#7620: Inconsistent ordering when composing functors
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Reporter: SimonKing | Owner: nthiery
Type: defect | Status: new
Priority: critical | Milestone: sage-4.3
Component: categories | Keywords: Functor composition order
Work_issues: | Author: Simon King
Upstream: N/A | Reviewer:
Merged: |
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Apparently the composition of construction functors is inconsistent.
'''__Examples__'''
{{{
sage: from sage.categories.pushout import construction_tower
sage: P = QQ['x','y']
sage: construction_tower(P)
[(None, Multivariate Polynomial Ring in x, y over Rational Field),
(MPoly[x,y], Rational Field),
(FractionField, Integer Ring)]
}}}
Let us see what the product of the two functors above does:
{{{
sage: F = prod([X[0] for X in construction_tower(P) if X[0] is not None])
sage: F
MPoly[x,y](FractionField(...))
}}}
OK, that's reasonable, we have {{{F1*F2(X) = F1(F2(X))}}}.
But in a slightly more complicated example, the product gets messed up:
{{{
sage: P = QQ['x'].fraction_field()['y']
sage: construction_tower(P)
[(None,
Univariate Polynomial Ring in y over Fraction Field of Univariate
Polynomial Ring in x over Rational Field),
(Poly[y],
Fraction Field of Univariate Polynomial Ring in x over Rational Field),
(FractionField, Univariate Polynomial Ring in x over Rational Field),
(Poly[x], Rational Field),
(FractionField, Integer Ring)]
}}}
Now we do the same product as above:
{{{
sage: F = prod([X[0] for X in construction_tower(P) if X[0] is not None])
sage: F
FractionField(Poly[x](Poly[y](FractionField(...))))
}}}
So, apparently the order is perturbed.
Related with it, it seems counter-intuitive that the product over the
expansion of a functor does not return the functor:
{{{
sage: F
FractionField(Poly[x](Poly[y](FractionField(...))))
sage: prod(F.expand())
FractionField(Poly[x](FractionField(Poly[y](...))))
}}}
'''__Conventions__'''
Possible conventions on the order of composition are:
{{{F1*F2(X)=F1(F2(X))}}} and {{{F1*F2(X)=F2(F1(X))}}}
My personal preference is {{{F1*F2(X)=F1(F2(X))}}}, and it happens to be
used in the generic multiplication method of ConstructionFunctor:
{{{
class ConstructionFunctor(Functor):
def __mul__(self, other):
if not isinstance(self, ConstructionFunctor) and not
isinstance(other, ConstructionFunctor):
raise CoercionException, "Non-constructive product"
return CompositConstructionFunctor(other, self)
}}}
So, I think the convention {{{F1*F2(X)=F1(F2(X))}}} should be (or is
already) the official Sage convention.
'''__About expand()__'''
{{{
class CompositConstructionFunctor(ConstructionFunctor):
def expand(self):
return self.all
}}}
Since the convention {{{F1*F2(X)=F1(F2(X))}}} is used, this method should
return {{{list(reversed(self.all))}}}.
'''__Wrong multiplication order__'''
{{{
class CompositConstructionFunctor(ConstructionFunctor):
def __init__(self, *args):
self.all = []
for c in args:
if isinstance(c, list):
self.all += c
elif isinstance(c, CompositConstructionFunctor):
self.all += c.all
else:
self.all.append(c)
Functor.__init__(self, self.all[0].domain(),
self.all[-1].codomain())
def __mul__(self, other):
if isinstance(self, CompositConstructionFunctor):
all = self.all + [other]
else:
all = [self] + other.all
return CompositConstructionFunctor(*all)
}}}
That means {{{self}}} is applied ''before'' {{{other}}}!
'''__Suggested fix__'''
1. I suggest that {{{CompositConstructionFunctor.expand()}}} returns
{{{list(reversed(self.all))}}}. Then, we would have
{{{prod(F.expand())==F}}}.
2. Change the order of {{{self}}} and {{{other}}} in the multiplication
method of {{{CompositFunctor}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7620>
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