reduce base field for scheme morphisms

[bhutz]

It is possible that the field defined by the coefficients is strictly contained in base field of the morphism. This can be happen in a number of situations, especially from conjugations or computing normal forms. There should be a general function to reduce to the field of definition of the coefficients.

[bhutz]

Here is an initial implementation that could use some more testing.

This just implements the function and does not have any of the 'client' functions utilize this; like conjugate or normal form. I'm not sure those additional modifications should be part of this ticket.

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New commits:

​6c9c01f	28161: from_algebraics return ds
​b33de77	28161 returns ds
​5a75f00	Merge branch 8.9.beta2 into t/28161/master
​f9db110	28161: update docs
​c7b03d7	28200: implement reduce_base_field for schememorphisms
​4f462a0	28174: Fix dehomogenization error for non-endomorphisms
​222c9aa	Merge commit '4f462a0255fef1590a6979d4b95fee204f55b432' of git://trac.sagemath.org/sage into reduce_base

[gh-HTalbott]

On line 1684 of src/sage/schemes/projective/projective_morphism.py, the method finds the max of the the degrees of the coefficients. This should find the LCM rather than the max. For instance, the following code currently gives the minimal field as GF(5 to 3), when it should give GF(5 to 6), as below:

sage: K.<t>=GF(5^6)
sage: A.<x>=AffineSpace(K,1)
sage: H=End(A)
sage: f=H([x^2+x*(t^3 + 2*t^2 + 4*t)+(t^5 + 3*t^4 + t^2 + 4*t)])
sage: f.reduce_base_field()
Scheme endomorphism of Affine Space of dimension 1 over Finite Field in t of size 5^6
  Defn: Defined on coordinates by sending (x) to
        (x^2 + (t^3 + 2*t^2 - t)*x + (t^5 - 2*t^4 + t^2 - t))

[git]

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

​1ad13ae	Merge branch 8.9.beta4 into t/28200/28200_reduce_base_field
​e9fc3fa	28200: fix to lcm and add example

[git]

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

​a0e7824

28200: fixed example formatting

[gh-HTalbott]

Fixed small documentations errors. Everything else looks good!

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New commits:

​482ed83	Merge branch 'u/bhutz/28200_reduce_base_field' of git://trac.sagemath.org/sage into test
​a0e7824	28200: fixed example formatting