acyclicClosure(...,EndDegree=>...) -- Option to specify the degree to stop computing the acyclic closure

Usage:

A = acyclicClosure(B,EndDegree=>n)
Inputs:
- B, an instance of the type DGAlgebra,
- n, an integer,

Description

All generators of the acyclic closure will be found up to homological degree n. Note that B can be an ordinary ring, a factor ring of a polynomial ring, treated as a DGAlgebra generated in homological degree 0, as in the following example:

The default value of EndDegree is 3.

i1 : R = ZZ/101[x,y,z,w]/(ideal"x3,y3,z3,x2yz")

o1 = R

o1 : QuotientRing

i2 : acyclicClosure R

o2 = {Ring => R                                                                                                                                 }
      Underlying algebra => R[T ..T  ]
                               1   17
                                    2     2     2                       2     2     2     2      2                                 2       2
      Differential => {x, y, z, w, x T , y T , z T , x*y*z*T , y*z*T , z T , y T , z T , y T , -x T T , -x*y*z*T T , -x*y*z*T T , y T   - z T  }
                                      1     2     3         1       5     8     8     9     9      1 8          1 7          1 6     10      11

o2 : DGAlgebra

i3 : acyclicClosure(R,EndDegree => 3)

o3 = {Ring => R                                                                                                                                 }
      Underlying algebra => R[T ..T  ]
                               1   17
                                    2     2     2                       2     2     2     2      2                                 2       2
      Differential => {x, y, z, w, x T , y T , z T , x*y*z*T , y*z*T , z T , y T , z T , y T , -x T T , -x*y*z*T T , -x*y*z*T T , y T   - z T  }
                                      1     2     3         1       5     8     8     9     9      1 8          1 7          1 6     10      11

o3 : DGAlgebra

Functions with optional argument named EndDegree:

acyclicClosure(...,EndDegree=>...) -- Option to specify the degree to stop computing the acyclic closure
isAcyclic(...,EndDegree=>...) -- Option to specify the degree to finish checking acyclicity
killCycles(...,EndDegree=>...) -- Option to specify the degree to stop looking for cycles
liftToDGMap(...,EndDegree=>...) -- see liftToDGMap -- Lift a ring homomorphism in degree zero to a DG algebra morphism
toComplexMap(...,EndDegree=>...) -- see toComplexMap -- Construct the ComplexMap associated to a DGAlgebraMap

Further information

Default value: 3
Function: acyclicClosure -- Compute the acyclic closure of a DGAlgebra.
Option key: EndDegree -- Option to specify the degree to stop computing killing cycles and acyclic closure

The source of this document is in DGAlgebras.m2:3219:0.