# Singular

#### D.8.3.7 lex_solve

Procedure from library `solve.lib` (see solve_lib).

Usage:
lex_solve( i[,p] ); i=ideal, p=integer,
p>0: gives precision of complex numbers in decimal digits (default: p=30).

Assume:
i is a reduced lexicographical Groebner bases of a zero-dimensional ideal, sorted by increasing leading terms.

Return:
ring `R` with the same number of variables but with complex coefficients (and precision p). `R` comes with a list `rlist` of numbers, in which the complex roots of i are stored.

Example:
 ```LIB "solve.lib"; ring r = 0,(x,y),lp; // compute the intersection points of two curves ideal s = x2 + y2 - 10, x2 + xy + 2y2 - 16; def R = lex_solve(stdfglm(s),10); ==> ==> // 'lex_solve' created a ring, in which a list rlist of numbers (the ==> // complex solutions) is stored. ==> // To access the list of complex solutions, type (if the name R was assig\ ned ==> // to the return value): ==> setring R; rlist; setring R; rlist; ==> [1]: ==> [1]: ==> 1 ==> [2]: ==> -3 ==> [2]: ==> [1]: ==> -2.828427125 ==> [2]: ==> -1.414213562 ==> [3]: ==> [1]: ==> 2.828427125 ==> [2]: ==> 1.414213562 ==> [4]: ==> [1]: ==> -1 ==> [2]: ==> 3 ```