D.7.2.12 triang_solve

Procedure from library solve.lib (see solve_lib).

Usage:

triang_solve(l,p [, d] ); l=list, p,d=integers,
l a list of finitely many triangular systems, such that the union of their varieties equals the variety of the initial ideal.
p>0: gives precision of complex numbers in digits,
d>0: gives precision (1<d<p) for near-zero-determination,
(default: d=1/2*p).

Assume:

the ground field has char 0;
l was computed using Algorithm of Lazard or Algorithm of Moeller (see triang.lib).

Return:

nothing

Create:

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