DGAlgebra ** DGAlgebra -- Tensor product of a DGAlgebra and another ring.

i1 : R = ZZ/101[a,b,c,d]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA({a,b})

o2 = {Ring => R                      }
      Underlying algebra => R[T ..T ]
                               1   2
      Differential => {a, b}

o2 : DGAlgebra

i3 : B = koszulComplexDGA({c,d})

o3 = {Ring => R                      }
      Underlying algebra => R[T ..T ]
                               1   2
      Differential => {c, d}

o3 : DGAlgebra

i4 : C = A ** B

o4 = {Ring => R                      }
      Underlying algebra => R[T ..T ]
                               1   4
      Differential => {a, b, c, d}

o4 : DGAlgebra

i5 : Cdd = toComplex C

      1      4      6      4      1
o5 = R  <-- R  <-- R  <-- R  <-- R
                                  
     0      1      2      3      4

o5 : ChainComplex

i6 : Cdd.dd

          1                   4
o6 = 0 : R  <--------------- R  : 1
               | a b c d |

          4                                 6
     1 : R  <----------------------------- R  : 2
               {1} | -b -c 0  -d 0  0  |
               {1} | a  0  -c 0  -d 0  |
               {1} | 0  a  b  0  0  -d |
               {1} | 0  0  0  a  b  c  |

          6                           4
     2 : R  <----------------------- R  : 3
               {2} | c  d  0  0  |
               {2} | -b 0  d  0  |
               {2} | a  0  0  d  |
               {2} | 0  -b -c 0  |
               {2} | 0  a  0  -c |
               {2} | 0  0  a  b  |

          4                  1
     3 : R  <-------------- R  : 4
               {3} | -d |
               {3} | c  |
               {3} | -b |
               {3} | a  |

o6 : ChainComplexMap