things that Python gets wrong started getting on my way and I
> certainly wouldn't like to get things wrong that Python got right, but I
> guess I can't avoid it more than getting things wrong that Python got wrong.
>
> I did look into NumPy a bit, but like Richard Fateman did before you
It might be useful to list the points of friction that you are aware of in
the design of python with
respect to use in sympy,
to see if people have work-arounds that you might have missed, or to
encourage
people to point out solutions that exist in alternative languages that
already exist.
Presumably det() is using a method which requires exact division /
cancellation
with polynomials, so it will work if all those floats are converted to
rationals
and the arithmetic done exactly. The results will typically be numbers with
many many digits.
There are many papers on different
Instead of just informing us of your name and a question "how can I help?"
perhaps such messages could include
(a) level of familiarity with python (years of programming, previous
projects)
(b) mathematical education level (high school / ... / PhD?)
(c) particular expertise (physics? biology?
What is the rationale (not rational :) ) for simplifying asin(sin(x)) to
x ?
I suppose one rationale is that you haven't really looked at the consequence
and therefore think it is a good idea. But it is a bad idea.
Also log(exp(x)) --> x is a bad idea. The reason is, asin and log are
apologies for apparently responding to myself. This link may provide a
useful, if somewhat long-winded explanation.
http://people.bath.ac.uk/masjhd/Slides/CalculemusSchool2002.pdf
>>
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Another way of explaining this is to say that sympy (and all its
competitors) implement arithmetic in a field of fractions, in
which that cancellation is valid. The perspective of
abstract algebra provides a computational framework for
polynomials and rational functions. See for example
Sometimes programs get slower because they are getting smarter. It often
happens
in the other direction --- especially in symbolic mathematics systems.
That is, someone writes a new program that does "the same thing" as an
existing program, but much faster. The reality may be that the
new
see, for example,
https://people.eecs.berkeley.edu/~fateman/papers/mly-psmath.pdf
for a discussion. It is really a consideration of "optical character
recognition"
of math equations, where the characters are mostly perfectly represented,
and the spacing is perfectly represented. But what is
What ideas or past work from "artificial intelligence" do you believe
will be relevant to your work?
On Monday, May 22, 2017 at 9:16:28 AM UTC-7, Tayyip yetiş wrote:
>
> Hi,
> We starting artificial intelligence project using sympy.
> MindRun Project is an artificial intelligence application for
for what it is worth
(1) rearranging expressions does not guaranteed that they
will evaluate to the same values, given floating-point data.
(2) this ad hoc searching for common subexpressions is
not going to extract the best way of evaluating (say)
polynomials that can be factored, or can be
.. I said
you could snarf down huge
> piles of "application" code -- at least at some superficial level --
> and then cut in the sympy alternatives as necessary for the
> application,.
>
>
which is what Mathics might do, if my understanding of the
documentation is correct. I have not tried
TLDR.
1. The difference between an if-then-else tree and "pattern matching"
is two-fold.
(a) The "pattern matching" is probably referring to a purely rule-driven
algorithm, where each time there is a transformation, the rule set is
re-applied again. A clever system will only look at the rules
There is a version of Albert Rich's project that
uses if-then-else rather than a rule set.
Writing a pattern matcher that mimicks Mathematica's pattern
matcher would be irrelevant if you used that alternative.
On the other hand, mimicking Mathematica might have other
uses. There are at least
Hi Marco.
I suggest you learn to use the "subject" line for something relevant.
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There are 4 values for (-1)^(1/4) and there are 2 values for sqrt(-I).
the Maxima program has a command cabs() that returns 1/2 for this
expression.
Figure out what cabs does, and you are set. :)
On Sunday, September 4, 2016 at 9:16:31 AM UTC-7, bsdz wrote:
>
> Hi
>
> Can anyone recommend a
it, it
>> can be replaced with 0, which is what SymPy's limit() appears to be doing.
>> I am curious how you are ending up with an expression with a DiracDelta
>> that you need to take a limit of, though.
