id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
6231 Solving a system of equations ignores multiplicities 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?
" enhancement new major sage-wishlist symbolics multiplicities system of equations