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D.8.8.12 rootIsolationPrimdec
Procedure from library rootisolation.lib (see rootisolation_lib).
- Usage:
rootIsolationPrimdec(I);
I ideal
- Assume:
I is a zero-dimensional radical ideal
- Return:
L, where L
contains boxes which contain exactly one element of V(I)
- Purpose:
- same as
rootIsolation, but speeds up computation and improves output
by doing a primary decomposition before doing the root isolation
- Theory:
- For the primary decomposition we use the algorithm of Gianni-Traeger-Zarcharias.
- Note:
- This algorithm and some procedures used therein perform Groebner basis
computations in
basering. It is thus advised to define I
w.r.t. a fast monomial ordering.
Example:
| | LIB "rootisolation.lib";
ring R = 0,(x,y),dp;
ideal I = 2x2-xy+2y2-2,2x2-3xy+3y2-2; // V(I) has four elements
list result = rootIsolationPrimdec(I);
result;
==> [1]:
==> [1, 1] x [0, 0]
==> [2]:
==> [1/2, 1/2] x [1, 1]
==> [3]:
==> [-1/2, -1/2] x [-1, -1]
==> [4]:
==> [-1, -1] x [0, 0]
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