[sage-support] Re: Infinite sum
I asked this question myself a few months ago, and the easiest 2
solutions seem to be utilizing sympy or maxima.
Via sympy it is:
import sympy
sympy.var('x')
print sympy.sum(2**(-x), (x, 1, oo))
I'm taking this from a question I posed on the sympy message list:
http://groups.google.com/group/sympy/browse_frm/thread/5348ded3ebe8a25e?tvc=1
It should return a result of 1, but in sage 3.1.1 it returns 1-2*2**(1-
Infinity). While technically correct, this should clearly return 1
when simplified so I guess there is some complication when
transferring between modules. Ondrej will assuredly give more useful
information if he sees this.
More specifically , your example using m=2 is:
sympy.sum(1/((x+2)**3)),(x,1,oo))
Unfortunately this returns
Sum((2 + x)**(-3), (x, 1, Infinity))
n() on this function does not work, maybe a sympy equivalent would?
It may work better with a %python header, though I haven't tested this
yet (if you use the notebook).
I don't remember the maxima parsing offhand. I believe I got some
information about it from delving into the sage/washington undergrad
mail list. I'll try to look into it tomorrow. Making a natural
implementation for infinite series seems quite valuable and hopefully
a short-term goal considered for Sage. This is a specific dismay I've
come across when trying to broadcast Sage to an otherwise quite pro-
opensource professor.
Would a function called nsum or such that called sympy/maxima be
feasible? This would lead to a supplementation rather than a
replacement for the python sum().
Thomas
On Aug 29, 5:54 pm, Raouf <[EMAIL PROTECTED]> wrote:
> Hi,
> I am a newbie in sage and i want to compute an infinite sum with
> parameter m, like sum(1/(k+m)^3) k=1 to infinity.
> Can you please help me?
> thanks
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[sage-support] Re: convert string to sage expression
On Fri, Aug 29, 2008 at 5:12 PM, Simon King <[EMAIL PROTECTED]> wrote:
>
> Hi Geir,
>
> If you really want to use strings, it may work like that:
> sage: var('x y')
> (x, y)
> sage: EqL=['y==x**%d-%d'%(i,i) for i in range(10)]
> sage: for X in EqL:
> : print X
> : print solve(eval(X))
Use sage_eval instead of eval, unless you want to
confusing results:
sage: eval('2/3')
0
sage: eval('2^3')
1
> :
> y==x**0-0
> [
> y == 1
> ]
> y==x**1-1
> [
> x == y + 1
> ]
> y==x**2-2
> [
> x == - sqrt(y + 2),
>x == sqrt(y + 2)
> ]
>
> etc...
>
> Note that double-= yields an equation (not a boolean!) if symbolic
> expressions such as x and y are involved. A single "=" is an
> assignment.
>
> Cheers
>Simon
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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[sage-support] Re: convert string to sage expression
Hi Geir,
If you really want to use strings, it may work like that:
sage: var('x y')
(x, y)
sage: EqL=['y==x**%d-%d'%(i,i) for i in range(10)]
sage: for X in EqL:
: print X
: print solve(eval(X))
:
y==x**0-0
[
y == 1
]
y==x**1-1
[
x == y + 1
]
y==x**2-2
[
x == - sqrt(y + 2),
x == sqrt(y + 2)
]
etc...
Note that double-= yields an equation (not a boolean!) if symbolic
expressions such as x and y are involved. A single "=" is an
assignment.
Cheers
Simon
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[sage-support] Re: convert string to sage expression
Hello,
On Fri, Aug 29, 2008 at 4:00 PM, [EMAIL PROTECTED]
<[EMAIL PROTECTED]> wrote:
> I want to construct a set of equations using strings. For example:
>
> for i in range(0,10):
> eq1="eq=x^"+str(i)+"-"+str(i)
Is there a reason why you wanted to do it using strings? It's a bit
cleaner/easier to do it without strings:
sage: eq = var('eq')
sage: eqs = [0== x^i - i for i in range(1,10)]
sage: eqs
[0 == x - 1,
0 == x^2 - 2,
0 == x^3 - 3,
0 == x^4 - 4,
0 == x^5 - 5,
0 == x^6 - 6,
0 == x^7 - 7,
0 == x^8 - 8,
0 == x^9 - 9]
But, I doubt that those are the actual equations you want. you just
need to modify the eqs = ... line to be what you need.
--Mike
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[sage-support] convert string to sage expression
Hi, I want to construct a set of equations using strings. For example: for i in range(0,10): eq1="eq=x^"+str(i)+"-"+str(i) Is there a way to convert the string eq1 to a sage expression that can be used by the sage solver ? geir --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Infinite sum
Hi, I am a newbie in sage and i want to compute an infinite sum with parameter m, like sum(1/(k+m)^3) k=1 to infinity. Can you please help me? thanks --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: saving as C code?
On Fri, 29 Aug 2008, Martin Albrecht wrote:
>
> On Friday 29 August 2008, Jason Grout wrote:
>> Martin Albrecht wrote:
For various objects and various software systems (like mathematica,
magma, maxima, etc.), we have a _mathematica_init_, _magma_init_, etc,
which convert an expression into syntax for the target system. A lot of
these are defined in calculus.py for converting symbolic expressions to
syntax for other systems. I don't think we have an "interface" to C
code; can anyone think of a reason why we shouldn't? (or do we already
have one?)
