[sage-support] Re: NVIDIA Tesla

2008-11-23 Thread Alec Mihailovs

Thank you!

> http://groups.google.com/group/mpir-devel/t/df88735e6d4e678c

I should search the group before posting.

Alec


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[sage-support] Re: NVIDIA Tesla

2008-11-23 Thread mabshoff



On Nov 23, 9:48 pm, "Alec Mihailovs" <[EMAIL PROTECTED]> wrote:
> Is it possible to run SAGE on NVIDIA Tesla (with 4 teraflops)?
>
> http://www.nvidia.com/object/personal_supercomputing.htmlhttp://tech.slashdot.org/article.pl?sid=08/11/23/068234&from=rss
>
> Alec

Nope, not yet and in the future one would only be able to run a subset
of Sage on the GPU anyway. The 4 TFlop number is pretty misleading
marketing crap by the way. For more details on Sage and GPUs check out
http://groups.google.com/group/mpir-devel/t/df88735e6d4e678c

Cheers,

Michael
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[sage-support] NVIDIA Tesla

2008-11-23 Thread Alec Mihailovs

Is it possible to run SAGE on NVIDIA Tesla (with 4 teraflops)? 

http://www.nvidia.com/object/personal_supercomputing.html
http://tech.slashdot.org/article.pl?sid=08/11/23/068234&from=rss

Alec

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[sage-support] Re: bug in integral?

2008-11-23 Thread Robert Dodier

On 11/19/08, Mike Hansen <[EMAIL PROTECTED]> wrote:

>  Yep, these are coming from Maxima:
>
>  (%i11) integrate(x*abs(9-x^2), x, -6, 0);
>  (%o11) 162
>  (%i12) integrate(x*abs(9-x^2), x, -6, -3);
>  (%o12) -729/4
>  (%i13) integrate(x*abs(9-x^2), x, -3, 0);
>  (%o13) -81/4
>
>  I've CC'd Robert Dodier on this.

For future reference, please forward such reports directly to the
Maxima mailing list, or, better still, make a bug report and then
forward the bug report to the mailing list.

If there is no bug report for this problem yet, I hope someone will make one.

Thanks for your help.

Robert Dodier

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[sage-support] Re: [fricas-devel] Re: [sage-support] Re: Quitting sage

2008-11-23 Thread William Stein

On Sun, Nov 23, 2008 at 5:45 PM, Gabriel Dos Reis <[EMAIL PROTECTED]> wrote:
> "William Stein" <[EMAIL PROTECTED]> writes:
>
> | On Sun, Nov 23, 2008 at 12:30 PM, Gabriel Dos Reis <[EMAIL PROTECTED]> 
> wrote:
> | > "William Stein" <[EMAIL PROTECTED]> writes:
> | >
> | > | Martin Rubey wrote:
> | > | > By the way, I think that "axiom.someop" should become "fricas.someop" 
> in SAGE.
> | > | > "axiom" is (meanwhile) quite misleading, FriCAS and axiom have parted.
> | > |
> | > | Could the people involved in Sage/Fricas/Axiom vote on this?  If they 
> vote for
> | > | the change, somebody can post a patch on the sage trac, and it'll get 
> accepted.
> | > | I'm thinking of  you, Waldek, Bill Page, etc.  and say if the majority
> | > | vote for this
> | > | switch then we do it.  I'm generally for it, since the Sage interface 
> is being
> | > | developed with FriCAS (rather than Axiom) as the standard test 
> interface.
> | >
> | > Just as three projects have agreed to using distinct driver names, it
> | > would make sense for Sage to use distinct interface names too.
> | >
> | > -- Gaby
> | >
> |
> | Are you suggesting that sage have three separate interfaces:
> |
> |   sage: axiom.eval('2+2')
> |   4
> |   sage: open_axiom.eval('2+2')
> |   4
> |   sage: fricas.eval('2+2')
> |
> | William
>
> I'm suggesting that since the three software can coexist on a single
> filesystem and as standalone binaries, it makes the most sense that
> Sage's interface does also make room for them to coexist in a Sage
> session as you show above -- would a user elect to install Sage
> optional packages for all three.  [ This, of course, does not mean
> that the Sage people have to implement all three. ]

Thanks for the clarification.  Let me re-ask my question.
Would you like to change so that the default  PanAxiom interface
in Sage, which is currently called "axiom" be instead called "fricas",
since it is currently being developed by Fricas developers, and
may end up using special features of Fricas?
[ ] Yes
[ ] No

