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Fix a bug in reduction of element modulo ideal in exterior algebra #37146

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merged 4 commits into from
Feb 2, 2024

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This adds a loop to continue doing reduction modulo a Grobner basis for an element modulo an ideal in the exterior algebra. This guarantees a unique representative for each element, and that representative will be $0$ if the element is in the ideal. This fixes #37108.

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⌛ Dependencies

None.

@trevorkarn trevorkarn self-assigned this Jan 23, 2024
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Thank you. Some minor things.

Does this also result in a reduced GB for the example you gave on #37108?

src/sage/algebras/exterior_algebra_groebner.pyx Outdated Show resolved Hide resolved
src/sage/algebras/exterior_algebra_groebner.pyx Outdated Show resolved Hide resolved
trevorkarn and others added 2 commits January 23, 2024 23:04
Co-authored-by: Travis Scrimshaw <[email protected]>
Co-authored-by: Travis Scrimshaw <[email protected]>
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Thank you. Some minor things.

Fixed - thanks!

Does this also result in a reduced GB for the example you gave on #37108?

No it does not.

sage: N = 4
sage: E = ExteriorAlgebra(QQ,binomial(N,2))
sage: e = E.gens()
sage: K = matroids.CompleteGraphic(N);
sage: C = K.circuits()
sage: ideal_gens = [sum([(-1)^j*E.prod(e[i] for i in list(c)[:j] + list(c)[j+1:]) for j in range(len(c))]) for c in C]
sage: OS = E.quo(ideal_gens)
sage: I = OS.defining_ideal()
sage: I.groebner_basis()
(e0*e1 - e0*e3 + e1*e3,
 e0*e2 - e0*e4 + e2*e4,
 e1*e2 - e1*e5 + e2*e5,
 -e0*e1*e2 + e0*e1*e5 - e0*e2*e3 - e0*e3*e5 + e1*e2*e3 + e1*e3*e5,
 e3*e4 - e3*e5 + e4*e5)
sage: GS = I._groebner_strategy
sage: GS.groebner_basis
(e0*e1 - e0*e3 + e1*e3,
 e0*e2 - e0*e4 + e2*e4,
 e1*e2 - e1*e5 + e2*e5,
 -e0*e1*e2 + e0*e1*e5 - e0*e2*e3 - e0*e3*e5 + e1*e2*e3 + e1*e3*e5,
 e3*e4 - e3*e5 + e4*e5)
sage: GS.reduce_computed_gb()
sage: GS.groebner_basis
(e0*e1 - e0*e3 + e1*e3,
 e0*e2 - e0*e4 + e2*e4,
 e1*e2 - e1*e5 + e2*e5,
 e3*e4 - e3*e5 + e4*e5)

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Documentation preview for this PR (built with commit fa766d2; changes) is ready! 🎉

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This is definitely the more important bug to fix, so let's get this in.

However, we should still fix that the GB is not reduced when it is claiming it is.

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Sounds like a plan! Thanks!

vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 27, 2024
…xterior algebra

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

This adds a loop to continue doing reduction modulo a Grobner basis for
an element modulo an ideal in the exterior algebra. This guarantees a
unique representative for each element, and that representative will be
$0$ if the element is in the ideal. This fixes sagemath#37108.

<!-- 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". -->
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- [x] I have updated the documentation accordingly.

### ⌛ Dependencies

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URL: sagemath#37146
Reported by: trevorkarn
Reviewer(s): Travis Scrimshaw
vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 29, 2024
…xterior algebra

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

This adds a loop to continue doing reduction modulo a Grobner basis for
an element modulo an ideal in the exterior algebra. This guarantees a
unique representative for each element, and that representative will be
$0$ if the element is in the ideal. This fixes sagemath#37108.

<!-- 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. -->

### 📝 Checklist

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appropriately -->
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here to help! -->
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- [x] The description explains in detail what this PR is about.
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- [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: ...
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None.

<!-- If you're unsure about any of these, don't hesitate to ask. We're
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URL: sagemath#37146
Reported by: trevorkarn
Reviewer(s): Travis Scrimshaw
vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 30, 2024
…xterior algebra

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

This adds a loop to continue doing reduction modulo a Grobner basis for
an element modulo an ideal in the exterior algebra. This guarantees a
unique representative for each element, and that representative will be
$0$ if the element is in the ideal. This fixes sagemath#37108.

