[sage-combinat-devel] Re: [sage-devel] Symmetric polynomial in terms of elementary symmetric polynomials
On Fri, Dec 09, 2011 at 10:19:22AM +0100, Jeroen Demeyer wrote: I am asking for: sage: e = SymmetricFunctions(QQ).e() sage: R.e1,e2,e3 = PolynomialRing(QQ) sage: e[3,1,1].express_as_polynomial([1,e1,e2,e3]) e1^2*e3 Ah, you want the result expressed as a plain polynomial. Then it's just a one-liner change of representation: sage: e = SymmetricFunctions(QQ).e() sage: x = e.an_element() sage: x 1/2*e[] + 3*e[1, 1, 1] + 2*e[2, 1, 1] sage: sum( c*prod( Re[i-1] if i=3 else R.zero for i in part ) for (part,c) in x ) 3*e1^3 + 2*e1^2*e2 + 1/2 However I agree this one-liner deserves to be wrapped for the user, especially since this one-liner won't handle properly corner cases (in particular x=0). So ... Free commutative algebras represented using a multiplicative basis (like this one) should have: - An algebra_morphism method - A morphism and its inverse, built using algebra_morphism, implementing the isomorphism with some plain Sage polynomial ring Any good suggestion of name? the obvious to_polynomial is ambiguous since we don't know if we want a polynomial in the x's or in the e's. - Functionalities like factor and such, implemented through the those isomorphisms Note: in MuPAD, had the algebra_morphism functionality, and we could also write expr(x) which returned x as an expression in (the analogue of) SR, and then we could just do poly(expr(x)). We also. That's probably why we had not come up with an appropriate interface for this functionality. Cheers, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
Re: [sage-combinat-devel] Re: dot2tex, combinat
Dear Bruce, On Fri, Nov 25, 2011 at 06:21:44PM -0800, Bruce Sagan wrote: I had the same problem as William, but I am even further back. I don't understand how to get sage -sh to work. I am running sage in notebook form via VirtualBox on a Windows 7 machine. Typing the command into the notebook prompt doesn't work, and I can't find a command prompt which might indicate the shell. Thanks for any help you can give. Sorry for the slow answer; I am not much of a Sage on windows user. Apparently there are instructions on Using the Sage shell in: http://www.sagemath.org/mirror/win/README.txt Please get back to us in case of trouble. Best, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
RE: [sage-combinat-devel] Re: dot2tex, combinat
I had one email exchange with Travis, but the issue is still not resolved. I will look at the web site. - Bruce From: sage-combinat-devel@googlegroups.com [sage-combinat-devel@googlegroups.com] on behalf of Anne Schilling [a...@math.ucdavis.edu] Sent: Friday, December 09, 2011 5:05 PM To: sage-combinat-devel@googlegroups.com Subject: Re: [sage-combinat-devel] Re: dot2tex, combinat On 12/9/11 1:55 PM, Nicolas M. Thiery wrote: Dear Bruce, On Fri, Nov 25, 2011 at 06:21:44PM -0800, Bruce Sagan wrote: I had the same problem as William, but I am even further back. I don't understand how to get sage -sh to work. I am running sage in notebook form via VirtualBox on a Windows 7 machine. Typing the command into the notebook prompt doesn't work, and I can't find a command prompt which might indicate the shell. Thanks for any help you can give. Sorry for the slow answer; I am not much of a Sage on windows user. Apparently there are instructions on Using the Sage shell in: http://www.sagemath.org/mirror/win/README.txt Please get back to us in case of trouble. As far as I know Travis already helped Bruce with this off-line. Cheers, Anne -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en. -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
[sage-combinat-devel] Re: base rings in SFA
Hi,
I don't know how to fix this problem at the moment. But the question
is, can you verify that the following is a bug?
The following works (although I find it weird that I have to have
the third line in this code):
sage: q = var('q')
sage: s = SFASchur(FractionField(QQ[q]))
sage: q = s.base_ring().gen()
sage: s([1]).plethysm(s([1])/(1-q))
while the same code with the Q-Schur functions gives an error:
sage: q = var('q')
sage: QS = HallLittlewoodQ(FractionField(QQ[q]),t=-1)
sage: q = QS.base_ring().gen()
sage: QS([1]).plethysm(QS([1])/(1-q))
Traceback (click to the left of this block for traceback)
...
TypeError: unsupported operand parent(s) for '*': 'Fraction Field of
Univariate Polynomial Ring in q over Rational Field' and 'Univariate
Polynomial Ring in t over Integer Ring'
-Mike
On Nov 23, 7:36 pm, Anne Schilling a...@math.ucdavis.edu wrote:
Hi Mike,
I am having some issues with the base rings using Schur's Q functions.
I am beginning to think that they may need to be made a separate basis
rather than a t=-1 specialization of the HallLittlewoodQ, but maybe
there is just too much that I am not following about how they work.
Here is my example:
Remember that HallLittlewoodQ is a symmetric function in the parameter
t
The following example seems to work as expected:
sage: q = var('q')
sage: HLQ = HallLittlewoodQ(FractionField(QQ[q]))
sage: p = SFAPower(HLQ.base_ring())
sage: p(HLQ([3,2]).plethysm(p[1]/(1-q)))
((1/120/(q^5-5*q^4+10*q^3-10*q^2+5*q-1))*t^7+(1/120/(-
q^5+5*q^4-10*q^3+1\
...
((1/5/(q-1))*t^7+(1/5/(-q+1))*t^6+(1/5/(-q+1))*t^2+(1/5/(q-1))*t)*p[5]
BUT, the next example doesn't work and I don't seem to know if it is a
bug or just really difficult for me to figure out what is going on.
It is the exact same example as above except with t=-1. I've tried
lots of variations of this example and nothing seems to give me a clue
about how to fix the ring. I've included the full error message.
sage: q = var('q')
sage: HLQ = HallLittlewoodQ(FractionField(QQ[q]), t=-1)
sage: p = SFAPower(HLQ.base_ring())
sage: p(HLQ([3,2]).plethysm(p[1]/(1-q)))
Traceback (most recent call last):
This looks like a bug and since I am not so familiar with the symmetric
function
code, I am not sure precisely what triggers the bug.
But here might be a way around it:
sage: q = var('q')
sage: HLQ = HallLittlewoodQ(FractionField(QQ[q]))
sage: p = SFAPower(HLQ.base_ring())
sage: f = p(HLQ([3,2]).plethysm(p[1]/(1-q)))
sage: sum(f.coefficient(a).subs(t=-1)*p(a) for a in f.support())
(8/15/(-q^5+5*q^4-10*q^3+10*q^2-5*q+1))*p[1, 1, 1, 1, 1] +
(-4/3/(-q^3+3*q^2-3*q+1))*p[3, 1, 1] + (-4/5/(q-1))*p[5]
Best,
Anne
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Re: [sage-combinat-devel] error with skew Schur functions
On 12/9/11 8:08 PM, Mike Zabrocki wrote: I reported the following bug on the trac server this evening: #12140: skew Schur function indexed by [[], []] causes Segmentation Fault I created a patch and attached it to the trac. Should I also put this into the sage-combinat queue? It might be a good idea to post it under Patches under review if others in the sage-combinat queue are likely to build on it. Best, Anne -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
