Opened 15 years ago

Closed 3 years ago

#2693 closed enhancement (fixed)

Sage should have generic resultant implementation for multivariate polynomials

Reported by: Carl Witty Owned by: William Stein
Priority: major Milestone: sage-8.8
Component: algebraic geometry Keywords: resultant
Cc: Travis Scrimshaw, Vincent Delecroix, vklein Merged in:
Authors: Frédéric Chapoton Reviewers: Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: 30bd620 (Commits, GitHub, GitLab) Commit: 30bd620a157659e603c855c76e6d8f87701c69dc
Dependencies: Stopgaps:

Status badges

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 9 years ago by Jeroen Demeyer

Milestone: sage-5.11sage-5.12

comment:2 Changed 9 years ago by For batch modifications

Milestone: sage-6.1sage-6.2

comment:3 Changed 8 years ago by For batch modifications

Milestone: sage-6.2sage-6.3

comment:4 Changed 8 years ago by For batch modifications

Milestone: sage-6.3sage-6.4

comment:5 Changed 8 years ago by Miguel Marco

Report Upstream: N/A

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:

def resultant(self, other, variable):
    m = self.sylvester_matrix(other, variable)
    return m.determinant()

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.

comment:6 Changed 3 years ago by Frédéric Chapoton

Keywords: resultant added

comment:7 Changed 3 years ago by Frédéric Chapoton

Authors: Frédéric Chapoton
Branch: u/chapoton/2693
Commit: add07d3bcb7521623ec1edd45f731213281f8b2d
Milestone: sage-6.4sage-8.8
Status: newneeds_review

New commits:

add07d3trac 2693 resultants for polynomials over inexact rings

comment:8 Changed 3 years ago by Frédéric Chapoton

Cc: Travis Scrimshaw Vincent Delecroix added

green bot, please review

comment:9 Changed 3 years ago by Frédéric Chapoton

hmm, the second doctest is more about univariate polynomials. Maybe it should go there ?

comment:10 Changed 3 years ago by git

Commit: add07d3bcb7521623ec1edd45f731213281f8b2d30bd620a157659e603c855c76e6d8f87701c69dc

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

30bd620trac 2693 resultants for polynomials over inexact rings

comment:11 Changed 3 years ago by Frédéric Chapoton

ok, test is now at the right place.

comment:12 Changed 3 years ago by Frédéric Chapoton

Cc: vklein added

and the bot is green.

comment:13 Changed 3 years ago by Travis Scrimshaw

Reviewers: Travis Scrimshaw
Status: needs_reviewpositive_review

LGTM.

comment:14 Changed 3 years ago by Volker Braun

Branch: u/chapoton/269330bd620a157659e603c855c76e6d8f87701c69dc
Resolution: fixed
Status: positive_reviewclosed
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