>>
>> Aaron Meurer
>>
>> On Sat, Aug 13, 2016 at 8:34 P
Since DiracDelta is a distribution, not a function, and presumably the
limit program is oriented toward finding limits of analytic functions,
it would be fairly reasonable for the limit program to not work on
this kind of expression. The mathematical context in which DiracDelta is
understood and
This strikes me as a rather weak idea from a genetic algorithms point of
view.
but you can create expressions by a recursive algorithm (given some chosen
maximum length) from the root
by picking an operation at each level, knowing the number of operands each
takes.
On Monday, July 25, 2016
Maybe you are mischaracterizing what you are doing, but in my view you
don't determine the domain and range of
a function by looking at its defining expression. That is something that
is part of the definition of the function.
What is the domain of sin()? Well, it could be the reals, it
(or whatever it is
> manualintegrate already uses)
>
> More general cases, say if p is a sum and the term is expanded, may
> require further simplification functions like powsimp() to bring it
> into canonical form.
>
> Aaron Meurer
>
>
> On Thu, Jun 9, 2016 at 5:2
1. You really need to tighten up the specification for what this algorithm
is supposed to do.
2. Probably brute force search will do the job, if you are talking about
the typical
puzzle that I am guessing you mean.
On Thursday, June 2, 2016 at 8:22:41 PM UTC-7, meInvent bbird wrote:
>
> is
).
This all works in Maxima; not sure how if it works in sympy.
RJF
On Wednesday, June 8, 2016 at 7:54:05 PM UTC-7, Richard Fateman wrote:
>
> I suggest you get rid of all factors not dependent on x by scanning
> through each term in a product, if you have a product.
> then you ne
I suggest you get rid of all factors not dependent on x by scanning through
each term in a product, if you have a product.
then you need only find if the expression is R= (e+f*x)^p.
compute t A= taylor series expansion around 0 of R and B=taylor series of
diff(R,x).
Some algebra should get you
I think you are merely trying to find common subexpressions to speed up
evaluation.
There are lots of ways to do that.
The simplest is to precompute sin(t), cos(t), exp(t) or whatever
non-elementary
functions are involved. Then you can also consider using horner's rule or
something like
I don't understand why you need it, but you could write your own
differentiation program
without simplification in about 1/2 page of code.
http://dl.acm.org/citation.cfm?id=307341=796040025=79612797
On Wednesday, June 1, 2016 at 6:34:28 AM UTC-7, Michi S wrote:
>
> Hello!
>
> Is there a way to
I suggest you first study ambiguous grammars and how to parse them.
Here's one paper http://www.cs.berkeley.edu/~fateman/papers/ambigmath.pdf
but there are others that you can find.
It is not a case of "writing a program" but solving the problem.
Is fx the same as f*x or f(x)?What about
Lisp answers this question by having a bunch of equality predicates.
EQ is true if the objects are identical in the sense of occupying the same
memory location.
EQUAL tests for equal trees, where the nodes are EQ
= is a test for numerical equality 1.0d0 and 1 for example.
There are also
I think it is nicer in the original Lisp.
The data is simply stuff like
( plus (times x (expt y -1)) 4) for x/y+4.
On Wednesday, December 30, 2015 at 12:37:33 PM UTC-8, Upendra Kumar wrote:
>
> Thanks, this link cleared the picture on what happens behind.
>
--
You received this
I thiink this hack is pretty worthless unless you have a better notion of
one more than.
e.g. factorial( (n-1)*(n+1)) * n^2 is factorial(n^2), right?
On Thursday, June 18, 2015 at 2:19:21 AM UTC-7, Gaurav Dhingra wrote:
Hi all
I was looking on the issue
I haven't studied all the notes prior to this, but it may be helpful to
look at Macsyma/ Maxima.
Series can be extended to several variables in different ways, e.g.
series in x to order xn with coefs as series in y to order yn etc
or to total order that is degree in(x) + degree in (y) +
I would not think it was the first CAS... but maybe the first at
something..
There were quite a few systems way back then. A big conference
with lots of system descriptions in papers was held in 1966.
