Changes http://wiki.axiom-developer.org/DistributedMultivariatePolynomial/diff
--
>The evaluation of 1/x x in 'DistributedMultivariatePolynomial([x],Polynomial
>Integer)' is equivalent to 1 but it is not equivalent to 1 in
>'DistributedMultivariatePolynomial([x],Fraction Polynomial Integer)'. It
Changes http://wiki.axiom-developer.org/DistributedMultivariatePolynomial/diff
--
Bill: One more thing: I am amazed that you keep insisting on using the same
symbol for two different mathematical objects in one expression. You did this
when you use the expression $Q(R[x])[x]$ and say that
>the
Changes http://wiki.axiom-developer.org/DistributedMultivariatePolynomial/diff
--
Bill Page wrote:
> I find your notation a little confusing. In Axiom notation I think you mean,
> for example:
There is nothing confusing about my notation in $R[x]$ where $R$ can be any
integral domain (or even r
Changes http://wiki.axiom-developer.org/FreeAldor/diff
--
Axiom basically stayed stagnant for many years and it took a tremendous effort
(due to Tim Daly, Bill Page, Camm Maquire and others) to bring it back to life.
If Aldor does not become free, it may suffer the same fate. Both Axiom and
Aldo
Changes http://wiki.axiom-developer.org/270IntegratingUTS/diff
--
++added:
??changed:
-(c) In the second line, Axiom fails (correctly) because the integral, which is
'log(x)', which is not given by a Laurent series about 'x=0'. A better example
is:
(c) In the second line, Axiom fails (correctl
Changes http://wiki.axiom-developer.org/DistributedMultivariatePolynomial/diff
--
??changed:
-Subject: These examples are wrong and due to user and Interpreter errors.
Subject: These examples are wrong and due to Interpreter errors.
--
forwarded from http://wiki.axiom-developer.org/[EMAIL PROTECT
Changes http://wiki.axiom-developer.org/DistributedMultivariatePolynomial/diff
--
The fact that one can "explain" what the Axiom's Interpreter does to an input
does not make its operation legitimate. Even though 'EXPR INT' (and similarly
'POLY INT') is designed to include 'Symbol' (that means *a
Changes http://wiki.axiom-developer.org/270IntegratingUTS/diff
--
> Now Axiom having been forced to output the same identifier for two different
> variables, the first x bound to a variable in FRAC POLY INT, and the second x
> bound to the main variable of ULS, should NOT then simplify the expres
Changes http://wiki.axiom-developer.org/270IntegratingUTS/diff
--
I think recently this issue of using the same 'identifier' 'x' to stand for two
different 'variables' in two different domains (either accidentally or on
purpose) has been thoroughly discussed, but not quite. Note that I distinguis
Changes http://wiki.axiom-developer.org/268AbbrevWithTooLittleDetail/diff
--
\begin{axiom}
)abbr domain XYZ
\end{axiom}
\begin{axiom}
)abbrev?
\end{axiom}
The error on the above is the missing space.
However, as shown below, ')abbrev ?' seems really not to have documentation,
but ')help ?' had,
Changes http://wiki.axiom-developer.org/227RandomIntegerIsAStrangeFunction/diff
--
>random() has meaning only if I specify a distribution.
True (but that's a bit arrogant? :-). So the flaw is not in 'random()', but in
the documentation because the distribution is not given. I never said that the
Changes http://wiki.axiom-developer.org/227RandomIntegerIsAStrangeFunction/diff
--
You are right, 'random()' is not implementd or specified in 'Float' (it
should!) and the above three categories are the only ones Hyperdoc shows. But
'random()' for 'Float' is available in almost any computation so
Changes http://wiki.axiom-developer.org/233TraceInFloatCausedFatalError/diff
--
Category: Aldor Library Compiler => Axiom Interpreter
--
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Changes http://wiki.axiom-developer.org/227RandomIntegerIsAStrangeFunction/diff
--
??changed:
-Are you serious? random() is a categorical specification and it is not
possible to be more specific without knowing the domain. It is certainly useful
in creating derived random functions that are mor
Changes http://wiki.axiom-developer.org/227RandomIntegerIsAStrangeFunction/diff
--
Are you serious? random() is a categorical specification and it is not
possible to be more specific without knowing the domain. It is certainly useful
in creating derived random functions that are more meaningful
Changes
http://page.axiom-developer.org/zope/mathaction/235WhereIsRadicalExtensionAndRationalRadical/diff
--
In Solvefor.spad.pamphlet:
)abbrev package SOLVEFOR PolynomialSolveByFormulas
-- Current fields with "**": (%, RationalNumber) -> % are
-- ComplexFloat, RadicalExtension(K) and Rationa
Changes http://wiki.axiom-developer.org/233TraceInFloatCausedFatalError/diff
--
In the (old) Windows binary version 0.1.4, tracing the following function
caused a fatal error.
