> System error: The function BOOT::|sayFunctionDeps| is undefined. (5) -> )read test.input )clear completely All user variables and function definitions have been cleared. All )browse facility databases have been cleared. Internally cached functions and constructors have been cleared. )clear completely is finished. x2:Integer := 1 (1) 1 Type: Integer y2:Integer == 1 Type: Void z2 == 1 Type: Void [x2,y2,z2] Compiling body of rule z2 to compute value of type PositiveInteger (4) [1, y2, 1] Type: List(Polynomial(Integer)) )display properties x2 y2 z2 Properties of x2 : Declared type or mode: Integer Value (has type Integer): 1 Properties of y2 : none Properties of z2 : This is an interpreter rule. >> System error: The function BOOT::|sayFunctionDeps| is undefined. [1] https://www.mail-archive.com/fricas-devel@googlegroups.com/msg12308.html -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] FricasUG metapatch: palindromes and eirule
Mainly for Ralf...
--
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug06.htex#L2410
REPLACE:
(s.i = s.j) and palAux?(s,i+1,i-1)
BY:
(s.i = s.j) and palAux?(s,i+1,j-1)
MOTIVATION:
IIUC, presently the function palAux? declare palindromes aggregates having
equal first and last element.
This results in an wrong stream FricasUG sec 6.20, pag 218, (9)
The nine-th term
11^2 = 1234567900987654321
is NOT palindrome and false would have been expected.
--
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug06.htex#L2735
REPLACE:
\spadcommand{eirule integral(sin u + exp u/u, u) \free{eirule}}
BY eg:
\spadcommand{eirule integral((sin u + exp u)/u, u) \free{eirule}}
MOTIVATION:
The current example does not test the ?y pattern in FricasUG sec 6.21, pag 223,
(17) as anticipated in the text.
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[fricas-devel] FricasUG metapatch: 7 and )set functions cache all all
Mainly for Ralf...
--
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug06.htex#L894
REPLACE:
What is the value for \spad{n = 7}?
BY:
What is the value for \spad{n = 3}?
MOTIVATION:
The line below contains facto(3)
--
https://github.com/fricas/fricas/blob/master/src/doc/htex/ug06.htex#L1218
REPLACE:
Use no list of names or ``all'' when you want to define the default
BY:
Use no list of names when you want to define the default
MOTIVATION:
IIUC, the original sentence suggests that the syntax is
)set functions cache (0||all) [f...|all]
while a test shows that the syntax is
)set functions cache (0||all) [f...]
Eg: the trailing ``all`` is interpreted as a function.
(1) -> )set functions cache 0 all
Caching for function all is turned off
(1) -> )set functions cache 3 all
function all will cache the last 3 values.
(1) -> )set functions cache all all
function all will cache all values.
(1) -> )set functions cache all f
function f will cache all values.
If I'm missing another more meaningful interpretation, I would say
that the statement should be rewritten to be unambiguous.
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[fricas-devel] interpreter (command line): weird syntax allowed for function of function
Hi, T,T2,T3 below are meant to implement the same map that takes a function x+->f(x) and returns a function x+->x+f(x), both functions of signature Integer->Integer. I understand the syntax of the assignments to T, T2 below, but I would have been happier to get back a "syntax error" after the definition of T3 (6). Any clue of how "thinks" the interpreter when dealing with (6)? It looks like if it interpreted 'f(x)' for 'f'... Some (undocumented) interpreter language feature ? Thanks for any clue riccardo (1) -> T: (Integer -> Integer) -> (Integer ->Integer) Type: Void (2) -> T2: (Integer -> Integer) -> (Integer ->Integer) Type: Void (3) -> T3: (Integer -> Integer) -> (Integer ->Integer) Type: Void (4) -> T(f) == (x+->f(x)+x) Type: Void (5) -> (T2(f))(x) == x+f(x) Type: Void (6) -> T3(f(x))==x+f(x) Type: Void (7) -> (T(x+->x^3))(3) Compiling function T with type (Integer -> Integer) -> (Integer -> Integer) (7) 30 Type: PositiveInteger (8) -> (T2(x+->x^3))(3) Compiling function T2 with type (Integer -> Integer) -> (Integer -> Integer) (8) 30 Type: PositiveInteger (9) -> (T3(x+->x^3))(3) Compiling function T3 with type (Integer -> Integer) -> (Integer -> Integer) (9) 30 Type: PositiveInteger (10) -> )display properties T T2 T3 Properties of T : Declared type or mode: ((Integer -> Integer) -> (Integer -> Integer)) This is an interpreter function. This depends on the following function or rule: x Definition: T f == x +-> f(x) + x Compiled function type: (Integer -> Integer) -> (Integer -> Integer) Properties of T2 : Declared type or mode: ((Integer -> Integer) -> (Integer -> Integer)) This is an interpreter function. This depends on the following function or rule: x Definition: T2 f == x +-> x + f(x) Compiled function type: (Integer -> Integer) -> (Integer -> Integer) Properties of T3 : Declared type or mode: ((Integer -> Integer) -> (Integer -> Integer)) This is an interpreter function. This depends on the following function or rule: x Definition: T3 f == x +-> x + f(x) Compiled function type: (Integer -> Integer) -> (Integer -> Integer) -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: [fricas-devel] interpreter (command line): syntax of "rule"
The escape symbel _ is necessary in order to defeat the magic. Great, many thanks Bill! I saw the API for RewriteRule and I was willing to try these functions, but I was unable to defeat interpreter's magics. riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] interpreter (command line): syntax of "rule"
Hi I do not understand how the syntax rule sin(x) == x -- see (1) below is accommodated to fit in the signature (EXPR(INT), EXPR(INT)) -> RULE(INT,INT,EXPR(INT)) see fricas message below In other words: in (1) I do not see a call to a function "rule" of two parameters, rule(f,g): what's happening? Is this an interpreter (command line) language construct that has nothing to do with standard function call of type rule(f,g)? Can one rewrite (1) as an equivalent function call rule(f,g) for some f,g? Thanks in advance for any hint, Riccardo (1) -> rule sin(x) == x -- unwise rule Function Selection for sin Arguments: VARIABLE(x) -> no appropriate sin found in Variable(x) -> no appropriate sin found in Symbol -> no appropriate sin found in Variable(x) -> no appropriate sin found in Symbol Modemaps from Associated Packages no modemaps Remaining General Modemaps [1] D -> D from D if D has TRIGCAT [1] signature: EXPR(INT) -> EXPR(INT) implemented: slot $$ from EXPR(INT) Function Selection for rule Arguments: (EXPR(INT), VARIABLE(x)) -> no appropriate rule found in Expression(Integer) -> no appropriate rule found in Variable(x) -> no appropriate rule found in Expression(Integer) -> no appropriate rule found in Variable(x) Modemaps from Associated Packages no modemaps Remaining General Modemaps [1] (D1,D1) -> RewriteRule(D2,D3,D1) from RewriteRule(D2,D3,D1) if D2 has SETCAT and D3 has Join(RING,PATMAB(D2),COMPAR, KONVERT(PATTERN(D2))) and D1 has Join(FS(D3),PATMAB(D2), KONVERT(PATTERN(D2))) [1] signature: (EXPR(INT), EXPR(INT)) -> RULE(INT,INT,EXPR(INT)) implemented: slot $(Expression (Integer))(Expression (Integer)) from RULE(INT,INT,EXPR(INT)) (1) sin(x) == x Type: RewriteRule(Integer,Integer,Expression(Integer)) (2) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Bugs in TransSolvePackage
PS
(6) -> solve(sinh(z)/cosh(z)=0,z) -- ??? AWFUL KO
(6) [z = 0, z = log(- 1)]
Type: List(Equation(Expression(Integer)))
I mean, if log it is defined also on the axis |z| e^{i pi } than z=i pi should
be ok, but what is bad is that one finds 0,1,2 solutions according to the
representation of the question.
