2
votes
1answer
41 views

Division by factorized polynomials in Macaulay2

I have this problem dividing by factorized polynomials, for example (x_1^4-x_2^4)//(factor(x_1^2-x_2^2)) does not work because the numerator is of "class R" (R is the ring kk[x_1..x_n]) and the ...
3
votes
0answers
38 views

Algorithms for solving overdetermined, homogeneous linear systems with multivariate polynomial coefficients

I would like to solve overdetermined, homogeneous linear systems of equations with multivariate polynomial coefficients, i.e., $Ap=0$ with $A$ an $m\times n$ matrix, $m\gg n$, and $a_{i,j} \in ...
0
votes
1answer
67 views

Computing univariate resultant via modified Euclidean algorithm

In an answer to the question Resultant of Two Univariate Polynomials, a PDF of course slides was linked which describes a modification of Euclid's algorithm for computing univariate polynomial ...
1
vote
1answer
70 views

Resultant of Two Univariate Polynomials

I am trying to implement an algorithm for computing Res(f(x),g(x),x) where f(x) and g(x) uni variate polynomials with integer coefficients. Could any one list the various algorithms for computing ...
1
vote
1answer
173 views

Symbolic polynomial interpolation

I'm trying to create polynomials from some symbolic points to discretize derivations. This means I'm having data like $(a, \phi(a)),\ (b, \phi(b) ) $and $(c, \phi(c))$ and want to fit a second order ...
3
votes
1answer
148 views

How to factorize $4x^4+12x^{10/3} y^{2/3}+ \dots $?

Does anyone know how to factorize the following expression: $$4x^4+12x^{10/3} y^{2/3}+33x^{8/3} y^{4/3}+46x^2 y^2+33x^{4/3} y^{8/3}+12x^{2/3} y^{10/3}+4 y^4$$ ?