# Singular          #### 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; ==> : ==> : ==> -2.82842712474619 ==> : ==> -1.414213562373095 ==> : ==> : ==> -1 ==> : ==> 3 ==> : ==> : ==> 1 ==> : ==> -3 ==> : ==> : ==> 2.82842712474619 ==> : ==> 1.414213562373095 ```

### Misc 