>>>
>>> One difference is that it is pretty clear what Magma can and cannot do +
>>> it can do a lot of mathematics. What would be the capabilities of C? C,
>>> stdlib, pari/NTL/BLAS/libSingular?
>>
>> I'd say that the _c_init_ should just be plain standard C (i.e., it
>> should compile with just gcc). This means that lots of functionality
>> won't be able to be translated (for example, most stuff over fields or
>> groups), but it would be able to translate generic symbolic expressions,
>> like originally asked.
>
> isn't fast float doing something very similar, i.e. building up stdlib C tress
> for evaluation?
Yes, it is doing a lot of the work for you.
>> We could have _c_NTL_init_ or _c_blas_init_, etc., for variants if
>> people want. Another thought is to pass options to the systems, like
>> _c_init_('blas','NTL','singular').
>
> That looks like an infinite amount of work compared to very little benefit.
> Anybody interested in writing code for these libraries, can look at our
> sources to see how we link into them. I doubt automatic code generation would
> be of much use here.
I have thought some about automatic code generation from fast_float
objects using a pluggable language/type. Then anything that can produce a
fast_float can produce code. Still haven't had time to implement much
along those lines though.
- Robert
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[sage-support] Re: Inert Integrals and Derivatives?
On Fri, 29 Aug 2008, Jason Grout wrote:
>
> Jason Merrill wrote:
>> On Aug 29, 3:07 am, Burcin Erocal <[EMAIL PROTECTED]> wrote:
>>> On Thu, 28 Aug 2008 15:28:03 -0400
>>>
>>>
>>>
>>> Tim Lahey <[EMAIL PROTECTED]> wrote:
Hi,
Maple has a really useful feature of inert integrals
and derivatives. Basically, the integrals and derivatives
show up in the equations, but aren't evaluated until
a command to evaluate them is explicitly given. So,
you can delay the evaluation until after you've processed
the expression to the point where it can be evaluated.
This feature comes in very handy during complicated
derivations because you can see which terms are integrals
or derivatives and manipulate them along side
non-integrals/derivatives.
Is there a way to do this in Sage?
>>> This is not supported in Sage at the moment, but it is definitely
>>> planned. It should be fairly simple to implement this using the new
>>> symbolic function interface from ginac, which allows one to specify
>>> custom simplify/automatic evaluation functions.
>>>
>>> I am not familiar with the maple syntax. Can you give some examples of
>>> how to use these features so I can play with them without having to dig
>>> through documentation?
>>
>> The Mathematica syntax is Hold[Integral[x,{x,0,1}]]. This remains
>> unevaluated until it is wrapped with an Evaluate[]. The nice thing
>> about this syntax is that it works for any kind of expression (not
>> just integrals).
>
> So maybe we could have something like a FormalExpression class which
> does the same thing (has an argument that it doesn't evaluate).
Not sure how one would do this in Python though... (Maybe via preparsing
somehow, it would still be pretty hard...)
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[sage-support] Re: failed to download cddlib-094b.p1
On Aug 29, 7:33 am, Thierry Dumont <[EMAIL PROTECTED]> wrote: > Trying to install polymake in sage 3.1, I got the message: > Hi Thierry, this is a known issue and I have a fixed spkg-install that should once and for all resolve the issue. We are tracking this at #3640 and I need to put up a spkg and get it reviewed since I have been sitting on this for a while. Sorry that this is taking so long :( > ** > * Unable to download cddlib-094b.p1 > * Please seehttp://www.sagemath.org//packagesfor a list of valid > * packages or check the package name. > ** > sage: Failed to download package cddlib-094b.p1 fromhttp://www.sagemath.org/ > > yours > t.d. Cheers, Michael > tdumont.vcf > < 1KViewDownload > > smime.p7s > 5KViewDownload --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: saving as C code?
Martin Albrecht wrote:
> On Friday 29 August 2008, Jason Grout wrote:
>> Martin Albrecht wrote:
>
>> We could have _c_NTL_init_ or _c_blas_init_, etc., for variants if
>> people want. Another thought is to pass options to the systems, like
>> _c_init_('blas','NTL','singular').
>
> That looks like an infinite amount of work compared to very little benefit.
> Anybody interested in writing code for these libraries, can look at our
> sources to see how we link into them. I doubt automatic code generation would
> be of much use here.
I agree. I certainly am not volunteering to do that sort of thing; just
pointing out that if we really wanted to, we could probably generate
code that would use various libraries to give C more capabilities.
Jason
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[sage-support] Re: [GAP Forum] GAP console frozen
On Fri, Aug 29, 2008 at 8:53 AM, David Joyner <[EMAIL PROTECTED]> wrote:
>
> Let me get this straight. Please correct me if I am wrong.
>
> You sarted GAP within Sage (using sage -gap?) and then
> started a long computation, whcih caused you to run out of memory.
> Then GAP and Sage froze, so you rebooted and restarted Sage.
> (Since you rebooted, I guess you are using windows?)
> Dis Sage freeze on restart? Or was the VMware program itself frozen?
> (I don't use windows, so can't help you, but I think this information will
> be helpful to whoever does.)
>
If you are using vmware you may want to greatly increase
the amount of RAM available to the virtual machine. You
can do that by editing (with notepad) the .vmx file in the virtual
machine folder under windows.
> On Fri, Aug 29, 2008 at 10:31 AM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
>> My GAP console seems to be frozen.
