#6231: Solving a system of equations ignores multiplicities
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Reporter: SimonKing | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-wishlist
Component: symbolics | Keywords: multiplicities system of equations
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Changes (by SimonKing):
* milestone: sage-4.0.2 => sage-wishlist
Old description:
> 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`` provides the correct answer:
> {{{
> sage: maxima.eval('solve(((x^2-1)^3,(x^2-1)^3),x)')
> '[x=-1,x=1]'
> sage: maxima.eval('multiplicities')
> '[3,3]'
>
> }}}
>
> Probably this bug can be easily done by working at the code of the
> ``solve`` command.
>
> 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?
New description:
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?
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6231#comment:1>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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