I know the Newton method.
My question: is there built-in support in sage and how in general find all
roots? You've got approximate solution, but there is another one.
On Thursday, May 7, 2015 at 12:59:22 PM UTC+3, vdelecroix wrote:
>
> On 06/05/15 14:55, Paul Royik wrote:
> > For example,
> > x^5+y^5=7
> > x*sin(y)=1
>
> Newton method is perfectly fine here
>
> var('x,y')
> f(x,y) = x^5 + y^5 - 7
> g(x,y) = x*sin(y) - 1
> F(x,y) = (f, g)
>
> m = F.derivative()
>
> V = VectorSpace(RDF, 2)
> v = V((2,2))
> for _ in range(10):
> fv = F(*v)
> v = V(m(*v).solve_right(-fv) + v)
>
> print v
> print F(*v)
>
> I obtain the approximate solution v which is
> x = 1.0102139894432696
> y = 1.428474139287505
>
> Vincent
>
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