#10529: dimension() and is_smooth() for algebraic subschemes of toric varieties
----------------------------------+-----------------------------------------
Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6.2
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by novoselt):
Comments on the second patch (trac_10529_MPolynomialIdeal_subs.patch)
1. The "two-line description" is a little hard to understand, I would
remove "while not touching other variables" part and instead demonstrate
it on examples. (But I don't insist on this point.)
2. The second example in the doctest works with a polynomial, not an
ideal, so it should be fixed.
3. The following fails for no reason:
{{{
sage: R.<a,b> = PolynomialRing(QQ,2)
sage: S = PolynomialRing(QQ,"x")
sage: S.inject_variables()
Defining x
sage: p = a^2+b^2+a-b+2
sage: p.subs(a=x, b=x)
2*x^2 + 2
sage: _.parent()
Univariate Polynomial Ring in x over Rational Field
sage: I = R.ideal(p)
sage: I
Ideal (a^2 + b^2 + a - b + 2) of Multivariate Polynomial Ring in a, b over
Rational Field
sage: I.subs(a=x, b=x)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
...
TypeError: Could not find a common ring for the substituted generators.
}}}
One solution is to add a check for univariate polynomial rings, but what
about fraction fields and symbolic rings
{{{
sage: var("x")
x
sage: x.parent()
Symbolic Ring
sage: I.subs(a=x, b=x)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
...
TypeError: Could not find a common ring for the substituted generators.
}}}
Maybe it is OK to try to construct an ideal using the sequence universe
if it has ideal method? So that the code looks like
{{{
ring = self.ring()
generators = [f.subs(in_dict, **kwds) for f in self.gens()]
if not all(gen in ring for gen in generators):
ring = Sequence(generators).universe()
try:
return ring.ideal(generators)
except AttributeError:
raise TypeError("cannot form an ideal from the substituted
generators!")
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10529#comment:7>
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