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Castelnuovo-Mumford regularity of a module
Reg(M: IDEAL or TAGGED("Quotient")): INT |
***** NOT YET IMPLEMENTED *****
These functions computes the Castelnuovo-Mumford regularity of a module.
The implementation of
Reg
is just implementation of the
definition (i.e. computes the resolution).
The implementation of
Reg5
implements Bermejo-Gimenez
Algorithm and uses functions from the CoCoAServer (linked with the
Frobby library). This algorithm has a chance when the computation of the
resolution is unfeasable.
Note: this is different from
RegularityIndex
, the regularity
of a Hilbert Function.
Use R ::= QQ[x,y,z];
I := ideal(x^3, y^2);
Res(I);
0 --> R(-5) --> R(-2)(+)R(-3)
-------------------------------
BettiDiagram(I);
0 1
---------------
2: 1 -
3: 1 -
4: - 1
---------------
Tot: 2 1
-------------------------------
Reg(I);
4
-------------------------------
Reg(R/I);
3
-------------------------------
Reg5(I);
4
-------------------------------
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