\begin{verbatim}
AXIOM Computer Algebra System
Version of Tuesday November 30, 2004
Changes
http://wiki.axiom-developer.org/232TraceCausesBindStackOverflowFromErroneousInput/diff
--
??changed:
-AXIOM Computer Algebra System
An accidental input typo when the domain EXPR is traced caused BIND stack
overflow. Correcting the typo does not return the system t
Changes
http://wiki.axiom-developer.org/232TraceCausesBindStackOverflowFromErroneousInput/diff
--
Category: Aldor Library Compiler => Axiom Interpreter
--
forwarded from http://wiki.axiom-developer.org/[EMAIL PROTECTED]
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Changes
http://page.axiom-developer.org/zope/mathaction/232TraceCausesBindStackOverflowFromErroneousInput/diff
--
AXIOM Computer Algebra System
Version of Tuesday November 30, 2004 at 21:11:14
---
Changes http://wiki.axiom-developer.org/226EqualityInFunctionCalled/diff
--
??changed:
-In fact, in variable.spad, the result should be true always.
In fact, in 'variable.spad', the result should be true always.
??changed:
-
Moreover, even this function gives the wrong answer. According to the '
Changes http://wiki.axiom-developer.org/226EqualityInFunctionCalled/diff
--
++added:
)set mess bot on
t:=(p=p)
++added:
In fact, in variable.spad, the result should be true always.
\begin{verbatim}
)abbrev domain FUNCTION FunctionCalled
++ Description:
++ This domain implements named functions
Changes http://wiki.axiom-developer.org/226EqualityInFunctionCalled/diff
--
??changed:
-t:Boolean:(p=p)
t:Boolean:=(p=p)
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ht
ssed as an object of the same type as the operands that
??changed:
-result is still and 'Expression Integer' even though Axiom decides
result is still an 'Expression Integer' even though Axiom decides
??changed:
-In princple in should be possible to ask Axiom to represent th
Changes
http://page.axiom-developer.org/zope/mathaction/193SymbolicValuesWithoutVariablesAreNotOrderedProperlyInEXPRINT/diff
--
??changed:
-(This is reminescent of FORTRAN: type promotion from INTEGER to REAL). In
other words, if one wants to test numerical inequalities involving symbolic
const
Changes
http://page.axiom-developer.org/zope/mathaction/193SymbolicValuesWithoutVariablesAreNotOrderedProperlyInEXPRINT/diff
--
Hi Martin:
You already know the reasons and I think the title of this page is unfair. It
is clear that the meaning of the operator '<' in 'EXPR INT' (or any domain tha
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
see [RealNumbers] and #167 for more info and discussions on infinite precision
floats and exact real number computations.
--
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Changes
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
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??changed:
-However, in my view, this still is not infinite precision in the sense of that
$2^(-35) + 2^34$ will not compute exactly because the system does not
*automatically* increase precision in 'FLOAT'
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
Thanks for this pointer. I would prefer to classify 'tan(3)' as belonging to
the hypothetical 'SymbolicFloat' rather than to 'EXPR INT' and the same for
'atan(tan(3))'. The definition of the single argument 'at
Changes http://page.axiom-developer.org/zope/mathaction/141AtanTan33/diff
--
see also discussions in #192.
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ht
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
??changed:
-OrderedRing probably. OrderedSet wouldn't make sense...
'OrderedRing', probably. 'OrderedSet', wouldn't make sense...
??changed:
-myatan2(y,x)
myatan2(x,y)
??changed:
-One possible way is to use a
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
Dear Martin:
Thanks, and yes, I was wrong again (shame on me): the range of the single
argument 'atan' does not cover $[0, 2\pi)$. But the only way to return results
in case variables are involved in the argum
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
Martin:
Thanks for pointing out my error. In coding 'myArgument', I was not aiming for
a general definition. I was experimenting to see if there is need for
'RealNumberSystem' or 'OrderedRing'.
As you propos
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
++added:
From: wyscc Thurs Jul 14 15:30:00 -5:00
>On the other hand, asking for 'TranscendentalFunctionCategory' also seems a
>lot, since only division by two is required.
Looking at th
Changes
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--
??changed:
-half: ()-> EXPR INT
myhalf: ()-> EXPR INT
??changed:
-Note, I think the current return of 'argument(0::Complex EXPR INT)' and
'argument(0::Complex INT)' as '%pi/2' are wrong.