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[fricas-devel] Fricas on SPAD vs Fricas on Aldor?
Dear Waldek Could you comment on my (naive) thoughts & questions below? I use quotes for admittedly-unprecise terms. I'm pretty sure you've talked about this in the last decade, but the information is quite spread around in the list. Thoughts: * The Aldor compiler is an improved version of the Spad compiler, written by one of its authors. So, as a non-expert, I would blindly tend to say that Aldor compiler is "better" than Spad compiler. At least it has written documentation and, I guess, it should produce faster compiled code (eg by compiling via the C compiler not the lisp one). * Spad syntax is, say, "90% equal" to Aldor, so moving the .spad files in algebra to .as files should not be impossible. * I guess the really "hard" problem is "porting" the interpreter to work on the top of Aldor, maybe using its -gloop shell. * On this list, I've never heard mentioning this "port to Aldor" even as a long term/dreamy project, while I've heard hypothetical mentions on rewriting the current fricas interpreter, which should also be "hard". So my questions: * would "porting" the interpreter on the top of aldor be much more difficult & unrealistic than rewriting the current fricas interpreter? * Which solution do you prefer, and, more important, could you somehow explain why? Thanks for your answer(s), and sorry for my impudence! riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: Re: Re: [fricas-devel] unique Value of Void
You seem to use different terminology. Spad is language of .spad files. They are intended for non-interactive use -- basicaly enhancements to FriCAS library. Spad is different than language of .input files. .input files are intended for interactive use. Now, with "interactive language" there is some confusion, as functions are normally compiled while command line gets special treatment. Dear Waldek, to explain: my answer relied on the following hypotheses * SPAD is the language of .spad files, invoked by )compile * the interpreter = interprets a subset of SPAD language (eg no definitions of domain) on command line and via )read .input files + heuristics guesses & coercitions on types + SPAD compilation of functions in case of complete type resolutions ... so naively I thought that, if the interpreter is so unpredictable on types, maybe it was more pedagogical to present things as subsets of SPAD, which is well defined, but now I realize that maybe the examples given maybe do not compile in SPAD, even if embedded in functions of user-defined packages, I do not know, I'm learning using the command line. I guess I need some official glossary, could you please enlighten me? * How should be called "The language of .input files?" * Is "The language of .input files" the same thing as "the language of command line"?, and if not how is called the latter? * Is the compiler invoked by the interpreter when compiling functions the same compiler (same language) as the SPAD compiler invoked by )compile ? * Which language is meant by 'The FriCAS language' and 'The FriCAS interactive language'? A post on a related question will follow. riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Bugs in TransSolvePackage
This is an improved revival of a 2007 bug [1] which seems still in good health (1) -> solve(tan(z)=0,z) -- OK (1) [z = 0] Type: List(Equation(Expression(Integer))) (2) -> solve(sin(z)/cos(z)=0,z) -- OK (2) [z = 0] Type: List(Equation(Expression(Integer))) (3) -> solve(cot(z)=0,z) -- OK %pi (3) [z = ───] 2 Type: List(Equation(Expression(Integer))) (4) -> solve(cos(z)/sin(z)=0,z)-- ??? (4) [] Type: List(Equation(Expression(Integer))) (5) -> solve(tanh(z)=0,z) -- ??? I'm wondering why fricas does not know that atanh(0) = 0 (5) [z = atanh(0)] Type: List(Equation(Expression(Integer))) (6) -> solve(sinh(z)/cosh(z)=0,z) -- ??? AWFUL KO (6) [z = 0, z = log(- 1)] Type: List(Equation(Expression(Integer))) (7) -> solve(coth(z)=0,z)-- ? Error??? >> Error detected within library code: Invalid argument (7) -> coth(z)=0 (7) coth(z) = 0 Type: Equation(Expression(Integer)) (8) -> PS The semantics of [] is not really crystal-clear... (8) -> solve(cos(z)/sin(z)=cot(z),z) (8) [] Type: List(Equation(Expression(Integer))) (9) -> solve(sin(z)/cos(z)=tan(z),z) (9) [] Type: List(Equation(Expression(Integer))) It seems to me that the natural output for general solvers should be a set, see [2]. [1] http://axiom-wiki.newsynthesis.org/104BranchCutsDiffer?root=IssueTracker [2] http://docs.sympy.org/latest/modules/solvers/solveset.html -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] [BUG] scoping problems in interpreter (nothing really new)
Hi, I'm now aware of the status of the interpreter in fricas: this is just for the record (fricas 1.3.4). fricas 1.3.4: interpreter bug on scopes similar the one reported in https://www.mail-archive.com/fricas-devel@googlegroups.com/msg12273.html (1) -> i:=1; for i in 1..3 repeat output(i^2); i 1 4 9 i is declared as being in PositiveInteger but has not been given a value. (1) -> i:=1; (for i in 1..3 repeat output(i^2)); i 1 4 9 i is declared as being in PositiveInteger but has not been given a value. (1) -> i (1) 1 Type: PositiveInteger -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: Re: [fricas-devel] unique Value of Void
@Bill: If the else clause is missing but the if condition is false then the value of the if-then expression is the unique value of Void. +1 I think an important though somewhat less technical addition to the user guide concerning the meaning and use of the Void and Exit domains would indeed be quite useful. +1 (Maybe adding also something on None if this Type will still be around. Somewhere near section 2.6 might be a good place.) @ Waldek The command line is not representative of FriCAS language. OK, crystal clear. The pedagogical problem is that, maybe not to scare the reader, the FricasUG is somehow vague on the differences among interpreter and compiler. For instance note that the chapter 5 (which raised my questions) is titled "Introduction to the FriCAS Interactive Language", while it is presently more like an (incomplete) SPAD reference. riccardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: [fricas-devel] unique Value of Void
