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D.8.2.9 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:
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:
 


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