Implement Weil restriction for affine schemes/points/morphisms

[bhutz]

#5569 implements Weil restriction (restriction of scalars) for ideals. This will extend that to affine schemes and also points and morphisms of affine schemes.

Component: algebraic geometry

Author: Ben Hutz

Branch/Commit: 8bacaf5

Reviewer: Joao Alberto de Faria

Issue created by migration from https://trac.sagemath.org/ticket/17729

[bhutz]

Branch: u/bhutz/ticket/17729

[bhutz]

Author: Ben Hutz

[bhutz]

comment:2

Note that when I implemented this I noticed that the original implementation for ideals was inconsistently ordering the coordinates. In particular it labelled a^2x2 + ax1 + ax0 and then created the coordinates (x2,x1,x0) in the ring k[x0,x1,x2]. This caused issues for morphisms, so I made this consistent: i.e. coordinates (x0,x1,x2). I also allowed for weil restrictions of relative number fields (to the base field) instead of just absolute number fields. These are the only two changes to the original implementation.

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New commits:

c1294c3

17729: implement weil restriction for affine schemes

[bhutz]

Commit: c1294c3

[sagetrac-jdefaria]

comment:3

Outside of the merge issue, in the affine point folder, the weil restriction function should be calling min_poly and not absolute_minpoly, otherwise it won't work for relative field extensions, (also put a better relative field extension example)

[sagetrac-jdefaria]

Reviewer: Joao Alberto de Faria

[sagetrac-git]

Changed commit from c1294c3 to e06c496

[sagetrac-git]

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

42b4cb1	Merge branch 'master' into ticket/17729
e06c496	17729: fixed minor issues from review

[sagetrac-git]

Changed commit from e06c496 to 8bacaf5

[sagetrac-git]

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

8bacaf5

Merge branch 'master' into ticket/17729

[bhutz]

comment:6

fixed a merge issues with beta0, then there was another merge issues with beta1. All fixed now.

[sagetrac-jdefaria]

comment:7

Went through and did some sanity checking, ran a long test just to be sure, looks clean, setting to positive review

[vbraun]

Changed branch from u/bhutz/ticket/17729 to 8bacaf5