William

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[sage-support] Re: [fricas-devel] Re: [sage-support] Re: Quitting sage

2008-11-23 Thread William Stein

On Sun, Nov 23, 2008 at 12:30 PM, Gabriel Dos Reis <[EMAIL PROTECTED]> wrote:
> "William Stein" <[EMAIL PROTECTED]> writes:
>
> | Martin Rubey wrote:
> | > By the way, I think that "axiom.someop" should become "fricas.someop" in 
> SAGE.
> | > "axiom" is (meanwhile) quite misleading, FriCAS and axiom have parted.
> |
> | Could the people involved in Sage/Fricas/Axiom vote on this?  If they vote 
> for
> | the change, somebody can post a patch on the sage trac, and it'll get 
> accepted.
> | I'm thinking of  you, Waldek, Bill Page, etc.  and say if the majority
> | vote for this
> | switch then we do it.  I'm generally for it, since the Sage interface is 
> being
> | developed with FriCAS (rather than Axiom) as the standard test interface.
>
> Just as three projects have agreed to using distinct driver names, it
> would make sense for Sage to use distinct interface names too.
>
> -- Gaby
>

Are you suggesting that sage have three separate interfaces:

  sage: axiom.eval('2+2')
  4
  sage: open_axiom.eval('2+2')
  4
  sage: fricas.eval('2+2')

William

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[sage-support] Re: creating a patch

2008-11-23 Thread William Stein

On Sun, Nov 23, 2008 at 1:26 PM, Chris Gorecki
<[EMAIL PROTECTED]> wrote:
>
> I've created some files I would like to post as a patch but after
> runngin
>
> hg_sage.add([filenames])
> hg_sage.commit([filenames])
> hg_sage.export()

Do hg_sage.log() to see the log and changset numbers.  Then do
hg_sage.export(changeset_number)
to export just that changeset.

>
>  the patch created starts with
>
> """
> # HG changeset patch
> # User [EMAIL PROTECTED]
> # Date 1139693613 0
> # Node ID bf5417bc8931e32cb9ed13663c71bff75b4b6b75
> # Parent  039f6310c6fe66477338a91a327b4ad2fd55a5b1
> [project @ patch to sage-0.10.13]
>
> diff -r 039f6310c6fe -r bf5417bc8931 PKG-INFO
> --- a/PKG-INFO  Sat Feb 11 01:13:08 2006 +
> +++ b/PKG-INFO  Sat Feb 11 21:33:33 2006 +
> @@ -1,6 +1,6 @@
>  Metadata-Version: 1.0
>  Name: sage
> -Version: 0.10.12
> +Version: 0.10.13
>  Summary: SAGE: System for Algebra and Geometry Experimentation
>  Home-page: http://modular.ucsd.edu/sage
>  Author: William Stein
> """
>
> and contains none of the files added.  I've tried reinstalling sage
> etc., but yet to no avail.
>
> Does anyone know what I'm doing wrong?
>
> I'm running sage 3.1.4 on vmware if that helps.
>
> -Chris
>
> >
>



-- 
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org

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[sage-support] creating a patch

2008-11-23 Thread Chris Gorecki

I've created some files I would like to post as a patch but after
runngin

hg_sage.add([filenames])
hg_sage.commit([filenames])
hg_sage.export()

 the patch created starts with

"""
# HG changeset patch
# User [EMAIL PROTECTED]
# Date 1139693613 0
# Node ID bf5417bc8931e32cb9ed13663c71bff75b4b6b75
# Parent  039f6310c6fe66477338a91a327b4ad2fd55a5b1
[project @ patch to sage-0.10.13]

diff -r 039f6310c6fe -r bf5417bc8931 PKG-INFO
--- a/PKG-INFO  Sat Feb 11 01:13:08 2006 +
+++ b/PKG-INFO  Sat Feb 11 21:33:33 2006 +
@@ -1,6 +1,6 @@
 Metadata-Version: 1.0
 Name: sage
-Version: 0.10.12
+Version: 0.10.13
 Summary: SAGE: System for Algebra and Geometry Experimentation
 Home-page: http://modular.ucsd.edu/sage
 Author: William Stein
"""

and contains none of the files added.  I've tried reinstalling sage
etc., but yet to no avail.

Does anyone know what I'm doing wrong?

