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How to add term order to free module?

asked 2010-12-12 11:51:06 -0600

Jeff Stroomer gravatar image

updated 2010-12-15 02:02:21 -0600

niles gravatar image

I am working with a free module over a ring of polynomials, and need more than what's available in FreeModule. To be specific, I want to define an order on the terms in the module (think term orders for Grobner bases), and then to be able to obtain leading monomials of module elements.

I tried to augment sage.modules.free_module_element.FreeModuleElement.__bases__ with my own mix-in as described in the tutorial, but apparently FreeModuleElement cannot be augmented in this way.

Presumably I could also put together derived classes for FreeModule and FreeModuleElement, but I'm somewhat up in the air as how to do this.

I considered augmenting my ring of polynomials with extra variables as a back-door way to produce my free module, but the term orders available in polynomial rings are not general enough for my application.

Any suggestions? So far I have worked around the problem, but it's ugly.

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Have you tried "CombinatorialFreeModule" instead of "FreeModule"? For giving elements names, for example, it's very good, and it might suit your needs.

John Palmieri gravatar imageJohn Palmieri ( 2010-12-12 14:59:33 -0600 )edit

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answered 2010-12-14 03:29:42 -0600

Jason Bandlow gravatar image

updated 2010-12-14 03:31:30 -0600

To slightly elaborate on John's comment, "CombinatorialFreeModule" allows you to specify an arbitrary comparison function on the elements. Here is a sample doctest from sage.categories.modules_with_basis :

            sage: X = CombinatorialFreeModule(QQ, [1, 2, 3]); X.rename("X")
            sage: x = 3*X.monomial(1) + 2*X.monomial(2) + X.monomial(3)
            sage: x.leading_monomial()
            B[3]
            sage: def cmp(x,y): return y-x
            sage: x.leading_monomial(cmp=cmp)
            B[1]
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Asked: 2010-12-12 11:51:06 -0600

Seen: 145 times

Last updated: Dec 15 '10