>>
>> I received the following error:
>> exceeded the permitted memory ('-o' command line option at
>> B!.heads := gens.heads;
>> called from
>> BasisVectors(B) called from...
>> Entering break read-eval-print loop...
>> you can 'quit' to quit to outer loop, or
>> you can 'return to continue
>> brk>
>>
>> and I typed 'return' to see if perhaps with more time, I would get a result.
>> I was checking if an element was in an ideal. For those who read my
>> previous posting about "element in ideal (more specific)", I changed
>> Integers to Rationals, and was trying "gap>R4 in I;" This is the command
>> that led to the error above.
>> After leaving the program running overnight, it seems to be frozen. I can't
>> Cntl C to quit, or Cntrl D to exit to the SAGE console, I can't do
>> anything I closed the program, restarted the computer, and reopened the
>> program with no change. Can anyone help?
>> -Becky
>>
>>
>> Click to find information on your credit score and your credit report.
>> http://thirdpartyoffers.juno.com/TGL2131/fc/Ioyw6iifRxYPCB3t2fuc3AfAOjqmgjQDkKVG6xW0OOA4hyC2qDba57/
>>
>> ___
>> Forum mailing list
>> [EMAIL PROTECTED]
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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[sage-support] Re: [GAP Forum] GAP console frozen
Let me get this straight. Please correct me if I am wrong.
You sarted GAP within Sage (using sage -gap?) and then
started a long computation, whcih caused you to run out of memory.
Then GAP and Sage froze, so you rebooted and restarted Sage.
(Since you rebooted, I guess you are using windows?)
Dis Sage freeze on restart? Or was the VMware program itself frozen?
(I don't use windows, so can't help you, but I think this information will
be helpful to whoever does.)
On Fri, Aug 29, 2008 at 10:31 AM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
> My GAP console seems to be frozen.
>
> I received the following error:
> exceeded the permitted memory ('-o' command line option at
> B!.heads := gens.heads;
> called from
> BasisVectors(B) called from...
> Entering break read-eval-print loop...
> you can 'quit' to quit to outer loop, or
> you can 'return to continue
> brk>
>
> and I typed 'return' to see if perhaps with more time, I would get a result.
> I was checking if an element was in an ideal. For those who read my previous
> posting about "element in ideal (more specific)", I changed Integers to
> Rationals, and was trying "gap>R4 in I;" This is the command that led to the
> error above.
> After leaving the program running overnight, it seems to be frozen. I can't
> Cntl C to quit, or Cntrl D to exit to the SAGE console, I can't do
> anything I closed the program, restarted the computer, and reopened the
> program with no change. Can anyone help?
> -Becky
>
>
> Click to find information on your credit score and your credit report.
> http://thirdpartyoffers.juno.com/TGL2131/fc/Ioyw6iifRxYPCB3t2fuc3AfAOjqmgjQDkKVG6xW0OOA4hyC2qDba57/
>
> ___
> Forum mailing list
> [EMAIL PROTECTED]
> http://mail.gap-system.org/mailman/listinfo/forum
>
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[sage-support] Re: saving as C code?
On Friday 29 August 2008, Jason Grout wrote:
> Martin Albrecht wrote:
> >> For various objects and various software systems (like mathematica,
> >> magma, maxima, etc.), we have a _mathematica_init_, _magma_init_, etc,
> >> which convert an expression into syntax for the target system. A lot of
> >> these are defined in calculus.py for converting symbolic expressions to
> >> syntax for other systems. I don't think we have an "interface" to C
> >> code; can anyone think of a reason why we shouldn't? (or do we already
> >> have one?)
> >
> > One difference is that it is pretty clear what Magma can and cannot do +
> > it can do a lot of mathematics. What would be the capabilities of C? C,
> > stdlib, pari/NTL/BLAS/libSingular?
>
> I'd say that the _c_init_ should just be plain standard C (i.e., it
> should compile with just gcc). This means that lots of functionality
> won't be able to be translated (for example, most stuff over fields or
> groups), but it would be able to translate generic symbolic expressions,
> like originally asked.
isn't fast float doing something very similar, i.e. building up stdlib C tress
for evaluation?
> We could have _c_NTL_init_ or _c_blas_init_, etc., for variants if
> people want. Another thought is to pass options to the systems, like
> _c_init_('blas','NTL','singular').
That looks like an infinite amount of work compared to very little benefit.
Anybody interested in writing code for these libraries, can look at our
sources to see how we link into them. I doubt automatic code generation would
be of much use here.
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
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[sage-support] Re: Inert Integrals and Derivatives?
Jason Merrill wrote:
> On Aug 29, 3:07 am, Burcin Erocal <[EMAIL PROTECTED]> wrote:
>> On Thu, 28 Aug 2008 15:28:03 -0400
>>
>>
>>
>> Tim Lahey <[EMAIL PROTECTED]> wrote:
>>> Hi,
>>> Maple has a really useful feature of inert integrals
>>> and derivatives. Basically, the integrals and derivatives
>>> show up in the equations, but aren't evaluated until
>>> a command to evaluate them is explicitly given. So,
>>> you can delay the evaluation until after you've processed
>>> the expression to the point where it can be evaluated.
>>> This feature comes in very handy during complicated
>>> derivations because you can see which terms are integrals
>>> or derivatives and manipulate them along side
>>> non-integrals/derivatives.
