On Apr 14, 9:02 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Wed, Apr 9, 2008 at 1:21 PM, John Palmieri <[EMAIL PROTECTED]> wrote:
>
> > I'm trying to define a class based on Algebra, and I'm having
> > problems. I think the issue is that I don't understand how coercion
> > is supposed to work.
>
> > Right now I have
>
> > def class SteenrodAlgebra(Algebra)
>
> > and
>
> > def class SteenrodAlgebraElement(AlgebraElement)
>
> > In the second one, I've defined an _add_ method. Should I also define
> > an __add__ method explicitly, or should I do something with coercion
> > and the class SteenrodAlgebra?
>
> You should not define __add__. Just define _coerce_impl.
>
> (Of course, you already know this since I looked over your
> code in person today. But I'm answering this email for completeness.)
For more completeness, in case anyone else ever has the same problem
and finds this thread, my problem was that I was trying to add two
elements whose parents [excuse me while I stop being a mathematician
for a second] were equal but not identical.
>
> > I've tried reading the documentation
> > (like section 11.5.2 in the reference manual), and I've tried reading
> > various pieces of source code, but I'm just getting confused.
>
> > Here's the relevant code.
>
> > steenrod_prime = 2
>
> > class SteenrodAlgebra(Algebra):
>
> > def __init__(self, p=steenrod_prime):
> > """
> > INPUT:
> > p: positive prime integer
>
> > return mod p Steenrod algebra
> > """
> > if is_prime(p):
> > self.prime = p
> > ParentWithGens.__init__(self, GF(p))
> > else:
> > raise ValueError, "%s is not prime." % p
>
> > def __repr__(self):
> > return "mod %d Steenrod algebra" % self.prime
>
> > def __eq__(self,right):
> > return type(self) == type(right) and \
> > self.prime == right.prime
>
> > def __call__(self, x):
> > if isinstance(x, SteenrodAlgebraElement) and x.parent() is
> > self:
> > return x
> > else:
> > return SteenrodAlgebraElement(self,x)
>
> > # I don't know how to write this.
> > # I took this from FreeAlgebraQuotient, I think.
> > def _coerce_impl(self, x):
> > """
> > Return the coercion of x into this Steenrod algebra.
>
> > The algebras that coerce into this quotient ring are:
> > * this Steenrod algebra
> > * its base field
> > """
> > return self._coerce_try(x, [self, self.base_ring()])
>
> > def __contains__(self, x):
> > return isinstance(x, SteenrodAlgebraElement) and x.parent() ==
> > self
>
> > class SteenrodAlgebraElement(AlgebraElement):
>
> > def __init__(self, poly, p=steenrod_prime):
> > """
> > INPUT:
> > poly: dictionary with entries of form (monomial,
> > coefficient)
> > Each coefficient is in GF(p), and each monomial is a tuple
> > of non-negative integers (a, b, c, ...), corresponding to
> > the Milnor basis element Sq(a, b, c, ...).
> > p: positive prime number (default steenrod_prime)
> > """
> > if is_prime(p):
> > if p == 2:
> > RingElement.__init__(self,SteenrodAlgebra(p))
> > F = parent(self).base_ring()
> > self.base_field = F
> > new_poly = {}
> > for mono in poly:
> > trimmed = check_and_trim(mono)
> > if new_poly.has_key(trimmed):
> > coeff = F(poly[mono] + new_poly[trimmed])
> > else:
> > coeff = F(poly[mono])
> > if not coeff.is_zero():
> > new_poly[trimmed] = coeff
> > self.elt = new_poly
> > else:
> > raise NotImplementedError, "Only the mod 2 Steenrod
> > algebra has been implemented"
> > else:
> > raise ValueError, "%s is not prime." % p
>
> > def _add_(self, other):
> > F = self.base_field
> > poly1 = self.elt
> > poly2 = other.elt
> > for mono in poly2:
> > if poly1.has_key(mono):
> > coeff = F(poly1[mono] + poly2[mono])
> > else:
> > coeff = F(poly2[mono])
> > if coeff == 0:
> > del poly1[mono]
> > else:
> > poly1[mono] = coeff
> > return SteenrodAlgebraElement(poly1)
>
> > # should I do this?
> > # def __add__(self, other):
> > # return (self._add_(other))
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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