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DGAlgebras :: toComplex

toComplex -- Converts a DGAlgebra to a ChainComplex

Synopsis

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 :

For the programmer

The object toComplex is a method function.