The structure of the
Lisp simplifier written by Knut Korsvold (circa 1963) is still in
Typically the best system to use is the one that your colleagues (in the
same
application area, or company, or school) are using.
In the case of a textbook for electrical engineering graduate students, I
would expect them to know Matlab. They might know FORTRAN.
They might know Python. They
There has been extensive discussion over the years and continuing to today
about
what should be done when a computer algebra system is asked to solve
sometime.
The Maxima system mailing list, Mathematica stackexchange, and years of,
well,
mulling over what to do when (say) there are an
Thanks for the detailed explanation. I hope my further elaboration
will be of some use...
On Friday, December 19, 2014 8:02:04 PM UTC-8, Aaron Meurer wrote:
On Thu, Dec 18, 2014 at 5:47 PM, Richard Fateman fat...@gmail.com
javascript: wrote:
Please forgive me if this is off track -- I've
Please forgive me if this is off track -- I've never used assumptions in
sympy, and
don't know much about sympy implementation.
But here's a problem that has come up in a number of other computer algebra
system
that are (in some way) linked to a programming language.
If you say something about
On Saturday, December 13, 2014 6:08:58 AM UTC-8, Joachim Durchholz wrote:
Am 13.12.2014 um 06:27 schrieb Richard Fateman:
On Thursday, December 11, 2014 8:16:09 AM UTC-8, Joachim Durchholz
wrote:
Am 11.12.2014 um 00:40 schrieb Richard Fateman:
1994 paper by Adam Dingle
On Thursday, December 11, 2014 8:16:09 AM UTC-8, Joachim Durchholz wrote:
Am 11.12.2014 um 00:40 schrieb Richard Fateman:
1994 paper by Adam Dingle and Richard Fateman
Branch Cuts in Computer Algebra, (ISSAC '94 proceedings. also search
online).
That paper assumes that everything
1994 paper by Adam Dingle and Richard Fateman
Branch Cuts in Computer Algebra, (ISSAC '94 proceedings. also search
online).
When you say things about sqrt(), does it generalize to cuberoot? If it
does not, you are in trouble, or will be down the road.
What is the principal value of (1)^(1/6
On Sunday, November 30, 2014 12:30:02 PM UTC-8, Joachim Durchholz wrote:
snip...
Partial evaluation isn't doable at all.
I don't know what you mean by partial evaluation.
Difference between lazy and eager evaluation.
Is this something you
think that Lisp does? Maybe
On Sunday, November 30, 2014 1:52:08 AM UTC-8, Joachim Durchholz wrote:
Am 30.11.2014 um 06:53 schrieb Richard Fateman:
First-class functions are easy in Python (easier than in C/C++).
OK, I thought I read somewhere about some limitations.
What you can't do easily is macros. There's
On Friday, November 28, 2014 9:25:01 PM UTC-8, Joachim Durchholz wrote:
Am 29.11.2014 um 02:44 schrieb Richard Fateman:
On Thursday, November 27, 2014 10:35:34 PM UTC-8, Joachim Durchholz
wrote:
Awesome.
The papers I've read have been almost exclusively from the theorem
On Saturday, November 29, 2014 8:29:56 AM UTC-8, Aaron Meurer wrote:
big snip
.
Another question is, how can you teach the pattern matcher that a function
maps to an identity, like cos(a)*x can match x with a = 0, or x**a*y can
match y with a = 0?
You can do this (trivially)
compiler and matrun.lisp is its
runtime support.
RJF
On Saturday, November 29, 2014 9:58:10 PM UTC-8, Richard Fateman wrote:
On Saturday, November 29, 2014 8:29:56 AM UTC-8, Aaron Meurer wrote:
big snip
.
Another question is, how can you teach the pattern matcher that a
function
On Thursday, November 27, 2014 7:49:30 PM UTC-8, James Crist wrote:
Oh boy, this is going to be a big post. Responding to everyone in turn:
*@Aaron:*
Nonlinear, AC pattern matching is NP complete. Linear AC pattern matches
can be found in polynomial time.
Interesting. Why is that?
