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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]:
==> 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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