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D.7.2.9 triangLf_solve

Procedure from library solve.lib (see solve_lib).

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

Assume:
the ground field has char 0; i is a zero-dimensional ideal

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.
The proc uses a triangular system (Lazard's Algorithm with factorization) computed from a standard basis to determine recursively all complex roots with Laguerre's algorithm of input ideal i.

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;
triangLf_solve(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


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