>>> Is there a way to do this in Sage?
>> This is not supported in Sage at the moment, but it is definitely
>> planned. It should be fairly simple to implement this using the new
>> symbolic function interface from ginac, which allows one to specify
>> custom simplify/automatic evaluation functions.
>>
>> I am not familiar with the maple syntax. Can you give some examples of
>> how to use these features so I can play with them without having to dig
>> through documentation?
>
> The Mathematica syntax is Hold[Integral[x,{x,0,1}]]. This remains
> unevaluated until it is wrapped with an Evaluate[]. The nice thing
> about this syntax is that it works for any kind of expression (not
> just integrals).
So maybe we could have something like a FormalExpression class which
does the same thing (has an argument that it doesn't evaluate).
Jason
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[sage-support] Re: saving as C code?
Martin Albrecht wrote:
>> For various objects and various software systems (like mathematica,
>> magma, maxima, etc.), we have a _mathematica_init_, _magma_init_, etc,
>> which convert an expression into syntax for the target system. A lot of
>> these are defined in calculus.py for converting symbolic expressions to
>> syntax for other systems. I don't think we have an "interface" to C
>> code; can anyone think of a reason why we shouldn't? (or do we already
>> have one?)
>
> One difference is that it is pretty clear what Magma can and cannot do + it
> can do a lot of mathematics. What would be the capabilities of C? C, stdlib,
> pari/NTL/BLAS/libSingular?
I'd say that the _c_init_ should just be plain standard C (i.e., it
should compile with just gcc). This means that lots of functionality
won't be able to be translated (for example, most stuff over fields or
groups), but it would be able to translate generic symbolic expressions,
like originally asked.
We could have _c_NTL_init_ or _c_blas_init_, etc., for variants if
people want. Another thought is to pass options to the systems, like
_c_init_('blas','NTL','singular').
Jason
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[sage-support] Re: solve() fails to produce a solution
Jason Grout wrote:
> William Stein wrote:
>> On Thu, Aug 28, 2008 at 11:06 PM, Robert Dodier <[EMAIL PROTECTED]> wrote:
>>> On 8/28/08, William Stein <[EMAIL PROTECTED]> wrote:
>>>
Sage uses Maxima's solve command, and Maxima's solve
command is pretty wimpy, and we (Sage developers) intend
to write our own new solve command that can deal with
more general equations.
>>> Go nuts, man. Hope you can write it in Python since that will
>>> make it easier to port to Lisp.
>>>
>> We might start with Sympy's solve command, which is in Python,
>> and which also can't solve the above equations:
>>
>> sage: from sympy import *
>> sage: x,y = var('x,y')
>> sage: sympy.solve([x==0, 1-exp(y)==0],[x,y])
>> {}
>> sage: solve([y*sin(x)==0, cos(x)==0],x,y)
>> {}
>>
>
> For reference, it seems that axiom can't solve these either (at least
> with my naive attempts):
>
> (9) -> solve([x=0,1-exp(y)=0],[x,y])
> (9) ->
> (9) [[]]
>Type: List List Equation Expression
> Integer
> (10) -> solve([y*sin(x)=0,cos(x)=0],[x,y])
> (10) ->
> (10) [[]]
>Type: List List Equation Expression
> Integer
>
>
> while mathematica gives solutions:
>
> In[1]:= Solve[{x == 0, 1 - Exp[y] == 0}, {x, y}]
>
> Solve::ifun: Inverse functions are being used by Solve, so some
> solutions may
> not be found; use Reduce for complete solution information.
>
> Out[1]= {{x -> 0, y -> 0}}
>
> In[2]:= Solve[{y*Sin[x] == 0, Cos[x] == 0}, {x, y}]
>
> Solve::ifun: Inverse functions are being used by Solve, so some
> solutions may
> not be found; use Reduce for complete solution information.
>
> -Pi Pi
> Out[2]= {{y -> 0, x -> ---}, {y -> 0, x -> --}}
> 2 2
In fact, Mathematica can give general solutions:
In[3]:= Reduce[{x == 0, 1 - Exp[y] == 0}, {x, y}]
Out[3]= C[1] \[Element] Integers && x == 0 && y == (2 I) Pi C[1]
In[4]:= Reduce[{y*Sin[x] == 0, Cos[x] == 0}, {x, y}]
Out[4]= C[1] \[Element] Integers &&
-Pi Pi
>(x == --- + 2 Pi C[1] || x == -- + 2 Pi C[1]) && y == 0
2 2
(translation: the first is x==0 and y==(2*I)*C*Pi, where C is an
integer, etc.)
Jason
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[sage-support] Re: solve() fails to produce a solution
William Stein wrote:
> On Thu, Aug 28, 2008 at 11:06 PM, Robert Dodier <[EMAIL PROTECTED]> wrote:
>> On 8/28/08, William Stein <[EMAIL PROTECTED]> wrote:
>>
>>> Sage uses Maxima's solve command, and Maxima's solve
>>> command is pretty wimpy, and we (Sage developers) intend
>>> to write our own new solve command that can deal with
>>> more general equations.
>> Go nuts, man. Hope you can write it in Python since that will
>> make it easier to port to Lisp.