Hi, Thanks for your clarifications Bill. Just to say that my original question to Ralf was a much more low level quest for clarifications in the user guide: 1) A user reads: section 5.3 pag 149 "An if-then-else expression always returns a value. If the else clause is missing then the entire expression returns the unique value of Void. If both clauses are present, the type of the value returned by if is obtained by resolving the types of the values of the two clauses. See Section 2.10 on page 109 for more information." (Check also the boxed text above this statement.) 2) The user does not really understand the statement and, if he is motivated, tries to experiment: (1) -> if 1>2 then 1 -- here he expects Void Type: Void (2) -> if 2>1 then 1 -- here he expects Void but gets PositiveInteger (2) 1 Type: PositiveInteger (3) -> if 2>1 then 1 else [1,2,3] -- here he expects common supertype, but which one? (3) 1 Type: PositiveInteger (4) -> if 1>2 then 1 else [1,2,3] -- here he expects common supertype, which one? (4) [1, 2, 3] Type: List(PositiveInteger) 3) The user is puzzled because * in (2) below he gets Type: Positive Integer not Type: Void * in (3) and (4) below he sees 2 different types and not a "common supertype" From your explanations now I understand that there are a lot of hidden coercitions in the game and that what is said in the user guide does not contradict the experiments. But I feel it would be helpful to have some clarifying information in the user guide not after page 149. Writing "the unique value of Void" is not of help because what is not evident is the fact that "every value can be coerced to Void". I realize now that this is said at pag 763, sec 9.87 (in my version of FricasUG), but at least a footnote in page 149 would have helped. ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Re: [FricasUG] FIXME: sec 2.5.2 pag 96 osolete description & Feature suggestion for Union-s
Sorry, I retract my feature suggestion because Union with selectors are there also in Aldor and with more features that make such selectors more meaningful: i.e. assignment via selector, like u := [num == 3]. RiCCardo -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] [FricasUG] FIXME: sec 2.5.2 pag 96 osolete description & Feature suggestion for Union-s
Hi, if this is not the correct place for sending FricasUG fix requirements, please excuse me and let me now. RiCCardo [FricasUG] FIXME: sec 2.5.2 "Union-s with selectors" pag 96 "Note that case uses the selector name as its right-hand argument. If you accidentally use the branch type on the right-hand side of case, false will be returned. Now it returns error." (1) -> U := Union(i:Integer, s:String) (1) Union(i: Integer,s: String) Type: Type (2) -> x:U := "bam" (2) "bam" Type: Union(s: String,...) (3) -> x case Integer >> Error detected within library code: upcase: bad Union form (3) -> x case String >> Error detected within library code: upcase: bad Union form (3) -> x case i (3) false Type: Boolean (4) -> x case s (4) true The statements above prove that the fricasUG must be fixed. === Feature suggestion for Union-s === I must say that I would find more natural (and maybe it would have simpler code) to have the predicates x case Integer x case String as for non-selector Union-s and to use selectors only to get the values x.i x.s with "failed" instead of a coerce error when the inappropriate selector is called: relying on the fact that a coercion might rescue you if the value branch does not correspond to the selector looks somehow hackish. (5) -> x.i >> Error detected within library code: "bam" of mode Union(i: Integer,s: String) cannot be coerced to mode Integer (5) -> x.s (5) "bam" Type: String -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] There are questions one should not ask...
(18) -> typeOf(()) INFO: Control stack guard page unprotected Control stack guard page temporarily disabled: proceed with caution >> System error: Control stack exhausted (no more space for function call frames). This is probably due to heavily nested or infinitely recursive function calls, or a tail call that SBCL cannot or has not optimized away. PROCEED WITH CAUTION. (18) -> typeOf () INFO: Control stack guard page reprotected INFO: Control stack guard page unprotected Control stack guard page temporarily disabled: proceed with caution >> System error: Control stack exhausted (no more space for function call frames). This is probably due to heavily nested or infinitely recursive function calls, or a tail call that SBCL cannot or has not optimized away. PROCEED WITH CAUTION. (18) -> -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Unexpected behavior of commas in singleton blocks {expression}
Hi!
I bet that the behavior I describe below is well known to fricas developers,
but I report this because I find it fun and awful at the same time...
1) WARM-UP:
IF I understand well, my UG's readings, SPAD and Aldor have **different
semantics** for commas. N>=2 below.
* in Aldor (expr1, expr2,..,exprN) is a tuple (multivalue) and {expr1;
expr2;..; exprN}
is a sequence of expression evaluated in that order. Parentheses () and braces
{} are
used for precedence's sake and 99% interchangeable (different behavior for
external trailing semicolon).
Aldor allows internal trailing semicolon in blocks {e1;e2;e3;} while this is an
error in spad.
* In Spad (expr1, expr2,..,exprN) is a tuple (not really, see point 2)
while {e1;..; eN} **AND** {e1,..,eN} are sequences of expressions evaluated in
the order.
OK, I find Aldor semantics much more clean & logic than that of Spad, but this
is not the problem.
2) THE MYSTERY:
The mysterious behavior is this one: one would expect that "{expression}" has a
value equal to "expression,
but this is NOT the case in the interpreter if "expression" is a tuple.
(1) -> {1;2;3} -- this is a sequence of expressions in a block, OK.
(1) 3
Type: PositiveInteger
(2) -> {1,2,3} -- this is a sequence of expressions in a block, OK.
(2) 3
Type: PositiveInteger
(3) -> 1,2,3 -- tuple
(3) [1, 2, 3]
Type: Tuple(PositiveInteger)
(4) -> (1,2,3) -- tuple
(4) [1, 2, 3]
Type: Tuple(PositiveInteger)
(5) -> {"bum"} --{expr} same as expr? YES
(5) "bum"
Type: String
(6) -> {(1,2,3)} --{expr} same as expr? N
(6) 3
Type: PositiveInteger
(7) -> ((1,2),(3,4)) --tuple of tuples
(7) [(1, 2), (3, 4)]
Type: Tuple(Tuple(PositiveInteger))
(8) -> {((1,2),(3,4))} -- tuple of tuples? NO
(8) [3, 4]
Type: Tuple(PositiveInteger)
In the example above I would have expected [1,2,3] as result of (6) and
[[1,2],[3,4]] as result of (8).
As a second choice I would have expected syntax errors because, for instance,
in (6) I try to see "(1" as first expression in a comma separated sequence
of expressions but it is not a well formed expression. Same for "((1,2)" in (8).
It is like the semantics of commas (,...,) for tuple is forgotten inside
a singleton block and mutated to that of a sequence.
weird feature...
regards
ric
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[fricas-devel] Re: weird behavior of a weird anonymous function.
