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Implement algebra_containment from Singular #34502

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jhpalmieri opened this issue Sep 7, 2022 · 5 comments · Fixed by #36030
Closed

Implement algebra_containment from Singular #34502

jhpalmieri opened this issue Sep 7, 2022 · 5 comments · Fixed by #36030
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c: packages: standard p: minor / 4 t: enhancement
Milestone
sage-10.2

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@jhpalmieri
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Implement the algebra_containment procedure from Singular. Perhaps also inSubring.

Component: packages: standard

Branch/Commit: u/jhpalmieri/singular-subalgebra-containment @ 852b2c4

Issue created by migration from https://trac.sagemath.org/ticket/34502
@jhpalmieri jhpalmieri added this to the sage-9.8 milestone Sep 7, 2022
@rburing
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rburing commented Sep 14, 2022

comment:1

See my answer to https://ask.sagemath.org/question/58630/compute-minimal-number-of-generators-of-subring/ for a description of the algorithm and an implementation via the Singular interface.

@jhpalmieri
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comment:2

That's very helpful. For the particular case I was using, I had already implemented my own version using the algorithm you described there (item 1 below). Now I see at least three options:

  1. create a polynomial ring with new generators z_1, ..., z_m corresponding to the subalgebra generators y_1, ..., y_m and reduce using the ideal (z_i - y_i)
  2. use the in_subring function that you provided
  3. use an algebra_containment function with a very similar definition

By the way, regarding item 1, is there any advantage to replacing a line like

J = R.ideal(z1 - (whatever), z2 - (whatever))

with

J = R.ideal(z1 - (whatever), z2 - (whatever)).groebner_basis()

Does that speed up the f.reduce(J) computation, for example if you need to do this for many f?

@jhpalmieri
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Branch: u/jhpalmieri/singular-subalgebra-containment

@jhpalmieri
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comment:4

Here is a draft. Maybe it would be better to not use singular_lib and singular_function and instead define these at the same level as other Singular functions in Sage. Anyway, it's a start.

New commits:

852b2c4trac 34502: subalgebra containment tests for polynomial algebras

@jhpalmieri
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Commit: 852b2c4

@mkoeppe mkoeppe removed this from the sage-9.8 milestone Jan 29, 2023
@jhpalmieri jhpalmieri mentioned this issue Aug 3, 2023
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jhpalmieri added a commit to jhpalmieri/sage that referenced this issue Aug 3, 2023
@jhpalmieri
Implement algebra_containment from Singular (issue sagemath#34502)
301dfad
jhpalmieri added a commit to jhpalmieri/sage that referenced this issue Aug 3, 2023
@jhpalmieri
Implement algebra_containment from Singular (issue sagemath#34502)
729316e
vbraun pushed a commit to vbraun/sage that referenced this issue Aug 23, 2023
sagemathgh-36030: Implement algebra_containment from Singular (issue s…
99c46d4 
…agemath#34502)

    
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes sagemath#1234" use "Introduce new method to
calculate 1+1"
-->

This implements subalgebra containment for polynomials: whether a
polynomial is contained in the subalgebra determined by given
generators.

<!-- Describe your changes here in detail -->

<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes sagemath#12345". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->

This fixes sagemath#34502. It provides several algorithms for the calculution,
using Singular's algebra_containment, Singular's inSubring, or Sage's
Groebner basis tools.


### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->
<!-- If your change requires a documentation PR, please link it
appropriately -->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
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- [X] The title is concise, informative, and self-explanatory.
- [X] The description explains in detail what this PR is about.
- [X] I have linked a relevant issue or discussion.
- [X] I have created tests covering the changes.
- [X] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
-->

<!-- If you're unsure about any of these, don't hesitate to ask. We're
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URL: sagemath#36030
Reported by: John H. Palmieri
Reviewer(s): John H. Palmieri, Kwankyu Lee
vbraun pushed a commit to vbraun/sage that referenced this issue Aug 27, 2023
sagemathgh-36030: Implement algebra_containment from Singular (issue s…
811ac59 
…agemath#34502)

    
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes sagemath#1234" use "Introduce new method to
calculate 1+1"
-->

This implements subalgebra containment for polynomials: whether a
polynomial is contained in the subalgebra determined by given
generators.

<!-- Describe your changes here in detail -->

<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes sagemath#12345". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->

This fixes sagemath#34502. It provides several algorithms for the calculution,
using Singular's algebra_containment, Singular's inSubring, or Sage's
Groebner basis tools.


### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->
<!-- If your change requires a documentation PR, please link it
appropriately -->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
<!-- Feel free to remove irrelevant items. -->

- [X] The title is concise, informative, and self-explanatory.
- [X] The description explains in detail what this PR is about.
- [X] I have linked a relevant issue or discussion.
- [X] I have created tests covering the changes.
- [X] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
-->

<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
    
URL: sagemath#36030
Reported by: John H. Palmieri
Reviewer(s): John H. Palmieri, Kwankyu Lee
@mkoeppe mkoeppe added this to the sage-10.2 milestone Aug 27, 2023
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Implement algebra_containment from Singular (issue #34502) jhpalmieri/sage
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@rburing @jhpalmieri @mkoeppe