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D.4.24.8 modregCM
Procedure from library noether.lib (see noether_lib).
- Usage:
- modregCM(i); i ideal
- Return:
- an integer, the Castelnuovo-Mumford regularity of i.
(returns -1 if i is not homogeneous)
- Assume:
- i is a homogeneous ideal and the characteristic of base field is zero..
- Note:
- This is a probabilistic procedure, and it computes the initial of the ideal modulo the prime number 2147483647 (the biggest prime less than 2^31).
Example:
| | LIB "noether.lib";
ring r=0,(t,a,b,c,d),dp;
ideal i=b4-a3d, ab3-a3c, bc4-ac3d-bcd3+ad4, c6-bc3d2-c3d3+bd5, ac5-b2c3d-ac2d3+b2d4, a2c4-a3d3+b3d3-a2cd3, b3c3-a3d3, ab2c3-a3cd2+b3cd2-ab2d3, a2bc3-a3c2d+b3c2d-a2bd3, a3c3-a3bd2, a4c2-a3b2d;
modregCM(i);
==> // WARNING: The characteristic of base field must be zero.
==> // This procedure is probabilistic and it computes the initial
==> //ideals modulo the prime number 2147483647
==> // ** redefining zz ( list l11;int zz;) noether.lib::modregCM:937
==> mreg(i)=7 and the time of this computation: 3sec./100
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