I tried also with more parentheses but same message
(3) -> (():Void +-> {free x; x:=1; local y; y:= 1; output( sin(x+y));
output("ciao")})(());y
sin(2)
ciao
y is declared as being in PositiveInteger but has not been given a
value.
(3) -> ( (():Void +-> {free x; x:=1; local y; y:= 1; output( sin(x+y));
output("ciao")})(()) );y
sin(2)
ciao
y is declared as being in PositiveInteger but has not been given a
value.
ric
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[fricas-devel] weird behavior of a weird anonymous function.
Hi!
I'm playing with a weird anonymous function (motivation below)
and I'm stumbling on a weird error, like if information
on a local variable y is exiting from an anonymous function,
only in a specific case.
I'm reporting this to you in case it was a bug.
(1) -> (():Void +-> {free x; x:=1; local y; y:= 1; output( sin(x+y));
output("ciao"); ()})() -- no problem
sin(2)
ciao
Type: Void
(2) -> (():Void +-> {free x; x:=1; local y; y:= 1; output( sin(x+y));
output("ciao"); ()})(); output(x+1) -- no problem
sin(2)
ciao
2
Type: Void
(3) -> (():Void +-> {free x; x:=1; local y; y:= 1; output( sin(x+y));
output("ciao"); ()})();y --problem
sin(2)
ciao
y is declared as being in PositiveInteger but has not been given a
value.
Why? In the global scope, y should have been valued to a symbol or Variable(y)
with NO type declaration.
The message is absent if y is on another line:
(4) -> (():Void +-> {free x; x:=1; local y; y:= 1; output( sin(x+y));
output("ciao"); ()})()
sin(2)
ciao
Type: Void
(5) -> y
(5) y
Type: Variable(y)
ric
PS
Motivation for the weird anonymous function above (Thanks for any feedback)
I'm looking for a scoping construct that could keep clean the global environment
from a proliferation of temporary variables in interpreter computations / input
files.
The body of functions is obviously one solution, but it is slightly boring
to define and immediately execute:
hereIDoThis(globalPars) == {...body with temporary, local variables...}
hereIDoThis(globaPars)
In Aldor the "... where ..." construct is supposed to be another scoping
construct
but in Spad I have the impression that I can use only in domain declarations.
EG the following give me errors:
(4) -> a where a:=1
Line 1: a where a:=1
A
Error A: syntax error at top level
Error A: Improper syntax.
2 error(s) parsing
(4) -> a where {a:=1}
Line 1: a where {a:=1}
A
Error A: syntax error at top level
Error A: Improper syntax.
2 error(s) parsing
In Mathematica there are the command Block[{x,y,z}, statements] and
Module[{x,y,z}, statements]
that keep x,y,z "local" (actually in Block x,y,z are global but mask possible
global values).
All other symbols in the statements have global scope.
It is not optimal to have "global by default" but it is useful to have such
Block-s.
So, I was trying to implement a block macro that could execute a sequence of
statements
inside the body of an anonymous function and call it immediately.
Compared to plain functions this would avoid the explicit execution.
Compared to Mathematica Block, Module this would have the advantage
that undeclared variables in RHS of statements are local.
I ended with:
macro block(statements) == (():Void +-> { statements; () })()
... but I had the aforementioned error:
(3) -> x:=1; y:=1; z:= 1; t:=1; block(free x; local y; x:=2; y:=2; z:=2; t:=
2; w:=2; output([x,y,z,t])); [x,y,z,t,w]
[2, 2, 2, 2]
y is declared as being in PositiveInteger but has not been given a
value.
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[fricas-devel] Thoughts on Float-s
Hi, take these as mild suggestions... 1) I feel like if the current system of Float numbers as it is is quite user-unsafe (!) because it allows operations f(x,y) combining FloatS x,y with different number of digits resulting in the *highest* one (ie something like coerce a Float to higher precision). This is a convention that gives false sense of security to a user that plays with the global variable digits(). Example: (1) -> x:Float:=%pi (1) 3.1415926535_897932385 Type: Float -- all digits after 20-th will be set below to (?) zero but this is an arbitrary convention -- so they are "rubbish". Analog statement if the implementation is binary. (2) -> digits(50) (2) 20 Type: PositiveInteger (3) -> x (3) 3.1415926535_897932385 Type: Float (4) -> y:Float:=%pi (4) 3.1415926535_8979323846_2643383279_5028841971_693993751 Type: Float (5) -> (y-x)/y (5) 0.1287414678_9751207735_7225992816_9904172693_1308680622 E -20 Type: Float --- the 50 digits shown above are "rubbish", just convention dependent So my point is that ideally one should have domains no coercitions to higher precisions, maybe to lower ones, or user conversions. Say, domains Float(d:PositiveIntegers). I'm willingly not distinguishing here among absolute or relative precision, the problem being more general. Of course in the present state if a user does not mix precisions (the best choice which should be recommended) or knows that the error is influenced by the lowest precision number (s)he entered, everything will be fine. 2) Given that the precision of a Float x at runtime depends on its history and may be unrelated to the current value of digits(), it would be useful to have functions digits, precision of signature Float -> PositiveIntegers that estimate the corresponding quantities for a given x. Best ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Correctness
One big source of bogosity is '$Lisp' calls. Some are valid because the call is access to a primitive operation otherwise unavailable in Spad. Some are valid because assumptions they make are are always satisified (like Lisp EQ implaing equality). But there are buch of bogus things. One is recently mentioned 'Factored' issue: we can not assume that Lisp ordering predicate will do something sensible (which essentially means that the code should _not_ depend on order and use quadratic algorithm). I also noticed uses of 'mathObject2String$Lisp'. This is fine for specific things like strings, symbols or lists of them. But it is invalid when applied to general FriCAS data. In particular 'toString' in 'src/algebra/clifford.spad' needs to be fixed (removed ???). Hi, maybe I'm too naive or this is too difficult, but why you do not isolate all the allowed $Lisp operations by creating spad wrapper functions in a "Primitive" domain and forbid the use of $Lisp everywhere else in the code? -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] How to enter in multi-line mode?