On Thursday, November 27, 2014 10:35:34 PM UTC-8, Joachim Durchholz wrote:
Awesome.
The papers I've read have been almost exclusively from the theorem
proving
world.
I think you should be mostly fine working off these.
I disagree, unless you are able to find much better papers
Does sympy really spell simplify without the L?
On Thursday, November 27, 2014 5:29:16 AM UTC-8, Francesco Bonazzi wrote:
On Thursday, November 27, 2014 2:28:11 PM UTC+1, Francesco Bonazzi wrote:
your_mathematica_expr = '((-2x+5)(4x-1)-4(-x^2+5x+1))/(4x-1)^2'
new_math_expr =
There's a long history of pattern matching fast including work by Richard
Jenks,
(Scratchpad, predecessor of Axiom). The general scheme is to take a
collection
of patterns and compile them into a tree form so that partial results from
pattern 1
can be used to improve speed on pattern 2, etc.
answering my own question ... oh
it is creating a sympy object, not simplifying.
Sorry for the noise.
'RJF
On Thursday, November 27, 2014 11:46:39 AM UTC-8, Richard Fateman wrote:
Does sympy really spell simplify without the L?
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On Tuesday, November 4, 2014 2:48:02 PM UTC-8, Joachim Durchholz wrote:
Am 04.11.2014 um 20:36 schrieb Richard Fateman:
On Tuesday, November 4, 2014 1:02:54 AM UTC-8, Joachim Durchholz wrote:
Obviously, Red Hat does not exist in your reality.
It does; don't
On Monday, November 3, 2014 4:56:29 PM UTC-8, Matthew Brett wrote:
Hi,
On Mon, Nov 3, 2014 at 2:03 PM, Richard Fateman fat...@gmail.com
javascript: wrote:
On Monday, November 3, 2014 1:26:18 AM UTC-8, Joachim Durchholz wrote:
Am 03.11.2014 um 03:56 schrieb Richard Fateman
On Tuesday, November 4, 2014 1:02:54 AM UTC-8, Joachim Durchholz wrote:
Obviously, Red Hat does not exist in your reality.
It does; don't they deliver Pizza?
Oh, sorry,. yes I heard of them.
Nor the people who are doing SymPy, for example.
They get paid big bucks??
Or... why are
at 4:59 PM, Sergey B Kirpichev skirp...@gmail.com
javascript: wrote:
On Mon, Nov 03, 2014 at 02:39:41PM -0800, Richard Fateman wrote:
I checked with Gradshteyn and Rhyzik (1960, revised various times
later),
and they define sum if nm to be zero.
Yes, that's a different convention
On Tuesday, November 4, 2014 12:57:08 PM UTC-8, Aaron Meurer wrote:
On Tue, Nov 4, 2014 at 1:48 PM, Richard Fateman fat...@gmail.com
javascript: wrote:
I think your citing of Karr's paper is OK; the more modern notation
seems
to be
sum (i in the set{M} of f(i)) which avoids
On Tuesday, November 4, 2014 1:02:45 PM UTC-8, Aaron Meurer wrote:
Your advice is appreciated, but it would be helpful if you actually
took the time to look at what SymPy does, instead of just ranting
blindly.
I read what people write here. I make some assumptions, true.
It feels
On Monday, November 3, 2014 1:26:18 AM UTC-8, Joachim Durchholz wrote:
Am 03.11.2014 um 03:56 schrieb Richard Fateman:
There is a difference in the size of the user base and there is a
difference
in the sophistication of the code. The Cathedral and the Bazaar essay
doesn't work
On Monday, November 3, 2014 4:30:11 AM UTC-8, Sergey Kirpichev wrote:
On Sun, Nov 02, 2014 at 06:56:31PM -0800, Richard Fateman wrote:
The Cathedral and the Bazaar essay
doesn't work if bugs do not become shallow with enough eyes.
I'm giving up. Probably, I newer can understand
On Sunday, November 2, 2014 3:06:20 AM UTC-8, Sergey Kirpichev wrote:
On Sat, Nov 01, 2014 at 09:22:06PM -0700, Richard Fateman wrote:
Why this is impossible for open-source programs?
