Opened 13 years ago

Closed 5 years ago

## #7253 closed defect (wontfix)

# inefficient polynomial powering for positive characteristic

Reported by: | Robert Bradshaw | Owned by: | tbd |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |

Component: | algebra | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | Fixed upstream, in a later stable release. | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

One can take advantage of the fact that (a+b)^{p} = a^{p} + b^{p} to quickly expand f^{n} = f^{qp} * f^{r} (as r<p, and f^{p is sparse, the resulting product is easy to compute).
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See http://groups.google.com/group/sage-support/browse_thread/thread/38c3d619a7684a90

### Change History (7)

### comment:1 Changed 13 years ago by

Description: | modified (diff) |
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### comment:2 Changed 7 years ago by

Report Upstream: | → Reported upstream. No feedback yet. |
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### comment:3 Changed 5 years ago by

Report Upstream: | Reported upstream. No feedback yet. → Fixed upstream, in a later stable release. |
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This has been resolved upstream (see previous Singular link), so I propose to close this ticket.

### comment:4 Changed 5 years ago by

Milestone: | sage-wishlist → sage-duplicate/invalid/wontfix |
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### comment:5 Changed 5 years ago by

Status: | new → needs_review |
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### comment:6 Changed 5 years ago by

Status: | needs_review → positive_review |
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### comment:7 Changed 5 years ago by

Resolution: | → wontfix |
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Status: | positive_review → closed |

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This behavior still appears to be present in 2016. Since the underlying representation of multivariate polynomials over a finite field appears to be in Singular, I've raised the issue upstream:

http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2523

For univariate polynomials over a finite field, the underlying representation is in FLINT, and there this seems to be handled correctly (although I haven't looked at the source or asked a developer to confirm):