Sorry for the stupid question, (good for a FAQ) is a multi-line editing mode available when launching fricas from a linux shell? I cannot write "for" loops in more than one line. Thanks in advance, ric $ fricas (9) -> for i in 1..1000 repeat Line 1: for i in 1..1000 repeat .A Error A: syntax error at top level Error A: Improper syntax. 2 error(s) parsing -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Inaccuracies (?) in system help
Hi, take this as a ?bug report There are weird built-in synonyms referring to un-documented (?obsolete) commands )compiler (with R) and )display dependents ric PS: Thanks @Kurt for his hints. 1) -> )what synonym - System Command Synonyms - ... )co )compiler )d . )display )dep ... )display dependents )dependents )display dependents ... )help compiler -- => shows the help for )compile ... does )compiler exist? (1) -> )display dependents No option begins with dependents . -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Dependent types in Fricas interpreter (input files)
Hi, I have a couple of questions. 1) are dependent types supported by the interpreter (input files)? I feel like n in the image type of defFun below is really understood ... (1) -> )read dep-types defFun(n:PositiveInteger):SquareMatrix(n, Integer) == sample$SquareMatrix(n, Integer) Cannot convert the value from type Symbol to NonNegativeInteger . 2) Is there an assign function such that assign(x,z) would be equivalent to the statement x:= z ? thanks for any hint, ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: Re: [fricas-devel] )SET-tings
Hi RalF I still prefer the original spelling of my name. Sorry, the suggestion of changing name was unintentional. There is no "ph" in plain Italian so to compensate I tend to put "ph" in place of "f" in all foreign names & words. I'm not interested in including such pictures into any documentation. Neither I :) Actually, my suggestion was to include the *content* of these pictures in the fricas user guide because I have the impression the information on )set there listed is far from being complete... Have you ever tried )help set or )set Well, I was trying hard to see what hyperdoc has to offer to a user and I forgot )help. Shame on me! Enjoy. Thanks, great script! And if you like you can create more help pages of this kind at the axiom-wiki. Thanks for the kind invitation ... You know, I'm wondering if adding new information there would help users or just increase the entropy of the site (decreasing the probability for a user of recovering the wanted information) ...but maybe I'm joking here... :) ric PS: 1) Speaking of the fricasUG book.pdf , would it be possible to show version number or date in the first page to let people know that the content somehow changed? You know, downloading and checking every time the size of the pdf file is tedious and I cannot find the corresponding latex file on github. 2) Maybe you already know it, but I report the issue: the script that creates the API has problems with \newline \tab and \indent see the rendering of [1] [1] https://github.com/hemmecke/fricas/blob/master-hemmecke/src/algebra/numquad.spad -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] NIntegrate , arb, and FFI
Sorry, I've realized that numquad [1] works on Float and not only on machine
doubles, not bad!
Am I missing other quadrature packages (tanh-sinh, gaussian weights)?
thanks
ric
[1] https://fricas.github.io/api/NumericalQuadrature.html?highlight=numquad
--
(1) -> f(x:Float):Float == { m:=10, n:=11; k:= (4/%pi)^n*n*m; return k*
atan(x^m)^(n-1)*x^(m-1)/(1+x^(2*m))}
Function declaration f : Float -> Float has been added to workspace.
Type: Void
(2) -> digits(150);aromberg(f, 0::Float,1::Float,1.e-100,1.e-100,5,20,10)
Compiling function f with type Float -> Float
(2)
[
value
=
1.00_00_00_00_00_00_0
0_00_00_00_39_1966489901_0326774346_6
923646498_990324404
,
error
=
0.1832202195_2810277526_5224715964_4965694315_3906127288_2189970717_33840
04174_0332421811_9982065024_0030409954_5097041266_6646499458_3349608857_0
722547214_8324045347 E -100
,
totalpts = 3842113, success = true]
Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)
(3) ->
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[fricas-devel] Re: Re: Some questions about Fricas
@Erik: this might help, but the best is to take the time to read the fricas user guide (as I'm myself doing) ric fricas underlying language is strongly typed. You have to specify types (see f1,f2 below) or the interpreter will try to choose for you (see f3). Note that if you feed to f1 a float that cannot be recast to an integer without truncation you get an error. The last line shows how to see the signatures of the defined functions and their definition. (1) -> f1(x:Integer):Integer == x^2 Function declaration f1 : Integer -> Integer has been added to workspace. Type: Void (2) -> f2(x:DoubleFloat):DoubleFloat == x^2 Function declaration f2 : DoubleFloat -> DoubleFloat has been added to workspace. Type: Void (3) -> f1(2) Compiling function f1 with type Integer -> Integer (3) 4 Type: PositiveInteger (4) -> f1(2.0) (4) 4 Type: PositiveInteger (5) -> f1(2.3) Conversion failed in the compiled user function f1 . Cannot convert the value from type Float to Integer . (5) -> f2(2.3) Compiling function f2 with type DoubleFloat -> DoubleFloat (5) 5.289 Type: DoubleFloat (6) -> f2(2) (6) 4.0 Type: DoubleFloat (7) -> f3(x) == x^2 Type: Void (8) -> f3(2) Compiling function f3 with type PositiveInteger -> PositiveInteger (8) 4 Type: PositiveInteger (9) -> f3(2.3) Compiling function f3 with type Float -> Float (9) 5.29 Type: Float (10) -> )display properties f1 f2 f3 Properties of f1 : This is an interpreter function. Declared type or mode: (Integer -> Integer) 2 Definition: f1 x == x Compiled function type: Float -> Integer Compiled function type: Integer -> Integer Properties of f2 : This is an interpreter function. Declared type or mode: (DoubleFloat -> DoubleFloat) 2 Definition: f2 x == x Compiled function type: Float -> DoubleFloat Compiled function type: DoubleFloat -> DoubleFloat Properties of f3 : This is an interpreter function. 2 Definition: f3 x == x Compiled function type: Float -> Float Compiled function type: PositiveInteger -> PositiveInteger -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] NIntegrate , arb, and FFI
Hi again In fricasUG I cannot find mention of arbitrary precision numerical integration in 1D (NIntegrate in Mathematica.) Is this feature available? If not, have you ever thought (or, for lack of energies, at least dreamed) of interfacing fricas to some open source arbitrary precision C library, for instance Arb [1] which should have a good error control? Actually I was wondering, does the in-fricas spad compiler support calling external C code like does the aldor compiler (see aldorUG [2])? Thanks for your wise insights ric [1] http://arblib.org/ [2] http://www.aldor.org/docs/HTML/chap19.html -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] )SET-tings
Hi My question: If one changes the default settings in the REPL by performing the )set ... command or implicitly via the hyperdoc menu, are these new settings automatically stored somewhere and reloaded at REPL restart or are simply forgotten at next REPL restart (so that to permanently store settings one has to manually write them in the default initialization file)? It seems to me that the correct answer is the latter, could somebody confirm please? BTW, is the initialization file still axiom.input or fricas.input? (The latter would --hypothetically--- allow for installing axiom and fricas on the same system with no interference.) Aside comment: I was looking for a list of the options and parameters for the system command )set, which are not explicitly shown in the fricasUG. As far as I understand using hyperdoc (...Settings) is the only way to see the )set options/parameters/default for the user because looking at sources these options are hard encoded and mixed with boot code in fricas/src/interp/setvart.boot. For new users (and my) reference I attach 2 screen captures that show the available settings in full screen mode as I saw them. @Ralph it would be really great to have these lines listed in fricasUG. ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] CAS integration tests