<!-- 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. -->

### 📝 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: ...
-->
None.

<!-- If you're unsure about any of these, don't hesitate to ask. We're
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URL: sagemath#37146
Reported by: trevorkarn
Reviewer(s): Travis Scrimshaw
@vbraun vbraun merged commit 50cfa54 into sagemath:develop Feb 2, 2024
15 of 22 checks passed
@amanmoon amanmoon mentioned this pull request Feb 10, 2024
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vbraun pushed a commit to vbraun/sage that referenced this pull request Apr 18, 2024
    
I have implemented the `automatic size labeler`, which now assigns
labels to pull requests based on the number of lines changed

**Minimal**
Typically involves very small changes, bug fixes, or updates that
require only a few lines of code, often less than 50.
sagemath#37208 sagemath#37146 sagemath#37043

**Small**
Involves more substantial changes than minimal, potentially adding new
features or making modifications to existing ones. The range is usually
between 50 to 100 lines of code.
sagemath#37152 sagemath#37132

**Moderate**
Represents a significant portion of the codebase being modified, such as
adding new features, refactoring, or making extensive changes to
existing functionalities. This might involve between 100 to 300 lines of
code.
sagemath#36919 sagemath#37112

**Large**
Involves substantial and complex changes across various parts of the
codebase. This could include major architectural changes, the
introduction of new modules, or a significant overhaul of existing
features, often exceeding 300 lines of code.
sagemath#37125 sagemath#36977 sagemath#36972

### 📝 Checklist

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- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
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Fixes: sagemath#37254
    
URL: sagemath#37262
Reported by: Aman Moon
Reviewer(s): Sebastian Oehms
vbraun pushed a commit to vbraun/sage that referenced this pull request Apr 20, 2024
    
I have implemented the `automatic size labeler`, which now assigns
labels to pull requests based on the number of lines changed

**Minimal**
Typically involves very small changes, bug fixes, or updates that
require only a few lines of code, often less than 50.
sagemath#37208 sagemath#37146 sagemath#37043

**Small**
Involves more substantial changes than minimal, potentially adding new
features or making modifications to existing ones. The range is usually
between 50 to 100 lines of code.
sagemath#37152 sagemath#37132

**Moderate**
Represents a significant portion of the codebase being modified, such as
adding new features, refactoring, or making extensive changes to
existing functionalities. This might involve between 100 to 300 lines of
code.
sagemath#36919 sagemath#37112

**Large**
Involves substantial and complex changes across various parts of the
codebase. This could include major architectural changes, the
introduction of new modules, or a significant overhaul of existing
features, often exceeding 300 lines of code.
sagemath#37125 sagemath#36977 sagemath#36972

### 📝 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.

Fixes: sagemath#37254
    
URL: sagemath#37262
Reported by: Aman Moon
Reviewer(s): Sebastian Oehms
vbraun pushed a commit to vbraun/sage that referenced this pull request Apr 25, 2024
    
I have implemented the `automatic size labeler`, which now assigns
labels to pull requests based on the number of lines changed

**Minimal**
Typically involves very small changes, bug fixes, or updates that
require only a few lines of code, often less than 50.
sagemath#37208 sagemath#37146 sagemath#37043

**Small**
Involves more substantial changes than minimal, potentially adding new
features or making modifications to existing ones. The range is usually
between 50 to 100 lines of code.
sagemath#37152 sagemath#37132

**Moderate**
Represents a significant portion of the codebase being modified, such as
adding new features, refactoring, or making extensive changes to
existing functionalities. This might involve between 100 to 300 lines of
code.
sagemath#36919 sagemath#37112

**Large**
Involves substantial and complex changes across various parts of the
codebase. This could include major architectural changes, the
introduction of new modules, or a significant overhaul of existing
features, often exceeding 300 lines of code.
sagemath#37125 sagemath#36977 sagemath#36972

### 📝 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.

Fixes: sagemath#37254
    
URL: sagemath#37262
Reported by: Aman Moon
Reviewer(s): Sebastian Oehms
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Bug in reduction of exterior algebra elements modulo ideal
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