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. 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. I've been staring at the coercion code a lot lately. If there is an agreement on the design, I could try implementing it. Burcin --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