Hello again. I write the question here because I think that Nasser Abbasi is in the list and maybe he could comment on this topic that in my view is quite important for FriCAS. I was eager to know the results of Nasser's test [1] with Rubi' integration suite, which includes Maple, Mathematica and (beginning 2018) also FriCAS. Having a good rating in comparison with M&M would obviously be a very good advertisement for FriCAS ...but apparently FriCAS is not included in the final result with 7 10^4 integrals, only in the small benchmark. Why? Is this a problem that can be fixed? Thanks for any information riccardo [1]https://www.12000.org/my_notes/CAS_integration_tests/index.htm -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] FriCAS contribution
Hi to all. Let me clarify my point of view on the question raised by Ralf' post @Waldek: please take it as friendly, constructive criticism. Maybe I'm wrong, but following the exchanges in the fricas-devel list I've got the impression that development proceeds in a suboptimal way due to a lack of coordination in the tasks that should be pursued and in the way to pursue them. And this with just a really minimal staff of 1 project leader and 2 active developers! The current way of proceeding would be definitely unbearable in the ideal case when project would capture more skillful developers. My general idea is that a minimal to do list should be established in some way by the project leader, organizing the tasks by difficulty and priority level. A good way to proceed in these cases is to learn from other healthier open source projects. Take Sympy, for instance. They manage to proceed with tens of active developers (and a dozen of new gsoc students per year). I think that the most important lesson to learn for FriCAS is that they have an issue list in which all the issues (bugs and new features) are posted and labeled by topic and by difficulty [1] (maybe they have too much labels). My suggestion is that the project leader should invest a small fraction of his time time in preparing a short list of tasks, classed by say 2-3 levels of difficulties: hard, medium and "Easy to fix". More labels on topics might also be useful. I do not know if the "easy to fix" label might capture new volunteers but it is a good way to tempt people to participate. Furthermore having a "hard/medium difficulty" would improve the effectiveness of the work of Ralf and oldk3113. The list can be done on an ascii file but of course having an issue list like that on github would have the advantage of being a way to organize, store and archive bug reports and their historical evolution, better that posts on a mailing list. my best regards, riccardo [1] https://github.com/sympy/sympy/issues https://github.com/sympy/sympy/issues?q=is%3Aissue+is%3Aopen+label%3A%22Easy+to+Fix%22 https://github.com/sympy/sympy/labels/Needs%20Better%20Patch -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Re: sbcl-1.4.5 causes problems
https://git.wiki.kernel.org/index.php/GitSvnCrashCourse :) -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] FriCAS packages in Linux
Hi, For the record, a page listing Linux distributions/repositories with FriCAS packages and their versions: https://repology.org/metapackage/fricas/versions ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] FriCAS status
Hello Waldek Wish: If you plan to release binaries, would it be possible to compile and release in some contrib directory also the binaries of Kurt Parentani's fricas_jupyter [1] ... if the code works and Kurt agrees, I mean. Regards Riccardo [1] https://github.com/nilqed/fricas_jupyter -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Impressions
@oldk1331: >3. Online shell. I may produce a online shell similar to sympy in the next >few (3~6) months. ... nice, but it is not me who decides what is urgent or not. @oldk1331: >TeXmacs interface could provide more functionality than jupyter, >as the latter uses a web interface. I know TeXmacs... "thermonuclear bomb" was intended to be a positive statement. @oldk1331: >And you are right that TeXmacs >requires guile-1.8 which makes it more difficult to install. TeXmacs >and FriCAS faces a similar problem: lack of developers, which is >unfortunate for those promising projects. Sure ... I found a TeXmacs developer saying he is working on porting TeXmaX to guile 2.x http://texmacs-users.texmacs.narkive.com/7OqIM2U4/how-can-i-use-guile-2-0#post6 ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Impressions
Dear Waldek, thanks for your explanation on FriCAS long term goals. Below a few, mild replies. > In general > you need to figure out what package manager given disto uses and what > flavour of packages it needs. That already two extra steps compared to > using a tarball (OK, using a tarball you need to know if you run 32 > bit distro or 64 bit one and you are out of luck if the machine is > not PC-compatible, but still simpler). Mmm... you are skipping "...with a guarantee of future automatic upgrades.": I do "apt-get install" once, then I "apt-get dist-upgrade" (or apt-get safe-upgrade") and all the software in my machine is up to date with no effort what is simpler for a lazy|busy user? >_You_ may voice request at distribution to include FriCAS. OK, could be better written, but done: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=890525 I guess that FriCAS users interested in having binaries distributed by debian, if any around, should support my request for a new package fricas (reportbug, package: wnpp, bug: 890525), otherwise it will have zero measure... > Does it matter much what is official? Right, bad wording: replace "official" by "reliable". > That is a wiki: by definition it is unstructured and disorganised. Just for nut-picking's love: "Unstructured by definition" OK, but "disorganized" is not necessary the case if the goal of the wiki is to transmit information to users. I do not know the current software, but in eg Mediawiki you may organize articles in a graph of categories just by adding simple tags like [[SPAD]], [[Install]], [[Integration]], [[History]], [[Beginners]] and have the category page automatically generated. Overview or starting point pages describing stable content may be manually added for tree-like reading. Best, ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Impressions
Dear Andrey, Thanks for your reply. Below some additional explanations on my post. On 2/10/18 7:59:24 AM CET Andrey G. Grozin wrote: > On Fri, 9 Feb 2018, riccardo.gu...@gmail.com wrote: > > Well, by definition, NO user will ever manually compile a source code. > Well, I never run any program which I have not compiled myself. I use > Gentoo Linux, by the way. Call it paranoia, but I don't trust binaries > whic can contain anything, and I cannot know what they really do. Andrey, I can imagine what you do with FriCAS in your multi-loop calculations, and I would class you in the "power-user" category not in the definition of "average simple user" I gave in the post. I want to pinpoint that in my post by "manually" I meant: Read the list of dependencies and their versions, compare with what you have. For all needed tarballs: cd somewhere; wget the-package && tar -x && make && make install" Repeat this every time a new version comes out and for every laptop/desktop you have. That said, the"hypotethic average user" I described has nothing against compiling from the sources if this can done be done easily, painlessly, and flawlessly as it is done in Gentoo. I discover happily that there is a FriCAS package in Portage, so a simple "emerge" will do the first install job and one "emerge -e system && emerge -e world" from time to time will keep upgraded the whole status. My "average user" would accept that. > > The fricas binaries I downloaded worked, but an average user has to > > figure out how to proceeed with the tar file. > > I think it's one of the first things any Linux user learns. Well, Linux today is much easier than Linux 20 years ago, but I admit that I've exaggerated a little... In my defense I cite the excellent Gentoo handbook: they never hesitate to explicitly write down step by step instructions. Here they do explain how to untar a package: https://wiki.gentoo.org/wiki/Handbook:AMD64/Installation/Stage#Unpacking_the_stage_tarball > > --- Texmacs has a built-in fricas plug-ins. Problem here: texmacs is > > kicked out of debian because of dependency on guile. > TeXmacs and its FriCAS interface work fine (though I prefer the ascii > repl - TeXmacs is slow on long formulas). It's trivial to compile > guile-1.8.x and TeXmacs-1.99.6. Of course I can do that, just I do not know if my "hypothetic user" would find that trivial Just for the record, here are the links that explain in detail why texmacs has no package in debian (removed from testing on 2013-10-15, removed from experimental on 2016-05-25 ) https://tracker.debian.org/pkg/texmacs https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=797833 > > --- The project fricas_jupyter (with binaries) looked interesting but > > one is required to have binaries compiled with SBCL 1.2.x . > > Unfortunately the official released binaries are made with sbcl 1.1.1 > > so I dropped this solution. > WHAT? Both versions are ancient. The current sbcl is 1.4.4, and I use it > everywhere. When a new sbcl appears, I compile it, and re-compile FriCAS > and maxima. I'm innocent here: protest with the person who compiled FriCAS 1.3.2 and released the binaries... Best ric -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Impressions
Dear Ralf having a status-of-the-project message somewhere in the official site would indeed be quite useful for new users. That said, your message transmits a feeling of sadness :) I advice you to be a little more positive, like eg: FriCAS is a relatively young project. There is a group of developers who actively work to refactor, improve and debug the existing code. For lack of energies, the documentation of the project is still in a work-in-progress status and heavily relies on AXIOM's one. Expect multiple sources, inaccuracies, ... We are aware of that and we hope to improve the situation as soon as possible. In the meanwhile, we understand that it might be frustrating for a new user to install, learn, and use FriCAS. If this is your case, please do not give up and write an email to fricas-devel@googlegroups.com . Usually, one of the developers is around and will try to assist you to overcome your frustration. > I want to make fricas.github.io the main portal for FriCAS, but there is > still a lot to do. When I find time, I will put the code that produces > the documentation to github, maybe then others find a channel to send > pull requests. Very good idea! Also the FriCAS-latex-Book should be in a git repo. ric PS With no urgency at all, could you set my receiving preferences on fricas-devel to "no emails"? I preferer to read online when I have some time. Thanks. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] Impressions
Hi
Ralf & oldk1331 asked me to detail my first impressions as a user approaching
FriCAS. Below you'll find a reasoned (time-consuming) list where I tried to
(fearlessly and pitilessly) pinpoint what appears to be "sub-optimal". Of
course it migh well be that I'm missing some important point or that I'm
completely wrong. Take these remarks just as sample of what an average user
might feel when approaching FriCAS.
Please do not be upset or hurted!!! ...and also PLEASE do not ask me to fix all
these issues for you :)
By user below I mean a person with good mathematical skills, minimal
computer skills, high aesthetical sense, and very very limited patience to fix
things. (Sorry, but users are done this way, I know my colleagues...)
I understand that the fricas project needs developers, but capturing a lot of
users is a good way to interest (young) developers. (See PS at bottom page.)
1) INSTALL.
Well, by definition, NO user will ever manually compile a source code.
Furthermore a user has no virtual machines and just one working environment
which she does not want to screw up if something goes wrong.
The fricas binaries I downloaded worked, but an average user has to figure out
how to proceeed with the tar file. A step by step "for dummies" explanation is
important. (This is missing in INSTALL-bin.txt) . I'm at higher computer level
so to me the problem was hate for manual install and paranoia, so I had to
take the time to read the tar contents (I did not like to have usr and
usr/local system directories in the tar), write a script that untars, installs,
and creates hashes of all files to check for corruption. This took time...
COMPARE with (eg debian's) """ $ aptitude install axiom """ which in seconds
installs everything with no problems of reading instructins, broken installs,
broken environment, security, and with a guarantee of future automatic upgrades.
Having linux packages is strategic. I've seen here and there on fricas-devel
remarks about having debian packages soon but after months I do not see the
packages in debian repository. Having Mac/Windows installers would be surely
helpful, but I do not know how difficult it is, so I stop here.
2) WEBSITE(S).
The site fricas.sourceforge.net is simple and effective but it refers to a
"fricas wiki" (axiom-wiki.newsynthesis.org) and to a "fricas API"
(http://fricas.github.io/api/genindex.html).
The site fricas.github.io looks nice, and modern the API is as well very good
and modern (but it does not include all, where are the system commands??). Had
a good impression so I started browsing it, discovering that there is more
information. Happy but now confused, "what is official and what not official"?
The axiom-wiki.newsynthesis.org contains a lot of useful information but (sorry
to the maintainer!) looks old-fashioned, weakly mantained, and unstructured:
in practice it is difficult to extract information the first times. What human
being can take profit of this page:
http://axiom-wiki.newsynthesis.org/FrontPage/contents ? (I must say that after
3 weeks of browsing there I've just discovered the
http://axiom-wiki.newsynthesis.org/SiteIndex glossary, which is much helpful
that the contents page. I know I know the "Site index" link is just below the
"Content index" but I am a user so I'm dumb! )
Well, no big problems here but my advice is that there should be just one
website (possibly modern and nice-looking like fricas.github.io) with all the
relevant infomation structured in an accessible wayy.
COMPARE with www.sympy.org : beautiful, no comparison...
3) ONLINE SHELL.
Not strategic but many CAS have it.
Writing \begin{axiom}\end{axiom} at each command is *TEDIOUS*. Furthemore I
couldn't find a way to enlarge the window.
COMPARE with http://maxima-online.org/ http://live.sympy.org/
4) Latex friendly GUI.
It is *important*!!! The 2D output of fricas kernel is difficult to read. (BTW
I would definitely prefer a plain output equal to the input form but I cannot
find how to do it. Fortran or the weird script-stuff are not useful for plain
reading of results.) Users want to see nice formulas!
I looked for information... nothing of official. I digged more and more and I
found the following:
--- Texmacs has a built-in fricas plug-ins. Problem here: texmacs is kicked out
of debian because of dependency on guile. So I took the time to read inatsll
instructions and I've installed the binaries ... and it did not work. Result: 2
hours wasted in trials. Anyway, I'm confident that one day might work, but my
**personal** opinion is that using texmas to output CAS results is like using a
termonuclear bomb to kill the mosquitos in your bedroom. The good alternative
is Jupyter: Mathematica-like, modern, supported, widely known and relatively
light. so
--- I went to the official list of jupyter kernels,
https://github.com/jupyter/jupyter/wiki/Jupyter-kernels and I found ...