I'm running sage 3.1.4 on vmware if that helps.

-Chris

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[sage-support] Re: Font size with notebook and Firefox, OS/X

2008-11-23 Thread datajerk

On my system Typeset is smaller than jsmath(expression).

The jsmath scaling helps.  My only issue is that the fonts are smaller
for some expressions, e.g. 3/2 is a lot smaller than just 3.

Thanks.

On Nov 22, 6:22 pm, Jason Grout <[EMAIL PROTECTED]> wrote:
> datajerk wrote:
> > Is there away to adjust the Typeset fontsize?  It's a bit small with
> > Firefox and OS/X.  Clearly I can increase all the fonts, but would
> > prefer to only change the Typeset output font size.  The size used by
> > jsmath is about right.
>
> The Typeset checkbox just uses the normal jsmath.  To increase the
> jsmath font scaling, click on the jsmath box (in the lower right
> corner), click on Options, then change the scale size (at the top of the
> resulting box).
>
> Jason
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[sage-support] Re: Quitting sage

2008-11-23 Thread William Stein

Martin Rubey wrote:
> By the way, I think that "axiom.someop" should become "fricas.someop" in SAGE.
> "axiom" is (meanwhile) quite misleading, FriCAS and axiom have parted.

Could the people involved in Sage/Fricas/Axiom vote on this?  If they vote for
the change, somebody can post a patch on the sage trac, and it'll get accepted.
I'm thinking of  you, Waldek, Bill Page, etc.  and say if the majority
vote for this
switch then we do it.  I'm generally for it, since the Sage interface is being
developed with FriCAS (rather than Axiom) as the standard test interface.

William

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[sage-support] Re: latex output for real numbers without zeros at the end

2008-11-23 Thread Stan Schymanski

I was going to ask for a Trac login and find out how to review
patches, but I just noticed that more qualified people than me have
taken care of it - and encountered other problems. Pity. Thanks a lot
for pushing it a bit further!

Stan

On Nov 20, 11:03 pm, Robert Bradshaw <[EMAIL PROTECTED]>
wrote:
> On Nov 20, 2008, at 1:54 AM, Stan Schymanski wrote:
>
> > Thanks a lot for that, Robert!
>
> Seehttp://trac.sagemath.org/sage_trac/ticket/4572Do you want to  
> review it?
>
> > Is the ultimate "fix" the one that will
> > use pynac instead of maxima? I can't wait for this one.
>
> Yep, though we won't be replacing all of maxima's functionality any  
> time soon.
>
>
>
> > All the best,
> > Stan
>
> > On Nov 19, 6:46 pm, Robert Bradshaw <[EMAIL PROTECTED]>
> > wrote:
> >> On Nov 18, 2008, at 11:18 PM, Stan Schymanski wrote:
>
> >>> Hi Robert,
>
> >>> Will the fix of the interaction with Maxima allow conservation of
> >>> precision of arguments passed through Maxima? This would satisfy my
> >>> needs.
>
> >> Actually, the "fix" is avoiding Maxima for everything symbolic.
>
> >>> Depending on how long this is going to take, I would like Mike's
> >>> interim fix to be implemented. It doesn't make anything worse  
> >>> compared
> >>> with the current state, as currently latexification gives a false
> >>> sense
> >>> of precision, anyway. This does certainly not fit my definition of
> >>> usefulness. We would just have to make sure that the interim fix is
> >>> removed again when the maxima interaction is fixed.
>
> >> The problem with Mike's fix is that it affects *all* real numbers,
> >> not just ones in Maxima expressions. I would be OK with a fix that
> >> just impacts symbolic object's latex (and even string)
> >> representation. I'll implement this and see if it gets a positive
> >> review.
>
> >> - Robert
>
> >>> Robert Bradshaw wrote:
>  On Nov 18, 2008, at 5:57 AM, Stan Schymanski wrote:
>
> > Ah, I see:
>
> > dummy1 = RealField(8)(0.1);dummy1
> > 0.10
>
> > dummy2 = RealField(16)(0.1);dummy2
> > 0.1000
>
> > latex(x*dummy1)
> > {0.1001 x}
>
> > latex(x*dummy2)
> > {0.1 x}
>
> > This is not quite what one would expect. However, the behaviour
> > before
> > the fix was not much better in my opinion, as the precision was  
> > not
> > obvious from the latex output, either:
>
> > sage: dummy1 = RealField(8)(0.1);dummy1
> > 0.10
> > sage: dummy2 = RealField(16)(0.1);dummy2
> > 0.1000
> > sage: latex(x*dummy1)
> > {0.1001000 x}
> > sage: latex(x*dummy2)
> > {0.100 x}
>
> > Obviously, the fix does not fix all the problems, but it does make
> > latex output much more useful. Would you agree?
>
>  That depends on your definition of useful. Personally, I think it's
>  useful to see how many digits of precision a given number has, and
>  for most things it works fine.
>
>  The issue here is the interaction with Maxima, which is being  
>  fixed.
>  Making it so any latexification of all real numbers is truncated is
>  (IMHO) not the right fix because one component abuses precisions.
>
>  - Robert
>
>
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[sage-support] Re: symbolic integration

