Solving a system of equations ignores multiplicities

[simon-king-jena]

A follow-up from http://groups.google.com/group/sage-support/browse_thread/thread/d8e22deb18d97253 but different from #6228:

sage: solve((x^2-1)^3==0, x, multiplicities=True)
([x == -1, x == 1], [3, 3])
sage: solve(((x^2-1)^3==0,(x^2-1)^3==0), x, multiplicities=True)
[[x == 1], [x == -1]]

So, at least in this example, we get the correct multiplicities for a single equation, but we don't get any multiplicity when the same equation together with a copy of itself forms a system of equations.

Note that maxima does not seem to help here:

sage: maxima.eval('solve([(x^2-1)^3,(x^2-1)^3],x)')
'[[x=1],[x=-1]]'
sage: maxima.get('multiplicities')
'[]'

What format should the multiplicities be provided in?

• When one solves a single equation with a single variable, the solutions are given by a simple list. Accordingly, the multiplicities are given as a simple list.
• When a system of equations in a single variable is given, the solutions are given by a list of lists. So, should the multiplicities be given by a list of lists?

Component: symbolics

Keywords: multiplicities system of equations

Issue created by migration from https://trac.sagemath.org/ticket/6231