toComplex -- Converts a DGAlgebra to a ChainComplex

Synopsis

Usage:

C = toComplex A or C = toComplex(A,n)
Inputs:
- A, an instance of the type DGAlgebra,
Outputs:
- C, a chain complex, The DG algebra A as a ChainComplex

Description

i1 : R = ZZ/101[x_1..x_10]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA(R)

o2 = {Ring => R                                                }
      Underlying algebra => R[T ..T  ]
                               1   10
      Differential => {x , x , x , x , x , x , x , x , x , x  }
                        1   2   3   4   5   6   7   8   9   10

o2 : DGAlgebra

i3 : C = toComplex A

      1      10      45      120      210      252      210      120      45      10      1
o3 = R  <-- R   <-- R   <-- R    <-- R    <-- R    <-- R    <-- R    <-- R   <-- R   <-- R
                                                                                          
     0      1       2       3        4        5        6        7        8       9       10

o3 : ChainComplex

Warning: The term order that the internal command koszul uses to order the monomials is not GRevLex, and so the differentials used in koszul and koszulComplexDGA will not match up exactly. Also, this command will only execute if all of the variables of the DGAlgebra A are of odd homological degree. Otherwise, you need to use the function toComplex(DGAlgebra,ZZ).

Ways to use toComplex :

toComplex(DGAlgebra)
toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a ChainComplex

For the programmer

The object toComplex is a method function.