2008-11-23 Thread Tim Lahey


On Nov 23, 2008, at 6:01 AM, Paul Zimmermann wrote:

>
>> Unfortunately, I know little about symbolic
>> integration techniques. Does anybody have suggestions for references?
>
> there are basically two techniques for symbolic integration:
> 1) table lookup in some classes of integrals. Maple is quite good at  
> this.
> 2) recognition of some inputs that (may) admit an integral in a  
> given class,
>   and computation of that integral by an algorithm. Axiom is quite  
> good at
>   this.
>
> For 2), a good reference for the transcendental case is the  
> following book:
>
> @Book{Bronstein97,
>  author =  "Manuel Bronstein",
>  title =   "Symbolic Integration {I}. Transcendental Functions",
>  publisher =   "Springer",
>  year =1997,
>  volume =  1,
>  series =  "Algorithms and Computation in Mathematics"
> }
>
> Unfortunately Manuel Bronstein died before finishing vol. II on the  
> algebraic
> case, which is the difficult one. As far as I know, he did implement  
> his
> algorithms in Axiom, including (partly) the algebraic case.
>

Thanks. It looks like my library has both regular and electronic  
versions so I'll
take a look. The first case might be easier now with the new symbolics  
and the pattern matching it has. It seems like looking at FriCAS is a  
good idea too.

Cheers,

Tim.

---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo

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[sage-support] Re: Quitting sage

2008-11-23 Thread Martin Rubey

"William Stein" <[EMAIL PROTECTED]> writes:

> * Axiom?

Axiom does *elementary* integration.  That is, if the Risch algorithm applies,
it will find the result except in a few cases.  It does have some pattern
matching abilities, but these are not really worth mentioning.

FriCAS (axiom fork, which is the one used for Sage) fixes quite a few bugs in
the old axiom integrator.  We (FriCASers) are lucky to have Waldek as
maintainer, who knows integration fairly well.

I'd like to add that I'm working on a domain (in the FriCAS sense) that
implements "power series that satisfy an ADE", and these are closed under
integration, too.  Of course, in most cases, the result will be an ADE, not an
elementary function.  Below is a rudimentary example "on foot".

By the way, I think that "axiom.someop" should become "fricas.someop" in SAGE.
"axiom" is (meanwhile) quite misleading, FriCAS and axiom have parted.

Martin

Below, how to integrate "sum n^n/factorial n z^n" on foot:

(1) -> series([n^n/factorial n for n in 0..])$UTS(FRAC INT, x, 0)

   (1)
   2   9  3   32  4   625  5   324  6   117649  7   131072  8
 1 + x + 2x  + - x  + -- x  + --- x  + --- x  + -- x  + -- x
   2   3   24   5 720 315
   + 
 4782969  9   1562500  10  11
 --- x  + --- x   + O(x  )
   4480 567
  Type: UnivariateTaylorSeries(Fraction(Integer),x,0)

(2) -> l := [1,1,2,9/2,32/3,625/24,324/5];

Type: List(Fraction(Integer))
(3) -> guessADE l

   (3)
  n   ,  3   2
   [[function= [[x ]f(x): - xf (x) + f(x)  - f(x) = 0,f(0)= 1(0)!],order= 0]]

  Type: List(Record(function: Expression(Integer),order: NonNegativeInteger))

(4) -> integrate series([n^n/factorial n for n in 0..])$UTS(FRAC INT, x, 0)

   (4)
 1  2   2  3   9  4   32  5   625  6   324  7   117649  8   131072  9
 x + - x  + - x  + - x  + -- x  + --- x  + --- x  + -- x  + -- x
 2  3  8  15  144   35   57602835
   + 
 4782969  10  11
 --- x   + O(x  )
  44800
  Type: UnivariateTaylorSeries(Fraction(Integer),x,0)

