Singular

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