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D.7.2.7 lex_solve
Procedure from library solve.lib (see solve_lib).
- Usage:
- lex_solve( i[,p] ); i=ideal, p=integer,
| p>0: gives precision of complex numbers
in decimal digits (default: p=30),
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- Assume:
| i is a reduced lexicographical Groebner bases of a
zero-dimensional ideal (i), sorted by increasing leading terms.
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- Return:
- nothing
- Create:
| The procedure creates a complec ring with the same variables but
with complex coefficients (and precision p).
In this ring a list rlist of numbers is created,
in which the complex roots of i are stored.
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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;
lex_solve(stdfglm(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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