Singular

D.8.4.3 ures_solve

Usage:

ures_solve(i [, k, p] ); i = ideal, k, p = integers
k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky,
k=1: use resultant matrix of Macaulay which works only for homogeneous ideals,
p>0: defines precision of the long floats for internal computation if the basering is not complex (in decimal digits),
(default: k=0, p=30)

Assume:

i is a zerodimensional ideal given by a quadratic system, that is,
nvars(basering) = ncols(i) = number of vars actually occurring in i,

Return:

If the ground field is the field of complex numbers: list of numbers (the complex roots of the polynomial system i=0).
Otherwise: ring R with the same number of variables but with complex coefficients (and precision p). R comes with a list SOL of numbers, in which complex roots of the polynomial system i are stored:

LIB "solve.lib";
// compute the intersection points of two curves
ring rsq = 0,(x,y),lp;
ideal gls=  x2 + y2 - 10, x2 + xy + 2y2 - 16;
def R=ures_solve(gls,0,16);
==> 
==> // 'ures_solve' created a ring, in which a list SOL of numbers (the compl\
   ex
==> // solutions) is stored.
==> // To access the list of complex solutions, type (if the name R was assig\
   ned
==> // to the return value):
==>         setring R; SOL; 
setring R; SOL;
==> [1]:
==>    [1]:
==> -2.82842712474619
==>    [2]:
==> -1.414213562373095
==> [2]:
==>    [1]:
==>       -1
==>    [2]:
==>       3
==> [3]:
==>    [1]:
==>       1
==>    [2]:
==>       -3
==> [4]:
==>    [1]:
==> 2.82842712474619
==>    [2]:
==> 1.414213562373095