LINEAR: Compute the implication graph for linear magmas (Part 1) #535
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
As a first step for #364, I have created some scripts and data files.
linear_magmas/list_restrictions.pyreads all equations, insertsx ◇ y = a*x + b*yas the operation, expands the equation assuming thataandbdon't commute, and computes the coefficient of each variable in the equation. The result is written todata/linear_magma_restrictions.txt.Example:
linear_magmas/reduce.pythen uses this list and calls Singular to compute a Gröbner basis for each set of restrictions. This is done once assuming commutativity and once without.The restrictions for Equation101 then become:
[ab+b**2+a-1, a**2-b**2-2a+1, b**3-b**2-a-b+1]and[ab+b**2+a-1, a**2-b**2-2a+1, b**3+ab-b]