On 10/28/07, David Joyner <[EMAIL PROTECTED]> wrote:
> On 10/26/07, Jason Grout <[EMAIL PROTECTED]> wrote:
> >
> > I'm trying to numerically solve a system of equations. Currently I have:
> >
> > sage: var('x y p q')
> > sage: eq1 = p+q==9
> > sage: eq2 = q*y+p*x==-6
> > sage: eq3 = q*y^2+p*x^2==24
> > sage: solve([eq1,eq2,eq3,p==1],p,q,x,y)
> > [[p == 3, q == 6, x == (-2*sqrt(10) - 2)/3, y == (sqrt(2)*sqrt(5) -
> > 2)/3], [p == 3, q == 6, x == (2*sqrt(10) - 2)/3, y == (-sqrt(2)*sqrt(5)
> > - 2)/3]]
> >
> > I'd like the answer to be a numeric approximation, though (i.e.,
> > x==-2.77485177345). I can't find any other solving routines other than
> > the symbolic one, though. Is there a way to numerically approximate the
> > solution, other than going through each solution and calling n() on the
> > left side of each symbolic expression?
>
>
> Examples using numpy and octave are give in the constructions cookbook:
>
> http://www.sagemath.org/doc/html/const/node35.html
Note that his systems are nonlinear, but your examples
in the constructions book are linear. So it's sort of
a different thing.
Some options for solving systems of nonlinear equations *numerically* include:
* [100% sage] Use scipy, which wraps minpack:
Type
sage: import scipy.optimize
sage: scipy.optimize.fsolve ?
to hopefully get going. Also just try scipy.optimize.[tab]
* [Not sage] Use phcpack, which is open source (GPL'd) but not
included in Sage. It is able to do amazing things with solving
algebraic systems numerically, using a method called "Polynomial
Homotopy Continuation". There is a Sage interface to phcpack, that
Marshall Hampton worked on (he frequently posts on sage-devel).
Please report back, since I haven't even tried to solve your system
above using either of the above approaches.
William
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