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D.7.2.9 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:
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 with
factorization) 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;
triangLf_solve(s,10);
→ // name of new ring: rC
→ // list of roots: rlist
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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