Note, I think the cu
Changes
http://page.axiom-developer.org/zope/mathaction/TuplesProductsAndRecords/diff
--
Hi Bill:
Yes, we are finally agreeing on something. Use '(A,B,C, ...)" for vanilla
cartesian product and use 'Mapping(D, (A,B))' instead of 'Mapping(D,A,B)'; and
better still allow 'Mapping((C,D),(A,B))'.
p1 is $4^a-2^(2a)$, which is zero
Thus, in our case, at one point p1 is $4^a-2^{(2a)}$, which is zero
??changed:
-From wyscc Mon Jul 11 18:08:28 -0500 2005
-From: wyscc
-Date: Mon, 11 Jul 2005 18:08:28 -0500
-Subject: Step by step works
-Message-ID: <[EMAIL PROTECTED]>
>From billpage Wed
Changes
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
--
Bill, thanks for confirming what MathAction does. Actually, I simply did not
notice the "Click refresh to recalculate all" and now that I am aware of the
difference between edit and add
Changes
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
--
So Mathaction should give a warning that in using the reply box (instead of
directly editing the page), a new session of Axiom is initiated.
My analysis of Mon, 11 Jul 2005 18:18:25 -050
Changes
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
--
When I edit the message of Mon, 11 Jul 2005 18:18:25 -0500, by changing "p" in
the *text* to "'p'" and preview, the *answer* to 'gcd(p,r)' changes to the
correct one! When I cancel this
Changes
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
--
For some unknown reason, gcd(p,r) above *was* 1 but now becomes the correct
answer! (Actually, it turns back to 1 when I click the "reply", but for the
page, it gave the correct answer a
Changes
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
--
\begin{axiom}
dom:=UP('x,EXPR INT)
p:dom:=x-2^a
q:dom:=(x-2^a)*(x+2^a)
gcd(p,q)
exquo(q,p)
\end{axiom}
But note:
\begin{axiom}
simplify q
\end{axiom}
--
forwarded from http://page.axiom-de
Changes
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
--
The problem is
\begin{axiom}
r := simplify (x-2^a)*(x+2^a)
gcd(p,r)
\end{axiom}
ends up in EXPR INT, not 'UP(x,EXPR INT)' which is entirely reasonable. But
then the 'x' in 'r' is no lon
Changes
http://page.axiom-developer.org/zope/mathaction/TuplesProductsAndRecords/diff
--
++added:
From: wyscc Wed Jul 6 00:49:00 -5:00 2005
billpage wrote:
> makes no difference. My view is that
> (code snipped)
> should have the same meaning as the previous expression.
Of cours
Changes http://page.axiom-developer.org/zope/mathaction/MathActionProblems/diff
--
Bill:
Is it possible (and easy) to break the MathAction screen into two independent
scroll areas during editing mode, one for editing and one for preview? That
way, one can keep track of editing better. Currently
Changes
http://page.axiom-developer.org/zope/mathaction/TuplesProductsAndRecords/diff
--
??changed:
-Product can be looked up in hyperdoc. It is listed in Appendix C (p. 613 of
Axiom (paper) Book; p. 1028 of eBook). Tuple is more like Direct Product since
the entries must come from the same dom
Changes
http://page.axiom-developer.org/zope/mathaction/TuplesProductsAndRecords/diff
--
??changed:
-technology can? :-) Here in f you must take an integer and a float, wrap them
up
technology can? :-) Here in 'f' you must take an integer and a float, wrap them
up
??changed:
-'f:D -> C';
-let
Changes
http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
--
??changed:
-> \begin{axiom}
-> f1:Record(a:INT,b:FLOAT)->FLOAT
-
-> f1(arg)==arg.b+arg.a
-> f1[1,1.1]
-> \end{axiom}
->
-> should be viewed as equivalent to
-> \begin{axiom}
-> f2:(INT,FLOAT)->FLOAT
-> f2(a,b)==
Changes
http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
--
Product can be looked up in hyperdoc. It is listed in Appendix C (p. 613 of
Axiom (paper) Book; p. 1028 of eBook). Tuple is more like Direct Product since
the entries must come from the same domain. However, Pro
Changes
http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
--
??changed:
-This bug may be due to the Interpreter coercing 'Tuple INT' to 'PRIMARR INT'
and then to 'OutputForm', which perhaps uses the List output. Tim Daly may know
more.
This "bug" may be due to the Interp
Changes
http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
--
??changed:
-\par
??changed:
-\par
-Students and I make errors when the display is the same, even if there is a
type information.
Students and I make errors when the display is the same, even if there is a
Changes
http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
--
This page was renamed from #187 trouoble with tuples to #187 trouble with
tuples.
