Opened 12 years ago

Closed 11 years ago

# [with patch, positive review] Wrong multiplicities when solving a univariate polynomial equation

Reported by: Owned by: SimonKing major sage-4.2 symbolics multiplicities solve sage-4.2.alpha0 Karl-Dieter Crisman Mike Hansen

### Description

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:

```----------------------------------------------------------------------
| Sage Version 4.0, Release Date: 2009-05-29                         |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
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.

### comment:1 Changed 12 years ago by SimonKing

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"...

### comment:2 Changed 11 years ago by kcrisman

• Authors set to Karl-Dieter Crisman
• Milestone changed from sage-4.1.2 to sage-4.1.3
• Summary changed from Wrong multiplicities when solving a univariate polynomial equation to [with patch, needs review] Wrong multiplicities when solving a univariate polynomial equation

This is now fixed, presumably in the Maxima upgrade.

### Changed 11 years ago by kcrisman

Based on 4.1.2.alpha4

### comment:3 Changed 11 years ago by mhansen

• Reviewers set to Mike Hansen
• Summary changed from [with patch, needs review] Wrong multiplicities when solving a univariate polynomial equation to [with patch, positive review] Wrong multiplicities when solving a univariate polynomial equation

Looks good to me.

### comment:4 Changed 11 years ago by mhansen

• Merged in set to sage-4.2.alpha0
• Resolution set to fixed
• Status changed from positive_review to closed
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