It is not impossible, but I am unaware of (unpaid) maintainers of
open-source
On Saturday, November 1, 2014 5:02:30 AM UTC-7, Sergey Kirpichev wrote:
On Fri, Oct 31, 2014 at 11:45:19AM -0700, Richard Fateman wrote:
For closed-source commercial programs it is possible to report a bug
and
have an expert resolve the problem accurately and promptly.
Why
On Saturday, November 1, 2014 2:00:17 PM UTC-7, Aaron Meurer wrote:
On Thu, Oct 30, 2014 at 5:49 PM, Richard Fateman fat...@gmail.com
javascript: wrote:
On Tuesday, October 28, 2014 9:30:19 AM UTC-7, Aaron Meurer wrote:
Being open source is definitely a plus for SymPy here
On Friday, October 31, 2014 10:30:52 AM UTC-7, Sergey Kirpichev wrote:
On Friday, October 31, 2014 1:49:23 AM UTC+3, Richard Fateman wrote:
If they knew anything about debugging and SymPy, which is not so probable.
The point is - it's ultimately improbable for closed-source program
this
example...
Maybe solving some polynomial of degree 3 can give such complicated
formulas that a human would not use.
Christophe BAL
2014-10-30 23:53 GMT+01:00 Richard Fateman fat...@gmail.com
javascript::
There are even simpler examples. For instance, some systems multiply
On Tuesday, October 28, 2014 9:30:19 AM UTC-7, Aaron Meurer wrote:
Being open source is definitely a plus for SymPy here. The authors
could have stepped through SymPy with a debugger to help figure out
their problem, and submitted a pull request for a fix once they found
it.
If they
There are even simpler examples. For instance, some systems multiply
polynomials by some evaluation/interpolation scheme in finite fields. Or by
FFT
or by so-called Karatsuba or Cooke-Toom methods or a Kronecker method
evaluating a polynomial to a single huge integer...
Risch integration is
On Wednesday, October 29, 2014 3:38:47 AM UTC-7, Christophe Bal wrote:
Hello.
I'm writing a french book about SageMathCloud and I'm looking for known
wrong results given by Sage or Sympy due to floats calculations, or due to
the formal method used. Do you know such things ? My idea is to
Demo ware by necessity. How can you distinguish (d*y)/ (d*x)from
diff(y,x) written as \frac{dy}{dx} ?
And it gets worse as notation gets more subtle.
sure you can do a+b*c.
Why not allow speech input?
RJF
On Friday, October 24, 2014 2:27:48 PM UTC-7, Aaron Meurer wrote:
We don't have
Math InputPanel and InftyReader both work OK, but not perfect by any means.
I would expect this program to work only on very clean images well focused
and within
its probably quite limited domain of known notation. That is, excellent
demo-ware but
probably not ready for prime time. This
;
this should be one of the more straightforward parts.
Good luck
RJF
On Wed, Oct 15, 2014 at 2:20 PM, Richard Fateman fat...@gmail.com
javascript: wrote:
On Sunday, October 12, 2014 1:27:27 PM UTC-7, Aaron Meurer wrote:
I don't think integrate() tries any simplification. Ideally
On Sunday, October 12, 2014 1:27:27 PM UTC-7, Aaron Meurer wrote:
I don't think integrate() tries any simplification. Ideally it
shouldn't have to.
Why not? It seems to me quite the opposite. That is, integration is
much easier if the input is first converted to some canonical form
There are at least 2 open source parsers for Mathematica code.
The trivial stuff -- parsing x Sin[x] intox*sin(x) equivalent could be
done by following directions in any intro to compilers book.
The rest of the stuff, which requires pattern matching, simplification, and
a whole collection
computational structure in sympy that is
closed under cosine()?
2014-10-03 5:43 GMT+02:00 Richard Fateman fat...@gmail.com javascript:
:
On Thursday, October 2, 2014 11:11:14 AM UTC-7, Christophe Bal wrote:
And what about the following code ?
