resolution(NCMatrix) -- Compute the resolution of coker M as a map of free right modules

Synopsis

• Function: resolution

• Usage:

  res M

• Inputs:
  • M, an instance of the type NCMatrix,
• Optional inputs:
  • LengthLimit => an integer, default value infinity, The length of the resolution. This defaults to the number of variables of ring M.
  • DegreeLimit => ..., default value null,
  • FastNonminimal => ..., default value false,
  • HardDegreeLimit => ..., default value {},
  • PairLimit => ..., default value infinity,
  • ParallelizeByDegree (missing documentation) => ..., default value false,
  • SortStrategy => ..., default value 0,
  • StopBeforeComputation => ..., default value false,
  • Strategy => ..., default value null,
  • SyzygyLimit => ..., default value infinity,
• Outputs:
  • an instance of the type NCChainComplex,

Description

i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{x,y,z})
--Calling Bergman for NCGB calculation.
Complete!

o1 = A

o1 : NCQuotientRing

i2 : M = ncMatrix {{x,y,z}}

o2 = | x y z |

o2 : NCMatrix

i3 : Mres = res M
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!

      1      3      3      1
o3 = A  <-- A  <-- A  <-- A
                           
     0      1      2      3

o3 : NCChainComplex

i4 : Mres#0

o4 = | x y z |

o4 : NCMatrix

i5 : Mres#1

o5 = | 0  -z -y |
     | -z 0  -x |
     | -y -x 0  |

o5 : NCMatrix

i6 : Mres#2

o6 = | -x |
     | -y |
     | -z |

o6 : NCMatrix

i7 : betti Mres

            0 1 2 3
o7 = total: 1 3 3 1
         0: 1 3 3 1

o7 : BettiTally

See also

• resolution -- projective resolution