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Macaulay2Doc :: regularity

regularity -- compute the Castelnuovo-Mumford regularity

Synopsis

Description

For a free chain complex C, the regularity r is the smallest number so that each basis element of C_i has degree at most i+r. For a module M, the regularity is the regularity of a free minimal resolution of M.
i1 : R=ZZ/32003[a..d];
i2 : I=ideal(a^20,b^20,a*c^19-b*d^19);

o2 : Ideal of R
i3 : regularity I

o3 = 399

The regularity is the label of the last row in the betti diagram of a chain complex.

i4 : J=ideal(a^3,a^2*b,a*b^6,a^2*c);

o4 : Ideal of R
i5 : C=resolution J

      1      4      4      1
o5 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o5 : ChainComplex
i6 : betti C

            0 1 2 3
o6 = total: 1 4 4 1
         0: 1 . . .
         1: . . . .
         2: . 3 3 1
         3: . . . .
         4: . . . .
         5: . . . .
         6: . 1 1 .

o6 : BettiTally
i7 : regularity C

o7 = 6

See also

Ways to use regularity :