NOT
Re: [fricas-devel] Question on evaluation (2)
Hi again, just for reference, a simple and quite precise explanation of evaluation in a proposed variant of A^# called B^# is available here: [JenksTrager94] at p 39. The authors say that evaluation in B^# corresponds to scratchpad and Common Lisp, so I *hope* that it is what is used by Axiom/FriCAS. If you know of similar/better references, please let me know, there are tons of articles out there. Greetings ric [JenksTrager94] http://axiom-wiki.newsynthesis.org/public/refs/axiom-scratchpad.pdf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] Question on evaluation (2)
Dear Ralf, oldk1331 and Themos, thanks for your answers.
I'll comment on/answer various points below and I'll make up a list of my
impressions in another "constructive criticism" post.
>That's an interesting skill set. May I ask how did you get in touch
>with FriCAS?
I heard about Axiom more or less when I ended my PhD and Axiom was commercial.
At that time I computed in Macsyma (without x). Then in my post-doc I started
using Mathematica. Got a job and more time for "CAS fun", I started to look
around for viable Open Source alternatives to Mathematica (say beginning 2000).
I became aware that Axiom was OS but I was scared by the immensity of its
documentation, the strong type system, and by what seemed to me a slow source
development. I followed the Aldor transition to OS looking from time to time at
the forum, and after a while I realized that there were no more one but three
"Axioms" around. FriCAS looks to me the healthier project. (The strong type
system fear evaporated meanwhile thanks to a little immersion in Haskell.)
Concerning my question on evaluation, the motivation is just theoretical, to
understand the evaluation mechanism: I have no precise application in mind.
@oldk1331 and @Themos, thanks for suggesting delayed assignment. I knew about
==. If I write (a==b; b==1; a) then a is evaluated with b bound to 1. The post
was more about understanding of "what is a on the LHS and b on the RHS of the
assignment", that why I used := .
@oldk1331:
>Do you have any problems on installation?
I've installed installed the binaries in a test machine (linux debian) this we.
I'll talk about problems I faced in the "constructive criticism" email.
@oldk1331:
>The "fixed-point infinite evaluation" sounds like delayed assignment
>I mentioned above.
Mmm... in my Mathematica-biased understanding, immediate evaluation and delayed
evaluation refer to *when* the RHS of an assignment is evaluated, at the
assignment time or when a variable is re-used. My question was not about when
evaluation is performed but more about *how* evaluation is performed. In
Mathematica assignments ( = immediate and := delayed) define immediate or
delayed global rules that are stored somewhere in the environment and
evaluation means "repeatedly apply all the rules in scope until the result does
not change". That is what I meant by "fixed-point infinite evaluation" and the
they point is the fact that the rules are repeatedly evaluated.
@oldk1331:
> BTW, is this possible in Sympy?
In my knowledge, in Sympy the LHS of an assignment is a plain python variable
and in the RHS one has an object representing a mathematical object, say an
expression. Assignment of a python variable is immediate (unless one cheats and
uses a nullary function, but that has an heavy function-like syntax). There is
no rule-storing and repeated application as in Mathematica. I'm not aware of a
way to automatically have this fixed-point evaluation. On the other hand I
guess that if one has an *explicit* list of rules one might create a function
that applies them until the result is fixed.
@Ralf
Thanks for your enlightening explanation!
If I understand correctly, the "variables" on the LHS of assignments are Aldor
(whatever) variables that are bound (refer to) to more complicated Aldor
objects with type in some domain, like Variable(b).
Let me write down another example to test if I've understood (could you tell me
if I'm wrong?)
a:=a
-- "a" on the LHS is an Aldor variable (a reference to an object) , "a" on the
RHS is an object of type Variable(a) coercible to Symbol.
a:=1
-- "a" on the LHS is the same Aldor variable as above. "a" now reference to
"1:Integer" and the value a:Variable(a) -- no mor linked -- disappears from the
scope.
f(x) == x+a -- who is "a" on RHS?
f(z)
--- => z+1 so "a" above was an Aldor variable
If my understanding is correct, the situation is pretty much like Sympy, [1],
where you would write the above test as
a = Symbol("a")
-- "a" on LHS a python ref. On the RHS you create explicitly a Symbol
object named "a".
a = 1
-- "a" on LHS a python ref.
def f(x): return x+a
-- "a" on LHS a python ref, presently bounded to 1.
f(Symbol("z"))
-- returns Symbol("z")+1, which is shown as z+1
[1] http://docs.sympy.org/latest/gotchas.html#variables
>For example, tell me a CAS that distinguishes between a (multivariate)
>polynomial that is "distributed" (i.e. stored as a list of pairs where
>each pair consists of a coefficient and the corresponding exponent
>vector of the variables) or that is "recursive" (i.e. it is a
>(univariate) polynomial in the main variable whose coefficients are
>(recursive) polynomials in the other variables.
I understand. (Actually it seems that also mathemagix [2] does it :) but I'm
not a mathemagix user. )
[2] http://www.mathemagix.org/www/multimix/doc/html/multivariate.en.html
Thanks,
ric
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[fricas-devel] Question on evaluation (2)
Dear Fricas developers (I'm and not sure that this is the good forum to address my question, but I cannot find any other.) First, thanks you all for your engagement to keep this great project alive! I'm a researcher in theoretical & mathematical physics with some knowledge (at different levels) of Mathematica (the current standard in th phys), Sympy, Maxima and Haskell. (No Lisp/Boot/Spad/Aldor alas!) In these days I'm trying to learn Fricas and I'm playing with the online sandbox. (As a sad aside, I must say that the current status of fricas installation & language documentation is "sub-obtimal" (I can give more details if you're curious). One must be much much more motivated than an average cas-beginner not to run away, to stay & progress. Of course this is not a blame, I understand that these tasks are tedious & heavily time consuming, and I see that there is some promising effort in progress.) The first thing I like to understand about a CAS is how evaluation works ...so, unable to find this topic on the documentation, I did some trials... And here's my question: a:=b; b:=1; [a,eval(a),simplify(a)] returns [b, b,b]. How can I force the interpreter in using the information that VALUE(b) = 1 in expressions containing a? This one-level evaluation behavior is similar to the one found in masyma, but there there is ev(a, infeval) which does the job and one gets 1. On the other hand Mathematica uses fixed-point infinite evaluation by default so it returns 1 for a. The answer: eval(a, 'b = b) returns 1 but it is not satisfactory to me because it requires the apriori knowledge of all the variables involved in Value (a). Is there a better way to get 1 from a, or maybe not having it is a feature of the language? Thanks for your time ric PS sorry if you received also an early version of this email, the first trial seemed to be blocked/delayed. Please ignore it. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
