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feat: add iso_oscar_singular_[coeff/poly]_ring #4342

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@thofma thofma commented Nov 23, 2024

Implements the plan we agreed on #976, introducing

    iso_oscar_singular_coeff_ring
    iso_oscar_singular_poly_ring

This is similar to iso_oscar_gap, although here we must have two separate version.

This PR here applies it only as far as we need it to fix #976.

Comments/thoughts:

  • There are still many singular_poly_ring and singular_generators uses left, which can (and will with the right input) trigger ambiguity errors. But these might be fixed later.
  • @fieker this also fixes FqField if the field is not absolute.
  • This opens up the possibility to optimize the coercion for specific fields, so that Singular has a nice field to work with. For example:
    • if $K$ is an arbitrary number field, we could bring it into the form $\mathbf{Q}(\alpha)$,
    • if $R = K[e]/(e^2)$, we could turn $R[x_1,\dotsc,x_n]$ into $K[e,x_1,\dotsc,x_n]/(e^2)$

CC: @fieker @ederc

- use it in some places
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Oscar Singular coercion ambiguities
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