Wrong multiplicities when solving a univariate polynomial equation

[simon-king-jena]

At http://groups.google.com/group/sage-support/browse_thread/thread/d8e22deb18d97253 Michael Friedman asked how to get the multiplicities when solving a set of nonlinear equations.

It turns out that actually even the multiplicities for a single and rather simple equation are wrong:

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| Sage Version 4.0, Release Date: 2009-05-29                         |
| Type notebook() for the GUI, and license() for information.        |
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sage: z = var('z')
sage: solve((z^3-1)^3,z,multiplicities=True)
([z == (sqrt(3)*I - 1)/2, z == (-sqrt(3)*I - 1)/2, z == 1], [1, 1, 3])

I am afraid that symbolics isn't my field of expertise. So, I don't know how to cure it.

Component: symbolics

Keywords: multiplicities solve

Author: Karl-Dieter Crisman

Reviewer: Mike Hansen

Merged: sage-4.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/6228

[simon-king-jena]

comment:1

Note that it seems to be a problem in maxima:

sage: maxima.eval('solve((z^3-1)^3,z)')
'[z=(sqrt(3)*%i-1)/2,z=-(sqrt(3)*%i+1)/2,z=1]'
sage: maxima.eval('multiplicities')
'[1,1,3]'

So, I suspect this ticket will get a "won't fix"...

[kcrisman]

comment:2

This is now fixed, presumably in the Maxima upgrade.

[kcrisman]

Author: Karl-Dieter Crisman

[kcrisman]

Attachment: trac_6228-multiplicity-maxima.patch.gz

Based on 4.1.2.alpha4

[mwhansen]

comment:3

Looks good to me.

[mwhansen]

Reviewer: Mike Hansen