indeterminacy locus for rational maps

[sagetrac-mmanes]

Create function to compute the indeterminancy locus of a rational map on projective space.

Component: algebraic geometry

Author: Michelle Manes

Branch/Commit: 8680cc0

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/21104

[sagetrac-mmanes]

Branch: u/mmanes/indeterminacy_locus_for_rational_maps

[sagetrac-mmanes]

New commits:

61ce7d7

21104: define indeterminacy_locus function

[sagetrac-mmanes]

Author: Michelle Manes

[sagetrac-mmanes]

Commit: 61ce7d7

[sagetrac-mmanes]

comment:3

I want to add functionality for indeterminacy_points when the indeterminacy locus is a zero-dimensional subscheme.

[sagetrac-git]

Changed commit from 61ce7d7 to 3802039

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

3802039

21104: added function for indeterminacy_points

[sagetrac-mmanes]

New commits:

3802039

21104: added function for indeterminacy_points

[bhutz]

comment:6

Everything works find, just a couple minor things

• need to wrap long doc lines

• do not need the line

F = self.base_ring()

• output of indet_pts: spelling of indet.

• double quote F everywhere it occurs in docs

• if not F.is_field() should be inside F is not None if branch

• need doctest to test that F works

Here are some interesting examples I was trying. They all work, so add which ever you think

%time
set_verbose(None)
P.<x,y,z>=ProjectiveSpace(QQ,2)
H=End(P)
f=H([x^2+y^2,y^2-z^2,x^2+z^2])
f.indeterminacy_points(F=QuadraticField(-1))

%time
set_verbose(None)
K.<t>=FunctionField(QQ)
P.<x,y,z>=ProjectiveSpace(K,2)
H=End(P)
f=H([x^2-t^2*y^2,y^2-z^2,x^2-t^2*z^2])
f.indeterminacy_points()

%time
set_verbose(None)
P.<x,y,z>=ProjectiveSpace(Qp(3),2)
H=End(P)
f=H([x^2-7*y^2,y^2-z^2,x^2-7*z^2])
f.indeterminacy_points()

• you should add a warning/note of some kind in the docs about the fact that these functions do not normalize the coordinates for examples such as

P.<x,y,z>=ProjectiveSpace(QQ,2)
H=End(P)
f=H([x*x^2,x*y^2,x*z^2])
f.indeterminacy_locus()

[bhutz]

Reviewer: Ben Hutz

[sagetrac-git]

Changed commit from 3802039 to 8680cc0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8680cc0

21104: improved documentation and minor improvement to code

[vbraun]

Changed branch from u/mmanes/indeterminacy_locus_for_rational_maps to 8680cc0