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D.8.3.9 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:
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.

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

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 = triangLf_solve(s,10);
==> 
==> // 'triangLf_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]:
==> -2.828427125
==>    [2]:
==> -1.414213562
==> [2]:
==>    [1]:
==> 2.828427125
==>    [2]:
==> 1.414213562
==> [3]:
==>    [1]:
==> -1
==>    [2]:
==> 3
==> [4]:
==>    [1]:
==> 1
==>    [2]:
==> -3