ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 19 Apr 2014 12:12:09 -0500solving system of polynomial equations over reals using newton methodhttp://ask.sagemath.org/question/11359/solving-system-of-polynomial-equations-over-reals-using-newton-method/I have a set of polynomial equations and I want to find one of its real solutions close to some point, and I need only one solution. Here is an example:
This is the list of equations and variables:
Equations = [x_0*x_1*x_2*x_3 - x_0*x_1 - x_0*x_2 - x_0*x_3 - x_1*x_2 - x_1*x_3 + 2*x_0 + 2*x_1 - 448, -x_0*x_1*x_2 - x_0*x_1*x_3 - x_0*x_2*x_3 - x_1*x_2*x_3 + 3*x_0 +
3*x_1 + 2*x_2 + 2*x_3 + 452, x_0*x_1 + x_0*x_2 + x_0*x_3 + x_1*x_2 + x_1*x_3 + x_2*x_3 - 159, -x_0 - x_1 - x_2 - x_3 + 21]
Variables = [x_0, x_1, x_2, x_3]
If I ask Sage to solve this
S = solve(Equations,Variables)
it returns a bunch of solutions. But in some cases it doesn't give me any real solutions. I can prove that the above set of equations has a real solution close to `[2,4,7,8]`. Is there any way that I can perform an algorithm like the Newton's method with the start point `[2,4,7,8]`, and find that real solution?k1Sat, 19 Apr 2014 12:12:09 -0500http://ask.sagemath.org/question/11359/