The user of Sympy must know that types are different
Lisp has a variety of equality testing predicates.
EQ for same memory location
= for numeric equality
There's also EQL, EQUAL, CHAR=, STRING=. ...
One of the benefits of NOT having infix syntax for relations like = is
that
it puts these others on a more equal footing, language-wise.
I
On Thursday, October 2, 2014 11:11:14 AM UTC-7, Christophe Bal wrote:
And what about the following code ?
The user of Sympy must know that types are different and so that the
variable are not the same things. A float is not a rational.
A float type is a different type from some other
On Tuesday, September 2, 2014 11:17:35 PM UTC-7, Joachim Durchholz wrote:
Am 03.09.2014 um 02:07 schrieb Richard Fateman:
Sure. Unlikely to be easy to do by simply hacking on trees. Here's a
classic pattern:
a*x^2+b*x+c.a,b,c are pattern variables. x, in this context
I have not looked at your expression, however it may be that the methods
used for so-called Poisson Series in celestial mechanics and mathematically
analogous computations will solve your problems in a jiffy.
Maxima has Poisson series, which are special canonical forms
for sums of sines and
On Monday, September 1, 2014 10:21:25 PM UTC-7, Joachim Durchholz wrote:
Am 02.09.2014 um 05:58 schrieb Richard Fateman:
you could read
about inherited and synthesized attributes (usually in relation
to intermediate expression trees in the theory of compiling.)
Heh. I don't need
On Tuesday, September 2, 2014 12:23:31 PM UTC-7, Joachim Durchholz wrote:
The makers of RUBI insist that no two rules of a rule set can ever apply
to the same subexpression.
That's draconic, and verifying that would be, erm, interesting.
I'm not sure whether that's worth it, but they do
You could read about unification, unification with identity,
associativity, etc.
You could add solving as a method of matching but probably you don't want
to use this routinely. Maxima's matcher does a little of this and most
people
find it surprising.
I think it would be unfortunate if you
I think that to understand why this is unlikely, you could read
about inherited and synthesized attributes (usually in relation
to intermediate expression trees in the theory of compiling.)
RJF
On Monday, September 1, 2014 9:54:36 AM UTC-7, Joachim Durchholz wrote:
Am 01.09.2014 um 13:28
You realize that you cannot express roots of polynomials in terms of
radicals
generally?
Maybe you should figure what you are doing with apart().
If it is integration of rational functions, maybe you should find another
path.
RJF
On Thursday, August 21, 2014 1:05:42 PM UTC-7, Mateusz
What would the result from ab if a and b are not comparable by your
rule? false? error? abs(a)abs(b)?
On Wednesday, August 6, 2014 8:40:04 AM UTC-7, Chris Smith wrote:
Python and SymPy both raise an error for something like I 2*I -- is
there a good reason to disallow comparison of
I don't follow... if you can reason about a+b, why can't you reason
about lambda(a),a+bor some other
variation? Unless the lambda().. is changed into binary code, it is
still symbolic-ish.
Reasoning about binary can, of course, be done, but people usually don't
like to do that.
RJF
On Wednesday, July 16, 2014 8:35:49 PM UTC-7, James Crist wrote:
On Friday, July 11, 2014 11:13:28 PM UTC-5, Richard Fateman wrote:
The obvious brute force method would be to use software floats in which
case you could increase the precision and the range of the
numbers involved. I'm
not mean that a partial solution can't be very handy. Computer algebra
systems rely on this.
RJF
On Thu, Jul 17, 2014 at 6:38 PM, Ondřej Čertík ondrej...@gmail.com
javascript: wrote:
On Thu, Jul 17, 2014 at 7:27 PM, Richard Fateman fat...@gmail.com
javascript: wrote:
Rubi is apparently
Rubi is apparently structured so that at any time at most one rule will be
applicable,
and it should be easy to figure out how to exclude everything else. I
think that
Albert Rich even expressed the notion that Rubi did not actually need to be
structured as rules..
--- just If/then/else
The
In addition to Mathics, you could look at MockMMA, free of license
restrictions,
written in Lisp.