(5) -> guessADE entries complete first(coefficients %, 10)

   (5)
   [
   n,
 [function= [[x ]f(x): (- f(x) - x + 1)f (x) + f(x) - 1= 0,f(0)= 0(0)!],

  order= 0]
 ]
  Type: List(Record(function: Expression(Integer),order: NonNegativeInteger))


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[sage-support] Re: Quitting sage

2008-11-23 Thread Harald Schilly



On Nov 23, 8:34 am, Robert Bradshaw <[EMAIL PROTECTED]>
wrote:
> What I would like to see happen soon is some of the basic cases  
> solved in our own code, and then passing off to some other library  
> for the harder cases.

here is a blogposting about some of the difficulties:
http://blog.wolfram.com/2008/01/19/mathematica-and-the-fundamental-theorem-of-calculus/

i.e. it implies that even the test suite has to be intelligent,
because different answers could be the same and ok or otoh the same
answer could be a problem at some points, when calculating the
definite value

h
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[sage-support] Re: Plot in spherical coordinates.

2008-11-23 Thread David Joyner

I don't understand your question exactly.
Is this a paramateric plot in x,y,z space you want to plot?
For example, do you want to plot something like an ellipsoid?


On Sun, Nov 23, 2008 at 5:40 AM, A.Z. <[EMAIL PROTECTED]> wrote:
>
> I want to plot a function in spherical coordinates (rho, phi, theta),
> but i haven't found any examples in tutorial or reference manual. So,
> how can i do it in sage?
> >
>

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[sage-support] symbolic integration

2008-11-23 Thread Paul Zimmermann

> Unfortunately, I know little about symbolic
> integration techniques. Does anybody have suggestions for references?

there are basically two techniques for symbolic integration:
1) table lookup in some classes of integrals. Maple is quite good at this.
2) recognition of some inputs that (may) admit an integral in a given class,
   and computation of that integral by an algorithm. Axiom is quite good at
   this.
   
For 2), a good reference for the transcendental case is the following book:

@Book{Bronstein97,
  author =   "Manuel Bronstein",
  title ="Symbolic Integration {I}. Transcendental Functions",
  publisher ="Springer",
  year = 1997,
  volume =   1,
  series =   "Algorithms and Computation in Mathematics"
}

Unfortunately Manuel Bronstein died before finishing vol. II on the algebraic
case, which is the difficult one. As far as I know, he did implement his
algorithms in Axiom, including (partly) the algebraic case.

Implementing symbolic integration from scratch is a major task, that would
require years before reaching what Axiom can do. In any case, I suggest
reusing the Axiom test suite as starting point.

Paul Zimmermann



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[sage-support] Plot in spherical coordinates.

2008-11-23 Thread A.Z.

I want to plot a function in spherical coordinates (rho, phi, theta),
but i haven't found any examples in tutorial or reference manual. So,
how can i do it in sage?
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[sage-support] Re: Quitting sage

2008-11-23 Thread William Stein

On Sun, Nov 23, 2008 at 12:49 AM, Tim Lahey <[EMAIL PROTECTED]> wrote:
>
> On Nov 23, 2008, at 3:39 AM, William Stein wrote:
>
>>
>> On Sat, Nov 22, 2008 at 10:56 PM, Tim Lahey <[EMAIL PROTECTED]>
>> wrote:
>>> As for the option to use Maple/Mathematica, I think as long as there
>>> is relatively good conversion of expressions, it's best to just let
>>> the user call the Maple/Mathematica command directly. Otherwise, you
>>> need to write code to detect if one is installed and call it with
>>> a fallback plan if they're not.
>>
>> I don't envision any autodetection or anything like that.  What I
>> envision
>> is that the integrate command has an option algorithm='maple', say,
>> that
>> does the integral transparently using maple, e.g.,
>>
>> sage: integrate(sin(x)*cos(x)*x)
>> (sin(2*x) - 2*x*cos(2*x))/8
>> sage: integrate(sin(x)*cos(x)*x, algorithm='maple')
>> (sin(2*x) - 2*x*cos(2*x))/8
>> sage: integrate(sin(x)*cos(x)*x, algorithm='mathematica')
>> (sin(2*x) - 2*x*cos(2*x))/8
>> sage: integrate(sin(x)*cos(x)*x, algorithm='sympy')
>> (sin(2*x) - 2*x*cos(2*x))/8
>> sage: integrate(sin(x)*cos(x)*x, algorithm='axiom')
>> (sin(2*x) - 2*x*cos(2*x))/8
>>
>
> Ah, I like that option. To be honest, I haven't even really tried
> Maple from
> Sage yet. To be honest, one of the reasons I want to switch to Sage
> for is
> the LaTeX export. Maple's is awful and talking to the developers, they
> have
> no interest in improving it. I've been contemplating the possibility of
> exporting the notebook to LaTeX, but that requires that I get more
> familiar
> with the notebook code.

