Newton method is not useful to find all roots, it is useful to find one
solution and refine approximate solutions.
Built-in Sage solution: no that I know of.
Doable: certainly for a large class of functions that do have a
controlled behavior at infinity. You just need to localize the roots and
then applies the Newton method.
Do you know any software/library that does it? Any paper mentioning such
an algorithm for a given class of non-algebraic functions?
Vincent
On 08/05/15 09:26, Paul Royik wrote:
> 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
>>
>
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-support+unsubscr...@googlegroups.com.
To post to this group, send email to sage-support@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
