D.7.2.7 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:

nothing

Create:

The procedure creates a complec ring with the same variables but with complex coefficients (and precision p).
In this ring a list rlist of numbers is created, 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;
lex_solve(stdfglm(s),10);
→ // name of new ring: rC
→ // list of roots: rlist
rlist;
→ [1]:
→    [1]:
→       2.8284271247
→    [2]:
→       1.4142135624
→ [2]:
→    [1]:
→       -2.8284271247
→    [2]:
→       -1.4142135624
→ [3]:
→    [1]:
→       1
→    [2]:
→       -3
→ [4]:
→    [1]:
→       -1
→    [2]:
→       3