Opened 13 years ago
Closed 2 years ago
#2693 closed enhancement (fixed)
Sage should have generic resultant implementation for multivariate polynomials
Reported by: | cwitty | Owned by: | was |
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Priority: | major | Milestone: | sage-8.8 |
Component: | algebraic geometry | Keywords: | resultant |
Cc: | tscrim, vdelecroix, vklein | Merged in: | |
Authors: | Frédéric Chapoton | Reviewers: | Travis Scrimshaw |
Report Upstream: | N/A | Work issues: | |
Branch: | 30bd620 (Commits, GitHub, GitLab) | Commit: | 30bd620a157659e603c855c76e6d8f87701c69dc |
Dependencies: | Stopgaps: |
Description
Consider this example, which fails:
R.<x,y> = RR[] p = x + y q = x*y p.resultant(q)
(as reported here: http://groups.google.com/group/sage-support/browse_thread/thread/1d6289cead33d063#)
This is because multivariate resultants are implemented using the Singular pexpect interface, which does not support RR.
A workaround for this particular problem (and a possible basis for an improved version) is:
p.polynomial(x).resultant(q.polynomial(x))
That is, fall back to univariate resultants, which are implemented using Pari and are somewhat more generic. (This is still not truly generic, though, since there are Sage rings which have no Pari equivalent.)
Change History (14)
comment:1 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:2 Changed 7 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:3 Changed 7 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:4 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:5 Changed 7 years ago by
- Report Upstream set to N/A
comment:6 Changed 2 years ago by
- Keywords resultant added
comment:7 Changed 2 years ago by
- Branch set to u/chapoton/2693
- Commit set to add07d3bcb7521623ec1edd45f731213281f8b2d
- Milestone changed from sage-6.4 to sage-8.8
- Status changed from new to needs_review
New commits:
add07d3 | trac 2693 resultants for polynomials over inexact rings
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comment:9 Changed 2 years ago by
hmm, the second doctest is more about univariate polynomials. Maybe it should go there ?
comment:10 Changed 2 years ago by
- Commit changed from add07d3bcb7521623ec1edd45f731213281f8b2d to 30bd620a157659e603c855c76e6d8f87701c69dc
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
30bd620 | trac 2693 resultants for polynomials over inexact rings
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comment:11 Changed 2 years ago by
ok, test is now at the right place.
comment:13 Changed 2 years ago by
- Reviewers set to Travis Scrimshaw
- Status changed from needs_review to positive_review
LGTM.
comment:14 Changed 2 years ago by
- Branch changed from u/chapoton/2693 to 30bd620a157659e603c855c76e6d8f87701c69dc
- Resolution set to fixed
- Status changed from positive_review to closed
In fact, singular resultants are slow compared to other methods, so it would really be a good idea to write specific sage code for resultants.
See #16749 and #12174 for ideas about it.
Just something like:
Would be both general for any polynomial ring, and faster than the current implementation. And of course, there could be a lot of cases where things can be done much faster, using specific backends where they are better.