Hi!
I have a problem. Here is its formulation. I work in some polynomial
ring - lets say
R,(x,y) = PolynomialRing(QQ, 2, 'xy', order='lex').objgens()
and consider ideal in R
I = ideal(x+y^3-2,y+x^3-2)
then I calculate grobner basis for ideal I
B = I.groebner_basis(); B
B[0] is univariate polynomial. Here the real problem begins. I would
like to get real roots of polynomial B[0]. I can do B[0].factor() but
it gives only part of information us factorization is over Q[x,y].
More intuitive way for me is to treat it symbolicly. I want to write
solve(B[0] == 0, x) but it doesn't work us function solve() needs
symbolic object and gets boolean expression.
The question is: how to find real roots for polynomial object either
symbolicly (more desired) or numericly?
The only solution I have figured out is as follow. I write
x,y=var('x,y') and then declare f = ... (here I copy paste B[0]) but
it's not the way I want do this.
Does anyone know how to solve it?
Best regards
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