>>
>
> We might start with Sympy's solve command, which is in Python,
> and which also can't solve the above equations:
>
> sage: from sympy import *
> sage: x,y = var('x,y')
> sage: sympy.solve([x==0, 1-exp(y)==0],[x,y])
> {}
> sage: solve([y*sin(x)==0, cos(x)==0],x,y)
> {}
>
For reference, it seems that axiom can't solve these either (at least
with my naive attempts):
(9) -> solve([x=0,1-exp(y)=0],[x,y])
(9) ->
(9) [[]]
Type: List List Equation Expression
Integer
(10) -> solve([y*sin(x)=0,cos(x)=0],[x,y])
(10) ->
(10) [[]]
Type: List List Equation Expression
Integer
while mathematica gives solutions:
In[1]:= Solve[{x == 0, 1 - Exp[y] == 0}, {x, y}]
Solve::ifun: Inverse functions are being used by Solve, so some
solutions may
not be found; use Reduce for complete solution information.
Out[1]= {{x -> 0, y -> 0}}
In[2]:= Solve[{y*Sin[x] == 0, Cos[x] == 0}, {x, y}]
Solve::ifun: Inverse functions are being used by Solve, so some
solutions may
not be found; use Reduce for complete solution information.
-Pi Pi
Out[2]= {{y -> 0, x -> ---}, {y -> 0, x -> --}}
2 2
Jason
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[sage-support] failed to download cddlib-094b.p1
Trying to install polymake in sage 3.1, I got the message: ** * Unable to download cddlib-094b.p1 * Please see http://www.sagemath.org//packages for a list of valid * packages or check the package name. ** sage: Failed to download package cddlib-094b.p1 from http://www.sagemath.org/ yours t.d. begin:vcard fn:Thierry Dumont n:Dumont;Thierry org;quoted-printable:CNRS - Universit=C3=A9 Lyon 1. / Villeurbanne France.;Institut Camille Jordan adr:;;43 Bd du 11 Novembre;Villeurbanne Cedex;F;69621;France email;internet:[EMAIL PROTECTED] title;quoted-printable:Ing=C3=A9nieur de Recherche/Research Ingeneer tel;work:(33) 4 72 44 85 23 x-mozilla-html:FALSE url:http://math.univ-lyon1.fr/~tdumont version:2.1 end:vcard smime.p7s Description: S/MIME Cryptographic Signature
[sage-support] Re: Inert Integrals and Derivatives?
On Aug 29, 2008, at 8:17 AM, David Joyner wrote: I like this! (I assume you meant integral, not Integral?) But could you implement it in such a way that sage: A = integral(x,x,0,1, evaluate=False) sage: eval(A) 1/2 sage: latex(A) \int_0^1 x\, dx +1 I like this approach and is relatively consistent with Maple's because it still allows you to evaluate the integral in a straightforward manner. It also helps indicate to the user that "evaluate" is just a property of the integral and makes it easy to see that eval will change that state. Whether this is done for more than differentiation and integration, I'm not that concerned about, but it can be implemented in a similar manner if we have a state variable. Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo smime.p7s Description: S/MIME cryptographic signature
[sage-support] Re: Hall-Senior number vs. Small Groups library
Hi David! On Aug 29, 2:11 pm, "David Joyner" <[EMAIL PROTECTED]> wrote: > I doubt it - I've never even heard of the Hall-Senior number. See: Hall, Marshall, Jr.; Senior, James K. The groups of order 2n (n ≤ 6). The Macmillan Co., New York; Collier-Macmillan, Ltd., London 1964 225 pp. > How hard would it be to write one? Meanwhile i realize how stupid my question is. I didn't realize that they classified the 2-groups only up to order 64 -- i thought that the Hall-Senior number were also defined for larger groups. Sorry for bothering you. Cheers Simon --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Find_root bug
> This is actually a problem with how the symbolic functions/expressions > are handled. The find_root function cannot recognize that 1/z is a > function. This works: > > sage: z = 1/tan > sage: f = lambda x: z(x) > sage: find_root(f,1, 2) > 1.5707963267948968 > > and this: > > sage: find_root(z(x),1, 2) > 1.5707963267948968 > > I am working on making arithmetic with function objects more intuitive, > and free of these kinds of problems as a part of the effort to use > ginac as a basis for symbolics. This might result in some changes to > the user interface for such things, but hopefully there will be less > problems of this kind. > Thanks for the workaround idea. Actually, I was just reporting it as a ticket, which hopefully will be resolved (as you say) with ginac conversion. I am very excited about more robust symbolic behavior, because pedagogically one likes to reach students where they are at - and most freshmen nonmajors are definitely only at the math-as-symbolic- manipulation stage, yet should be able to use Sage as intuitively as possible. Thanks for your (and others'!) work on this! - kcrisman --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Inert Integrals and Derivatives?
On Aug 29, 3:07 am, Burcin Erocal <[EMAIL PROTECTED]> wrote:
> On Thu, 28 Aug 2008 15:28:03 -0400
>
>
>
> Tim Lahey <[EMAIL PROTECTED]> wrote:
> > Hi,
>
> > Maple has a really useful feature of inert integrals
> > and derivatives. Basically, the integrals and derivatives
> > show up in the equations, but aren't evaluated until
> > a command to evaluate them is explicitly given. So,
> > you can delay the evaluation until after you've processed
> > the expression to the point where it can be evaluated.
>
> > This feature comes in very handy during complicated
> > derivations because you can see which terms are integrals
> > or derivatives and manipulate them along side
> > non-integrals/derivatives.
