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--- status: Draft
--- author(s): Giulio
--- notes:
document {
Key => {regularity,(regularity,ChainComplex),(regularity,Ideal),(regularity,Module)},
Headline => "compute the Castelnuovo-Mumford regularity",
Usage => "regularity C",
Inputs => {
"C" => {"a ", TO ChainComplex, ", an ",TO Ideal, ", or a ", TO Module}
},
Outputs => {
ZZ} ,
"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.",
EXAMPLE {
"R=ZZ/32003[a..d];",
"I=ideal(a^20,b^20,a*c^19-b*d^19);",
"regularity I"
},
PARA{},
"The regularity is the label of the last row in the betti diagram of a chain complex.",
EXAMPLE {
"J=ideal(a^3,a^2*b,a*b^6,a^2*c);",
"C=resolution J",
"betti C",
"regularity C"
},
SeeAlso => {"resolution","betti"}
}
--document {
-- Key => regularity,
-- Headline => "compute the regularity",
-- TT "regularity M", " -- computes the regularity of a module or chain complex C.",
-- PARA{},
-- "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."
-- }
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