Re: [sage-combinat-devel] Hopf algebra methods

2012-08-02 Thread Anne Schilling
On 8/2/12 9:41 AM, Nicolas M. Thiery wrote: > On Thu, Aug 02, 2012 at 10:30:19AM +0200, Martin Rubey wrote: >> "factors" (I wouldn't look for tensor_factors in a Cartesian product) > > I like that. Other suggestions? Would it make sense to call it > `operands`, by analogy with symbolic expressions

Re: [sage-combinat-devel] Hopf algebra methods

2012-08-02 Thread Nicolas M. Thiery
On Thu, Aug 02, 2012 at 10:30:19AM +0200, Martin Rubey wrote: > "factors" (I wouldn't look for tensor_factors in a Cartesian product) I like that. Other suggestions? Would it make sense to call it `operands`, by analogy with symbolic expressions? sage: f = x+1 sage: f.operands() [x, 1

Re: [sage-combinat-devel] Hopf algebra methods

2012-08-02 Thread Martin Rubey
Anne Schilling writes: > On 8/1/12 12:23 PM, Nicolas M. Thiery wrote: >> On Fri, Jul 27, 2012 at 09:01:46PM +0200, Martin Rubey wrote: >>> Maybe f.parent()._sets is what you want? >> >> Speaking of which: we probably should expose that using some method >> foo, so that if F is the tensor/cartesi

Re: [sage-combinat-devel] Hopf algebra methods

2012-08-01 Thread Anne Schilling
On 8/1/12 12:23 PM, Nicolas M. Thiery wrote: > On Fri, Jul 27, 2012 at 09:01:46PM +0200, Martin Rubey wrote: >> Maybe f.parent()._sets is what you want? > > Speaking of which: we probably should expose that using some method > foo, so that if F is the tensor/cartesian/... product of A, B, C we > w

Re: [sage-combinat-devel] Hopf algebra methods

2012-08-01 Thread Nicolas M. Thiery
On Fri, Jul 27, 2012 at 09:01:46PM +0200, Martin Rubey wrote: > Maybe f.parent()._sets is what you want? Speaking of which: we probably should expose that using some method foo, so that if F is the tensor/cartesian/... product of A, B, C we would get: sage: F.foo() (A, B, C) Any suggesti

Re: [sage-combinat-devel] Hopf algebra methods

2012-08-01 Thread Nicolas M. Thiery
On Wed, Jul 25, 2012 at 06:39:57PM -0400, Franco Saliola wrote: > You can also define this using module_morphism on the basis elements, > as follows. > > sage: Sym = SymmetricFunctions(QQ) > sage: s = Sym.schur() > > sage: t = s.tensor_square() > sage: mu = t.module_morphism(on_basis=lambda (a,b)

Re: [sage-combinat-devel] Hopf algebra methods

2012-07-27 Thread Martin Rubey
Anne Schilling writes: > You can try > > sage: def mu(f): > : Sym = SymmetricFunctions(QQ) > : s = Sym.schur() > : coeffs = f.monomial_coefficients() > : return sum( coeffs[a]*s(a[0])*s(a[1]) for a in coeffs) > : > > sage: f = s[3].coproduct() > sage: mu(f) > 2

Re: [sage-combinat-devel] Hopf algebra methods

2012-07-25 Thread Franco Saliola
Hello, On Wed, Jul 25, 2012 at 12:24 AM, Anne Schilling wrote: > On 7/24/12 6:06 PM, Daniel Bump wrote: >> >> The symmetric function patch #5457 is a big step towards being >> able to work with the Hopf algebra of symmetric functions. > > I am glad you appreciate the new functionalities! > >> Her

Re: [sage-combinat-devel] Hopf algebra methods

2012-07-24 Thread Anne Schilling
On 7/24/12 6:06 PM, Daniel Bump wrote: > > The symmetric function patch #5457 is a big step towards being > able to work with the Hopf algebra of symmetric functions. I am glad you appreciate the new functionalities! > Here's an interesting fact. Recall that the elements of the > symmetric funct

[sage-combinat-devel] Hopf algebra methods

2012-07-24 Thread Daniel Bump
The symmetric function patch #5457 is a big step towards being able to work with the Hopf algebra of symmetric functions. Here's an interesting fact. Recall that the elements of the symmetric function Hopf algebra can be interpreted as representations of the symmetric group. For example, the Schu