That has been on my todo list forever, repeatedly.  I gave it also as a student
project once, but the student turned out to not know programming.

>  The code in,
>
> http://www.iwriteiam.nl/html2tex.html
>
> may be useful as a starting point. It's GPL so that's good.
>
> Cheers,
>
> Tim.
>
> ---
> Tim Lahey
> PhD Candidate, Systems Design Engineering
> University of Waterloo
>
> >
>



-- 
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org

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[sage-support] Re: Quitting sage

2008-11-23 Thread Tim Lahey

On Nov 23, 2008, at 3:39 AM, William Stein wrote:

>
> On Sat, Nov 22, 2008 at 10:56 PM, Tim Lahey <[EMAIL PROTECTED]>  
> wrote:
>> As for the option to use Maple/Mathematica, I think as long as there
>> is relatively good conversion of expressions, it's best to just let
>> the user call the Maple/Mathematica command directly. Otherwise, you
>> need to write code to detect if one is installed and call it with
>> a fallback plan if they're not.
>
> I don't envision any autodetection or anything like that.  What I  
> envision
> is that the integrate command has an option algorithm='maple', say,  
> that
> does the integral transparently using maple, e.g.,
>
> sage: integrate(sin(x)*cos(x)*x)
> (sin(2*x) - 2*x*cos(2*x))/8
> sage: integrate(sin(x)*cos(x)*x, algorithm='maple')
> (sin(2*x) - 2*x*cos(2*x))/8
> sage: integrate(sin(x)*cos(x)*x, algorithm='mathematica')
> (sin(2*x) - 2*x*cos(2*x))/8
> sage: integrate(sin(x)*cos(x)*x, algorithm='sympy')
> (sin(2*x) - 2*x*cos(2*x))/8
> sage: integrate(sin(x)*cos(x)*x, algorithm='axiom')
> (sin(2*x) - 2*x*cos(2*x))/8
>

Ah, I like that option. To be honest, I haven't even really tried  
Maple from
Sage yet. To be honest, one of the reasons I want to switch to Sage  
for is
the LaTeX export. Maple's is awful and talking to the developers, they  
have
no interest in improving it. I've been contemplating the possibility of
exporting the notebook to LaTeX, but that requires that I get more  
familiar
with the notebook code. The code in,

http://www.iwriteiam.nl/html2tex.html

may be useful as a starting point. It's GPL so that's good.

Cheers,

Tim.

---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo

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[sage-support] Re: Quitting sage

2008-11-23 Thread William Stein

On Sat, Nov 22, 2008 at 10:56 PM, Tim Lahey <[EMAIL PROTECTED]> wrote:
> As for the option to use Maple/Mathematica, I think as long as there
> is relatively good conversion of expressions, it's best to just let
> the user call the Maple/Mathematica command directly. Otherwise, you
> need to write code to detect if one is installed and call it with
> a fallback plan if they're not.

I don't envision any autodetection or anything like that.  What I envision
is that the integrate command has an option algorithm='maple', say, that
does the integral transparently using maple, e.g.,

sage: integrate(sin(x)*cos(x)*x)
(sin(2*x) - 2*x*cos(2*x))/8
sage: integrate(sin(x)*cos(x)*x, algorithm='maple')
(sin(2*x) - 2*x*cos(2*x))/8
sage: integrate(sin(x)*cos(x)*x, algorithm='mathematica')
(sin(2*x) - 2*x*cos(2*x))/8
sage: integrate(sin(x)*cos(x)*x, algorithm='sympy')
(sin(2*x) - 2*x*cos(2*x))/8
sage: integrate(sin(x)*cos(x)*x, algorithm='axiom')
(sin(2*x) - 2*x*cos(2*x))/8

 - William

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