Opened 10 years ago

Last modified 10 years ago

#6231 new enhancement

Solving a system of equations ignores multiplicities

Reported by: SimonKing Owned by:
Priority: major Milestone: sage-wishlist
Component: symbolics Keywords: multiplicities system of equations
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Description (last modified by SimonKing)

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?

Change History (1)

comment:1 Changed 10 years ago by SimonKing

  • Description modified (diff)
  • Milestone changed from sage-4.0.2 to sage-wishlist
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