Hi,
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.
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?
- Robert
On Dec 29, 2007, at 5:53 AM, Burcin Erocal wrote:
> Hello,
>
> I'm having trouble implementing arithmetic for BooleanMonomials, which
> are elements of a monoid.
>
> Multiplication of BooleanMonomials work fine using the coercion model,
> but the following doesn't work, since there is no coercion from ZZ to
> BooleanMonomialMonoid.
>
> sage: P.<x,y> = BooleanPolynomialRing(2)
> sage: M = P._monom_monoid
> sage: x_monom = M(x); y_monom = M(y)
>
> sage: x_monom*1
> boom!
> sage: 1*x_monom
> boom!
>
> This works, because of the code after sage/structure/element.pyx:1083
>
> sage:x_monom*int(1)
> x
> sage:int(1)*x_monom
>
>
> How should I fix this? By implementing right and left actions, and
> returning 0 (in ZZ) when multiplying by an even integer?
>
>
> I also need to have the functionality to add two BooleanMonomials, and
> get a BooleanPolynomial. This is a real grey area for the coercion
> model. For example:
>
> sage: x_monom + 1
> ???
>
> The common parent of these objects is a BooleanPolynomialRing,
> which is
> not the parent of either one, so the coercion model doesn't work here.
> At Sage Days 6, Robert B suggested bypassing the coercion model and
> implementing an __add__ method for BooleanMonomials. This solves the
> above problem, but fails for this case:
>
> sage: 1 + x_monom
> boom!
>
> I would also like the following to work:
>
> sage: 0 + x_monom
> x
> sage: x_monom + 0 #this works with the current solution
> x
>
> Again, since there is no coercion from ZZ to BooleanMonomialMonoids,
> especially no image of 0 as a BooleanMonomial, this seems to be a case
> to be handled outside of the coercion model.
>
>
> Any thoughts or suggestions?
>
> Burcin
>
>
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