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
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,
On Wednesday, 6 May 2015 07:27:36 UTC+1, Paul Royik wrote:
How can this be applied to systems?
nobody really knows how to solve systems of (non-polynomial) equations in
general.
There are heuristics implemented in various systems...
On Wednesday, May 6, 2015 at 1:28:55 AM UTC+3, Dima
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 =
On Thu, 7 May 2015, Dima Pasechnik wrote:
nobody really knows how to solve systems of (non-polynomial) equations in
general.
There are heuristics implemented in various systems...
What of those are built-in in Sage?
--
Jori Mäntysalo
How can this be applied to systems?
On Wednesday, May 6, 2015 at 1:28:55 AM UTC+3, Dima Pasechnik wrote:
On Tuesday, 5 May 2015 20:25:46 UTC+1, Paul Royik wrote:
I meant without discontinuous functions.
What is the general approach even in numerical solving of school
functions on the
On Tue, 5 May 2015, Paul Royik wrote:
How can this be applied to systems?
What kind of systems? Let us define f(x,y):
f(\sqrt{2}, \sqrt[3}) = 0
f(x,y) = x^2+y^2+1 if (x is not \sqrt{2}) or (y is not \sqrt[3})
Now this clearly has a root, but no numerical method can find it. So we
must have
For example,
x^5+y^5=7
x*sin(y)=1
On Wednesday, May 6, 2015 at 10:08:54 AM UTC+3, jori.ma...@uta.fi wrote:
On Tue, 5 May 2015, Paul Royik wrote:
How can this be applied to systems?
What kind of systems? Let us define f(x,y):
f(\sqrt{2}, \sqrt[3}) = 0
f(x,y) = x^2+y^2+1 if (x is not
How can I find numerical root for the system of equations?
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On Tuesday, 5 May 2015 20:25:46 UTC+1, Paul Royik wrote:
I meant without discontinuous functions.
What is the general approach even in numerical solving of school
functions on the interval?
on the interval it is the bisection method and its versions
I meant without discontinuous functions.
What is the general approach even in numerical solving of school
functions on the interval?
Can sage do that?
On Tuesday, May 5, 2015 at 9:53:22 PM UTC+3, Dima Pasechnik wrote:
This is an overtly optimistic point of view that find_root can solve
any
Thank you.
I have arbitrary system of equations.
I know, that find_root can solve any equation on interval.
Is there something similar to system of equations?
Your link didn't give answer.
On Tuesday, May 5, 2015 at 7:52:11 PM UTC+3, Alexander Lindsay wrote:
There's a good introduction on
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