
D.8.3.3 ures_solve
Procedure from library solve.lib (see solve_lib).
 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:
Example:
 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

