Opened 2 years ago
Closed 2 years ago
#25082 closed defect (fixed)
Fix symbolic power of matrix
Reported by: | slelievre | Owned by: | |
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Priority: | major | Milestone: | sage-8.2 |
Component: | linear algebra | Keywords: | matrix power, symbolic |
Cc: | mforets, slelievre, tmonteil, tscrim | Merged in: | |
Authors: | Samuel Lelièvre | Reviewers: | Frédéric Chapoton |
Report Upstream: | N/A | Work issues: | |
Branch: | fcee945 (Commits) | Commit: | fcee945ea54fad3483fbb5c6c46d3fe4362f9ea9 |
Dependencies: | Stopgaps: |
Description
The symbolic power of a matrix was requested and discussed in Ask Sage question 25658, and implemented in #22523.
That implementation works in basic cases (diagonalizable case, two by two case, ...).
As reported in Ask Sage question 41622 though, it fails in some cases.
The reason is that the general matrix power is computed on the Jordan form of the matrix, but the k-th block was placed at (k, k), which is incorrect if a Jordan block of size at least two occurs in any position but the last.
This ticket implements the fix suggested in an answer to Ask Sage question 41622.
Before this ticket:
sage: n = SR.var('n') sage: A = matrix(QQ, 3, [[2, 1, 0], [0, 2, 0], [0, 0, 3]]); A sage: B = A^n; B [ 2^n 2^(n - 1)*n 0] [ 0 3^n 0] [ 0 0 0]
After this ticket:
sage: B = A^n; B [ 2^n 2^(n - 1)*n 0] [ 0 2^n 0] [ 0 0 3^n]
Change History (5)
comment:1 Changed 2 years ago by
- Cc mforets tscrim added
comment:2 Changed 2 years ago by
- Status changed from new to needs_review
comment:3 Changed 2 years ago by
- Reviewers set to Frédéric Chapoton
- Status changed from needs_review to positive_review
ok
comment:4 Changed 2 years ago by
thanks for the fix.
comment:5 Changed 2 years ago by
- Branch changed from u/slelievre/fix_symbolic_power_of_matrix to fcee945ea54fad3483fbb5c6c46d3fe4362f9ea9
- Resolution set to fixed
- Status changed from positive_review to closed
Cc-ing authors and reviewers of #22523.
I pushed the fix from my answer at Ask Sage.