Little optimizations in CombinatorialFreeModule

[nthiery]

With the attached optimizations, the following typical calculation from Andrew Matthas goes twice faster (it involves a lot of arithmetic on module elements with very few terms)::

    sage: W = SymmetricGroup(4)
    sage: W.cartan_type = lambda: CartanType("A3")
    sage: R=FractionField(PolynomialRing(ZZ,'x')); x=R.gen()
    sage: H=IwahoriHeckeAlgebraT(W,x,base_ring = R)
    sage: L=[H.one()];                   # define Jucys-Murphy elements
    sage: for k in xrange(1,4): L.append(H._q1**-1*H.algebra_generators()[k]*L[k-1]*H.algebra_generators()[k])

    sage: content=[0,1,-1,0]   # content vector for Tableau([[1,2],[3,4]])

    sage: %time prod( (L[k]-x**c)/(x**content[k]-x**c) for k in xrange(len(content)) for c in xrange(-k,k+1) if c<>content[k])
    CPU times: user 2.26 s, sys: 0.00 s, total: 2.27 s
    Wall time: 2.27 s

Was 4.5s before the patch.

The patch also involve two changes in the Iwahori Hecke Algebra code to use better primitives of CombinatorialFreeModule.

(trivial syntactical dependency upon #12484)

Depends on #12484

CC: @sagetrac-sage-combinat @jhpalmieri

Component: linear algebra

Author: Nicolas M. Thiéry

Reviewer: Florent Hivert, John Palmieri

Merged: sage-5.0.beta6

Issue created by migration from https://trac.sagemath.org/ticket/12528

[nthiery]

Dependencies: #12484

[nthiery]

comment:3

The new patch fixes a (trivial?) doctest failure in sage.algebra/steenrod_algebra/steenrod_algebra.py (John, please double check it!), and includes further review improvements from Florent.

All test pass. I let Florent put the final positive review once John will have given his green light.

[nthiery]

Reviewer: Florent Hivert, John Palmieri

[hivert]

comment:4

Replying to @nthiery:

All test pass. I let Florent put the final positive review once John will have given his green light.

While we are waiting for John, can you add a proper commit message ? Jeroen will ask you to do so anyway...

[nthiery]

Attachment: trac_12528_free_module-optimize-nt.patch.gz

[nthiery]

comment:5

Replying to @hivert:

While we are waiting for John, can you add a proper commit message ? Jeroen will ask you to do so anyway...

Shoot, I was sure I had done it. Well, now its done :-)

[jhpalmieri]

comment:6

The Steenrod algebra change looks fine to me.

[hivert]

comment:7

Replying to @jhpalmieri:

The Steenrod algebra change looks fine to me.

Then it's good to go !

[jdemeyer]

Merged: sage-5.0.beta6