buchbergerResolution -- make a Buchberger resolution of a monomial ideal

i1 : R = ZZ/101[x_0..x_4];

i2 : L = {x_1^2, x_2^2, x_3^2, x_1*x_3, x_2*x_4};

i3 : BRes = (buchbergerResolution L);

i4 : BRes.dd

          1                                           5
o4 = 0 : R  <--------------------------------------- R  : 1
               | x_1^2 x_2^2 x_3^2 x_1x_3 x_2x_4 |

          5                                                                            9
     1 : R  <------------------------------------------------------------------------ R  : 2
               {2} | -x_2^2 -x_3 -x_2x_4 0      0       0    0    0       0       |
               {2} | x_1^2  0    0       -x_3^2 -x_1x_3 -x_4 0    0       0       |
               {2} | 0      0    0       x_2^2  0       0    -x_1 -x_2x_4 0       |
               {2} | 0      x_1  0       0      x_2^2   0    x_3  0       -x_2x_4 |
               {2} | 0      0    x_1^2   0      0       x_2  0    x_3^2   x_1x_3  |

          9                                                               7
     2 : R  <----------------------------------------------------------- R  : 3
               {4} | x_3    x_4   0      0     0      0       0      |
               {3} | -x_2^2 0     x_2x_4 0     0      0       0      |
               {4} | 0      -x_2  -x_3   0     0      0       0      |
               {4} | 0      0     0      x_1   x_4    0       0      |
               {4} | x_1    0     0      -x_3  0      x_4     0      |
               {3} | 0      x_1^2 0      0     -x_3^2 -x_1x_3 0      |
               {3} | 0      0     0      x_2^2 0      0       x_2x_4 |
               {4} | 0      0     0      0     x_2    0       -x_1   |
               {4} | 0      0     x_1    0     0      x_2     x_3    |

          7                         2
     3 : R  <--------------------- R  : 4
               {5} | -x_4 0    |
               {5} | x_3  0    |
               {5} | -x_2 0    |
               {5} | 0    -x_4 |
               {5} | 0    x_1  |
               {5} | x_1  -x_3 |
               {5} | 0    x_2  |

o4 : ChainComplexMap

i5 : BRes == chainComplex(buchbergerSimplicialComplex(L,R), Labels => L)

o5 = true

i6 : Scarf = scarfChainComplex L

      1      5      9      7      2
o6 = R  <-- R  <-- R  <-- R  <-- R
                                  
     0      1      2      3      4

o6 : ChainComplex

i7 : BRes == Scarf

o7 = true