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.)
> 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 Washington
http://wstein.org
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