>
> > Is there a way to do this in Sage?
>
> This is not supported in Sage at the moment, but it is definitely
> planned. It should be fairly simple to implement this using the new
> symbolic function interface from ginac, which allows one to specify
> custom simplify/automatic evaluation functions.
>
> I am not familiar with the maple syntax. Can you give some examples of
> how to use these features so I can play with them without having to dig
> through documentation?
The Mathematica syntax is Hold[Integral[x,{x,0,1}]]. This remains
unevaluated until it is wrapped with an Evaluate[]. The nice thing
about this syntax is that it works for any kind of expression (not
just integrals).
JM
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[sage-support] Re: Inert Integrals and Derivatives?
On Fri, Aug 29, 2008 at 8:01 AM, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > ... > I like the concept, though I'm also -1 on the capital/lowercase > syntax. Perhaps integral could take an extra argument, so one would have > > sage: integral(x,x,0,1) > 1/2 > sage: Integral(x,x,0,1, evaluate=False) > \int_0^1 x\, dx I like this! (I assume you meant integral, not Integral?) But could you implement it in such a way that sage: A = integral(x,x,0,1, evaluate=False) sage: eval(A) 1/2 sage: latex(A) \int_0^1 x\, dx works? > > Or maybe a new function formal_integral? > > - Robert > > > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Hall-Senior number vs. Small Groups library
On Fri, Aug 29, 2008 at 7:56 AM, Simon King <[EMAIL PROTECTED]> wrote: > > Dear all, > > finite 2-groups of appropriate size can be identified either by their > number in the Small Groups library or by their Hall-Senior number. > > The Small Groups library is an optional part of Sage (via gap). But is > there also some function available in Sage that translates between > Hall-Senior and Small Groups? I doubt it - I've never even heard of the Hall-Senior number. How hard would it be to write one? > > Cheers > Simon > > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Inert Integrals and Derivatives?
On Aug 29, 2008, at 4:53 AM, Tim Lahey wrote: > > On Aug 29, 2008, at 6:24 AM, William Stein wrote: > >> >> On Fri, Aug 29, 2008 at 2:46 AM, David Joyner <[EMAIL PROTECTED]> >> wrote: >>> >>> On Fri, Aug 29, 2008 at 3:07 AM, Burcin Erocal >>> <[EMAIL PROTECTED]> wrote: This is not supported in Sage at the moment, but it is definitely planned. It should be fairly simple to implement this using the new symbolic function interface from ginac, which allows one to specify custom simplify/automatic evaluation functions. I am not familiar with the maple syntax. Can you give some examples of how to use these features so I can play with them without having to dig through documentation? >>> >>> I agree this would be a very useful feature. Basically, something >>> like >>> >>> (1) >>> sage: integral(x,x,0,1) >>> 1/2 >>> sage: Integral(x,x,0,1) >>> \int_0^1 x\, dx >>> >>> (not the upper case I), or maybe >> >> I'm not enthuisiastic about using >> Foo and foo to denote different commands. If we have >> two cases of the exact same word in Sage, then they should >> be aliased. Isn't (2) below identical to (1) above? >> Or did you not mean to distinguish case above? >> > > It's what Maple does. In Maple, Int() is used to indicate an > inert integral, while int() is used to indicate an integral which > is evaluated at that time. I like the concept, though I'm also -1 on the capital/lowercase syntax. Perhaps integral could take an extra argument, so one would have sage: integral(x,x,0,1) 1/2 sage: Integral(x,x,0,1, evaluate=False) \int_0^1 x\, dx Or maybe a new function formal_integral? - Robert --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Hall-Senior number vs. Small Groups library
Dear all, finite 2-groups of appropriate size can be identified either by their number in the Small Groups library or by their Hall-Senior number. The Small Groups library is an optional part of Sage (via gap). But is there also some function available in Sage that translates between Hall-Senior and Small Groups? Cheers Simon --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Inert Integrals and Derivatives?
On Aug 29, 2008, at 6:24 AM, William Stein wrote: On Fri, Aug 29, 2008 at 2:46 AM, David Joyner <[EMAIL PROTECTED]> wrote: On Fri, Aug 29, 2008 at 3:07 AM, Burcin Erocal <[EMAIL PROTECTED]> wrote: This is not supported in Sage at the moment, but it is definitely planned. It should be fairly simple to implement this using the new symbolic function interface from ginac, which allows one to specify custom simplify/automatic evaluation functions. I am not familiar with the maple syntax. Can you give some examples of how to use these features so I can play with them without having to dig through documentation? I agree this would be a very useful feature. Basically, something like (1) sage: integral(x,x,0,1) 1/2 sage: Integral(x,x,0,1) \int_0^1 x\, dx (not the upper case I), or maybe I'm not enthuisiastic about using Foo and foo to denote different commands. If we have two cases of the exact same word in Sage, then they should be aliased. Isn't (2) below identical to (1) above? Or did you not mean to distinguish case above? It's what Maple does. In Maple, Int() is used to indicate an inert integral, while int() is used to indicate an integral which is evaluated at that time. (2) sage: A = Integral(x,x,0,1) sage. latex(A) \int_0^1 x\, dx sage: A Integral(x,x,0,1) I don't really care which syntax is used, as long as there is a consistent way of doing this. Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo smime.p7s Description: S/MIME cryptographic signature
[sage-support] Re: Inert Integrals and Derivatives?