--
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Changes
http://page.axiom-developer.org/zope/mathaction/187TrouobleWithTuples/diff
--
++added:
From: William Sit, July 1, 2005 06:26:00 -5:00
The following works (not as neat as it should be, of course)
\begin{axiom}
f1:INT->Tuple INT
f1(x)==(x,2+x)
f2:(INT,INT)->INT
f2(x,y)==x*y -- fixed ty
Changes
http://page.axiom-developer.org/zope/mathaction/1833161AnyAndEveryShouldExitWhenTheResultIsClear/diff
--
How about just adding a more efficient any? and every? (don't overload them
though) in an auxilliary package? Nothing will be broken and you can have both
at your finger tips. I belie
Changes http://page.axiom-developer.org/zope/mathaction/185AppendVsConcat/diff
--
??changed:
-L1 := [1,2,3] ; L2 := [10,11,12] ; L := append (L1, L2) ; L2.2 := 100
\begin{axiom}
L1 := [1,2,3] ;
L2 := [10,11,12] ;
L := append (L1, L2) ;
L2.2 := 100
++added:
\end{axiom}
??changed:
-L1 := [1,2,
Changes
http://page.axiom-developer.org/zope/mathaction/184ComplexArgumentIsFalse/diff
--
++added:
\begin{axiom}
argument(-%i)
argument(-1+0*%i)
argument(-1)
\end{axiom}
--
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Changes http://page.axiom-developer.org/zope/mathaction/BuildAxiom/diff
--
??changed:
- (from William Sitt, email of Monday, February 21, 2005 2:51 AM)
(from William Sit, email of Monday, February 21, 2005 2:51 AM)
??changed:
-From unknown Wed Jun 8 11:20:38 -0500 2005
-From: unknown
-Date:
Changes
http://page.axiom-developer.org/zope/mathaction/168LinuxHyperdocSearchesDoNotWork/diff
--
??changed:
-I think the most urgent task is not to reimplement hyperdoc, but to make sure
that it still works as it was (say in the NAG version). This meant all the
searches and links must work. Cu
Changes
http://page.axiom-developer.org/zope/mathaction/168LinuxHyperdocSearchesDoNotWork/diff
--
I think the most urgent task is not to reimplement hyperdoc, but to make sure
that it still works as it was (say in the NAG version). This meant all the
searches and links must work. Currently (at l
Changes http://page.axiom-developer.org/zope/mathaction/RealNumbers/diff
--
++added:
>From wyscc Wed Jun 15 01:36:00 -4:00
Bill, thanks for creating this page. I enjoyed reading the links and was
wondering how a site on labor laws need to know the foundations of mathematics.
Actually, t
Changes
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
--
++added:
>From William Sit, Tuesday June 14 20:06:00 -4:00
Subject: Float, Real, RealClosure
Tim wrote:
>This raises the same kind of implementation issue that indefinite computation
>raises except that i
Changes
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
--
??changed:
-Most people would expect the answer of 'z-x' to be '0.16887242 E-20' but this
ignores the fact that the display is converted from an internal binary
representation to a decimal one. During the co
Changes
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
--
??changed:
-$m$ has 53 bits stored in a 52 bit field (not including sign, note that in
base 2, the most significant digit normalized must be 1, so no need to store
it!) and $e$ has 11 bits (including sign, r
Changes
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
--
??changed:
-In 'FLOAT', conceptually the infinite precision floating point system, is
basically also finite precision floating point system, with the ability to
increase precision as requested. However, this
'FRAC INT'? How does it relate
to standard (IEEE ?) definitions of floating point? How does
it differ mathematically from the reals, c.f. 'RealClosure',
etc.
Regards,
Bill Page.
>From wyscc Mon, 13 Jun 2005 07:00:00 -4:00
Axiom has 'DoubleFloat' (used to be called
Changes http://page.axiom-developer.org/zope/mathaction/MathActionProblems/diff
--
Great, and thanks. So it's time to break up the Sandbox page into shorter
pages. I tried to move Rubey's guessing sequence to a new
Sandbox.GuessingSequence and it seems to work well. I did make a mistake by
namin
Changes http://page.axiom-developer.org/zope/mathaction/GuessingSequence/diff
--
This page was renamed from QuestionMark to Guessing Sequence.
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Changes http://page.axiom-developer.org/zope/mathaction/GuessingSequence/diff
--
This page makes test uses of the Guess package by Martin Rubey. Feel free to
change the sequence to ones you like to try.
We need to load these packages:
\begin{axiom}
)lib RINTERPA RINTERP PCDEN GUESS GUESSINT GUES
Changes http://page.axiom-developer.org/zope/mathaction/SummerOfCode/diff
--
??changed:
-DOCUMENTATION
-
-Axiom is documented with 4 books which are under development,
Summer of Code: Axiom Projects
Information on Google's Summer of Code project is available at
http://code.google.com/summerofcod
Changes
http://page.axiom-developer.org/zope/mathaction/150ToCreateAFunctionFromAnExpresion/diff
--
??changed:
--
\begin{axiom}
??changed:
--
-I get an otput of 3x; I would like an otput of 15.
-Is there a way to do it rigth?
\end{axiom}
I get an outpu
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