On Wed, Jun 23, 2010 at 05:40:04PM -0700, John H Palmieri wrote:
> (I would raise an error unless each monomial has the same degree:
> degree for elements of a general graded algebra should only be defined
> for homogeneous elements.)
If the grading is over NN/ZZ, or some naturally ordered monoid, I
would definitely argue for keeping degree for all elements.
Otherwise, I am indeed fine with the following:
assert self.is_homogeneous()
return self.parent().degree_on_basis(self.leading_support())
which becomes constant time when assertion tests are turned off.
> > - Could WeightedIntegerVectors(d, degrees) possibly replace
> > basis_function(d, degrees)?
>
> More or less. I think I'll redefine basis_function so that it returns
> WeightedIntegerVectors(d, degrees).list().
What's the rationale for forcing the list? This makes it expensive to
compute with elements of large degree (say, getting the homogeneous
component of x^100 in 5 variables of degree 1 requires listing 4598126
elements).
> I was actually doing it to force coercion of the coefficient into the
> base ring:
>
> sage: A = AlgebrasWithBasis(GF(2)).example()
> sage: A.from_base_ring(12)
> 12*B[word: ]
> sage: A.from_base_ring(12) == 0
> False
>
> That's a bug, too, I guess.
This one is by design. from_base_ring is responsible for implementing
the morphism from GF(2) to self. It's the job of coercion to build
from it the morphism from ZZ:
sage: A = AlgebrasWithBasis(GF(2)).example()
sage: A(12)
0
sage: phi = A.coerce_map_from(ZZ)
sage: phi(12)
0
Feel free to update the documentation if this was ambiguous.
> > - self.term(tuple([a+b for a,b in zip(w1, w2)])) ->
> > self.monomial(tuple(a+b for a,b in zip(w1, w2)))
> >
> > (in general, self.term -> self.monomial; see #7938)
>
> What about self.term(x, coeff)? Is there a replacement for that?
> Should I use self._from_dict({x: coeff})?
Oops, no, self.term(x,coeff) is fine. I just meant self.term(12) ->
self.monomial(12). #7938 swapped the definitions of term and monomial
(we formerly used MuPAD's convention for polynomials with was reversed
with Sage's)
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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