On Fri, Aug 29, 2008 at 6:24 AM, William Stein <[EMAIL PROTECTED]> wrote: > > On Fri, Aug 29, 2008 at 2:46 AM, David Joyner <[EMAIL PROTECTED]> wrote: >> >> On Fri, Aug 29, 2008 at 3:07 AM, Burcin Erocal <[EMAIL PROTECTED]> wrote: >>> >>> On Thu, 28 Aug 2008 15:28:03 -0400 >>> Tim Lahey <[EMAIL PROTECTED]> wrote: >>> Hi, Maple has a really useful feature of inert integrals and derivatives. Basically, the integrals and derivatives show up in the equations, but aren't evaluated until a command to evaluate them is explicitly given. So, you can delay the evaluation until after you've processed the expression to the point where it can be evaluated. This feature comes in very handy during complicated derivations because you can see which terms are integrals or derivatives and manipulate them along side non-integrals/derivatives. Is there a way to do this in Sage? >>> >>> This is not supported in Sage at the moment, but it is definitely >>> planned. It should be fairly simple to implement this using the new >>> symbolic function interface from ginac, which allows one to specify >>> custom simplify/automatic evaluation functions. >>> >>> I am not familiar with the maple syntax. Can you give some examples of >>> how to use these features so I can play with them without having to dig >>> through documentation? >> >> I agree this would be a very useful feature. Basically, something like >> >> (1) >> sage: integral(x,x,0,1) >> 1/2 >> sage: Integral(x,x,0,1) >> \int_0^1 x\, dx >> >> (not the upper case I), or maybe > > I'm not enthuisiastic about using > Foo and foo to denote different commands. If we have Okay. I just tried to answer Burcin's question of what Maple does, using Sage as an analogy. > two cases of the exact same word in Sage, then they should > be aliased. Isn't (2) below identical to (1) above? > Or did you not mean to distinguish case above? I think you are right. I wasn't thinking that at the time but now I can't see a way to implement (1) and (2) differently. > >> >> (2) >> sage: A = Integral(x,x,0,1) >> sage. latex(A) >> \int_0^1 x\, dx >> sage: A >> Integral(x,x,0,1) >> >>> >>> >>> Thanks. >>> >>> Burcin >>> >>> > >>> >> >> > >> > > > > -- > William Stein > Associate Professor of Mathematics > University of Washington > http://wstein.org > > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: using latex packages
Hi William, That sounds great to me. As long as it'll allow me to load the ngerman package in the notebook version of Sage, that'll do. Thanks! Maike P.S. And thanks Stan for the hint! I didn't know sagetex. As I'm using the notebook to combine latex typesetting with the interact functionality of Sage, it's probably not the best idea. But it might be helpful for future projects! --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: saving as C code?
> For various objects and various software systems (like mathematica, > magma, maxima, etc.), we have a _mathematica_init_, _magma_init_, etc, > which convert an expression into syntax for the target system. A lot of > these are defined in calculus.py for converting symbolic expressions to > syntax for other systems. I don't think we have an "interface" to C > code; can anyone think of a reason why we shouldn't? (or do we already > have one?) One difference is that it is pretty clear what Magma can and cannot do + it can do a lot of mathematics. What would be the capabilities of C? C, stdlib, pari/NTL/BLAS/libSingular? Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Inert Integrals and Derivatives?
On Fri, Aug 29, 2008 at 2:46 AM, David Joyner <[EMAIL PROTECTED]> wrote: > > On Fri, Aug 29, 2008 at 3:07 AM, Burcin Erocal <[EMAIL PROTECTED]> wrote: >> >> On Thu, 28 Aug 2008 15:28:03 -0400 >> Tim Lahey <[EMAIL PROTECTED]> wrote: >> >>> Hi, >>> >>> Maple has a really useful feature of inert integrals >>> and derivatives. Basically, the integrals and derivatives >>> show up in the equations, but aren't evaluated until >>> a command to evaluate them is explicitly given. So, >>> you can delay the evaluation until after you've processed >>> the expression to the point where it can be evaluated. >>> >>> This feature comes in very handy during complicated >>> derivations because you can see which terms are integrals >>> or derivatives and manipulate them along side >>> non-integrals/derivatives. >>> >>> Is there a way to do this in Sage? >> >> This is not supported in Sage at the moment, but it is definitely >> planned. It should be fairly simple to implement this using the new >> symbolic function interface from ginac, which allows one to specify >> custom simplify/automatic evaluation functions. >> >> I am not familiar with the maple syntax. Can you give some examples of >> how to use these features so I can play with them without having to dig >> through documentation? > > I agree this would be a very useful feature. Basically, something like > > (1) > sage: integral(x,x,0,1) > 1/2 > sage: Integral(x,x,0,1) > \int_0^1 x\, dx > > (not the upper case I), or maybe I'm not enthuisiastic about using Foo and foo to denote different commands. If we have two cases of the exact same word in Sage, then they should be aliased. Isn't (2) below identical to (1) above? Or did you not mean to distinguish case above? > > (2) > sage: A = Integral(x,x,0,1) > sage. latex(A) > \int_0^1 x\, dx > sage: A > Integral(x,x,0,1) > >> >> >> Thanks. >> >> Burcin >> >> > >> > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: using latex packages
On Fri, Aug 29, 2008 at 1:22 AM, Maike <[EMAIL PROTECTED]> wrote:
>
> Hello again,
>
> is there any way to use latex packages within sage? I'd like to write
> a german text, and that will be a pain if
>
> %latex
> \usepackage{ngerman}
>
> doen't work. Maybe I first have to install the package somewhere??
