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D.7.2.11 triangL_solve
Procedure from library solve.lib (see solve_lib).
- Usage:
- triangL_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) 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;
triangL_solve(s,10);
==> // name of new ring: rC
==> // list of roots: rlist
rlist;
==> [1]:
==> [1]:
==> 2.8284271247
==> [2]:
==> 1.4142135624
==> [2]:
==> [1]:
==> -2.8284271247
==> [2]:
==> -1.4142135624
==> [3]:
==> [1]:
==> 1
==> [2]:
==> -3
==> [4]:
==> [1]:
==> -1
==> [2]:
==> 3
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