On Jan 11, 2008, at 4:19 AM, Burcin Erocal wrote: > On Fri, 4 Jan 2008 18:03:23 -0800 > Robert Bradshaw <[EMAIL PROTECTED]> wrote: > >> I'm going to separate the issues here--multiplication and addition. >> The former is easily handled by implementing the coercion ZZ -> >> BooleanMonomials via Z/2Z. David Roe and I still need to finish >> pushing the new coercion model through, but I've been sidetracked >> doing 3d and other stuff. > > In this case there is no coercion between Z/2Z and BooleanMonomials, > but I can live with the fact that 1*x or x*1 doesn't work.
Is this because 0 is not a BooleanMonomial? Otherwise, I think there is a coercion (as multiplicative groups, and as rings if one looks at the "ambient algebra"). > An argument for making these work is that 1 should be treated as > the unit in any multiplicative structure and it is really > counterintuitive to get an error message after typing 1*x. This was > probably the intention behind including a special case for 1 in > MonoidElement.__mul__. > >> As for addition, this violates the underlying assumption that >> arithmetic on M is closed in M (with the exception of division which >> passes to the fraction field). Here is the solution I propose: >> >> Monoid parents (such as BooleanMonomials) would implement an >> ambient_algebra() function. It could optionally take a basering (for >> groups returning a group ring, for monomials returning a polynomial >> ring). This would be kind of like Mark Hansen's Combinatorial >> Algebras. In element.pyx one would have >> >> cdef class MonoidElement(Element): >> >> def __add__(left, right): >> if not have_same_parent(left, right): >> return coercion_model.bin_op_c(left, right, add) >> A = left. ambient_algebra() >> return A(left) + A(right) >> >> Thoughts? > > I like the idea of the ambient_algebra function, though I cannot > follow > the code. I guess bin_op_c would have to be modified to consider the > ambient_algebra if the operation is addition. No, I don't think there is a need to modify bin_op_c at all. > I've been staring at the coercion code a lot lately. If there is an > agreement on the design, I could try implementing it. Yes. Just one question--why do you need to separate the monomial and polynomial types? Why not just have everything be a polynomial? - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