There is no current supported way to do the above.
It shouldn't be hard for somebody to add though. How complicated
of a pre-amble do you want? Would something like the following
be acceptable to you?
sage: latex.set_preamble('\\usepackage{ngerman} [etc]')
then henceforth %latex would always include
the \usepackage{ngerman} code before typesetting
a cell. The above would be extremely easy to implement.
-- William
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[sage-support] Re: Inert Integrals and Derivatives?
On Fri, Aug 29, 2008 at 3:07 AM, Burcin Erocal <[EMAIL PROTECTED]> wrote: > > On Thu, 28 Aug 2008 15:28:03 -0400 > Tim Lahey <[EMAIL PROTECTED]> wrote: > >> Hi, >> >> Maple has a really useful feature of inert integrals >> and derivatives. Basically, the integrals and derivatives >> show up in the equations, but aren't evaluated until >> a command to evaluate them is explicitly given. So, >> you can delay the evaluation until after you've processed >> the expression to the point where it can be evaluated. >> >> This feature comes in very handy during complicated >> derivations because you can see which terms are integrals >> or derivatives and manipulate them along side >> non-integrals/derivatives. >> >> Is there a way to do this in Sage? > > This is not supported in Sage at the moment, but it is definitely > planned. It should be fairly simple to implement this using the new > symbolic function interface from ginac, which allows one to specify > custom simplify/automatic evaluation functions. > > I am not familiar with the maple syntax. Can you give some examples of > how to use these features so I can play with them without having to dig > through documentation? I agree this would be a very useful feature. Basically, something like (1) sage: integral(x,x,0,1) 1/2 sage: Integral(x,x,0,1) \int_0^1 x\, dx (not the upper case I), or maybe (2) sage: A = Integral(x,x,0,1) sage. latex(A) \int_0^1 x\, dx sage: A Integral(x,x,0,1) > > > Thanks. > > Burcin > > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: using latex packages
Hi Maike,
Have you heard of sagetex? This allows sage computations as part of the
compilation of a latex file. From my experience, this is not very good
for interactive work because all the code within the latex file is
compiled every time you run sage over your document, but it's great for
getting a nicely typeset document that does all the sage calculations
and plots you want.
Check out: http://www.ctan.org/tex-archive/macros/latex/contrib/sagetex/
I believe that this would allow you to use any latex functionality you like.
Stan
Maike wrote:
> Hello again,
>
> is there any way to use latex packages within sage? I'd like to write
> a german text, and that will be a pain if
>
> %latex
> \usepackage{ngerman}
>
> doen't work. Maybe I first have to install the package somewhere??
>
>
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[sage-support] using latex packages
Hello again,
is there any way to use latex packages within sage? I'd like to write
a german text, and that will be a pain if
%latex
\usepackage{ngerman}
doen't work. Maybe I first have to install the package somewhere??
Maike
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-~--~~~~--~~--~--~---
[sage-support] Re: Find_root bug
On Thu, 28 Aug 2008 13:36:53 -0700 (PDT) kcrisman <[EMAIL PROTECTED]> wrote: > > The reciprocal of tangent is not a constant function, but Sage says > otherwise. This is now http://trac.sagemath.org/sage_trac/ticket/3980 > . > > (Incidentally, using z(x)=tan(x) also doesn't work, as it yields a > NotImplementedError (whose message could be better) for 1/z; > presumably the bug below would occur even if it were implemented, > though.) > > - kcrisman > > sage: z=tan > sage: z > tan > sage: 1/z > 1/tan > sage: find_root(1/z,1,2) > --- > RuntimeError Traceback (most recent call > last) > RuntimeError: no zero in the interval, since constant expression is > not 0. This is actually a problem with how the symbolic functions/expressions are handled. The find_root function cannot recognize that 1/z is a function. This works: sage: z = 1/tan sage: f = lambda x: z(x) sage: find_root(f,1, 2) 1.5707963267948968 and this: sage: find_root(z(x),1, 2) 1.5707963267948968 I am working on making arithmetic with function objects more intuitive, and free of these kinds of problems as a part of the effort to use ginac as a basis for symbolics. This might result in some changes to the user interface for such things, but hopefully there will be less problems of this kind. Cheers, Burcin --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Inert Integrals and Derivatives?
On Thu, 28 Aug 2008 15:28:03 -0400 Tim Lahey <[EMAIL PROTECTED]> wrote: > Hi, > > Maple has a really useful feature of inert integrals > and derivatives. Basically, the integrals and derivatives > show up in the equations, but aren't evaluated until > a command to evaluate them is explicitly given. So, > you can delay the evaluation until after you've processed > the expression to the point where it can be evaluated. > > This feature comes in very handy during complicated > derivations because you can see which terms are integrals > or derivatives and manipulate them along side > non-integrals/derivatives. > > Is there a way to do this in Sage? This is not supported in Sage at the moment, but it is definitely planned. It should be fairly simple to implement this using the new symbolic function interface from ginac, which allows one to specify custom simplify/automatic evaluation functions. I am not familiar with the maple syntax. Can you give some examples of how to use these features so I can play with them without having to dig through documentation? Thanks. Burcin --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