Also, the syntactic sugar for patterns in Mathematica goes rather further
than
x_
for a start, there is x__ and x___. Then there are restrictions on the
Head[]
of the item matched. Then there are
The obvious brute force method would be to use software floats in which
case you could increase the precision and the range of the
numbers involved. I'm assuming the NaNs come from division by zero where
the denominator is not actually zero but computes to zero.
And the infs come from machine
On Saturday, July 5, 2014 5:10:26 AM UTC-7, F. B. wrote:
On Friday, July 4, 2014 4:12:25 PM UTC, Matthew wrote:
Only semi-related, but here is a small pattern matching project. It's
strictly for non-associative operators and so not appropriate for SymPy.
It does function decently
On Wednesday, July 2, 2014 6:32:56 AM UTC-7, Harsh Gupta wrote:
The last meeting with Matthew implanted a really cool idea about solving
equations. Suppose we have an equation f(x) which has finitely many
solution
a1, a2, a3, ... an. Then we can say that the solutions of equation f(x) =
I haven't tried your example, so I am guessing what you are doing. BUT...
You could read about how other computer algebra systems deal with this
problem.
For example Maxima has two methods for multiple-variable series,
recursive-by-variable or
total-degree truncation.
I think it is ok to
yes, there is a bug. the terms should start..
- 1/(x-pi/2) + (x-pi/2)/3 +
On Saturday, June 7, 2014 9:02:19 PM UTC-7, Ondřej Čertík wrote:
The series exists, and has the 1/x term in general, but it is missing
the shift by pi/2:
Here are some comments on sets in CAS
http://www.cs.berkeley.edu/~fateman/papers/sets.pdf
I think that if you want to deal with subsets of the real numbers you
should look
at the literature from interval arithmetic to see how you can get your
underwear in knots, even with such a simple domain
I came across this discussion when searching for info on FriCAS and sympy
together,
and found the comments to be worthy of some response.
1. The Axiom languages do not go back to the 1960s. Anything you might say
about
them blaming defects on historical ignorance of those ancient times is
I suppose my objection to the PRESS program is not the organization per
se, It could be that knowledge
of mathematics can be encoded procedurally or functionally or as pattern
matches or as rules. Frankly,
I have my own bias, having worked with several of these.
What I object to is the mind
On Wednesday, May 28, 2014 9:16:46 PM UTC-7, Aaron Meurer wrote:
How does it return invalid results? Does it not check if spurious
solutions were introduced through multiplying both sides of an
equation?
yes.
Also, if one is inclined to say that computer programs know things, then
You could look at it, but I think that, unless it has been changed since
I last looked, it has nothing at all to offer vs. an algorithmic approach.
And some real problems in that it returns answers that are wrong, sometimes.
The authors of the program are assuming that the (human?) recipient
You are right! So sorry! I copied the wrong program into my note.
Here is a correct version. (Again, Peter's article is fun to read...)
(defun ff(n m) (if (= n m) n (*(ff n (+ m m))(ff (- n m) (+ m m)
For this one, (ff 10 1) computes 10! and
does the following multiplications.
(ff
in the posting. When I try it, I just get regular linear
recursion. Presumably there is a typo in my translation or in the
original posting.
On Saturday, May 3, 2014 4:35:41 PM UTC-7, Richard Fateman wrote:
On Tuesday, April 1, 2014 2:58:34 PM UTC-7, Ondřej Čertík wrote:
On Mon, Mar 31
I think the issue is really one of the computational domain, and whether the
cancellation is always valid in that domain. In the formal algebraic
structure
(rational field extended by the indeterminate [x]) the cancellation is
valid.
The behavior of (x^2-1)/(x-1)is always
On Tuesday, April 1, 2014 2:58:34 PM UTC-7, Ondřej Čertík wrote:
On Mon, Mar 31, 2014 at 9:14 PM, Matthew Rocklin
mroc...@gmail.comjavascript:
wrote:
http://www.evanmiller.org/mathematical-hacker.html
I reference that blog post pretty often. I fully intend to reference it
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