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Reg, Reg5

Castelnuovo-Mumford regularity of a module

Syntax
Reg(M: IDEAL or TAGGED("Quotient")): INT

Description
***** 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.

Example
  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
-------------------------------

See Also