WeylAlgebras Fourier documentation example error?

[mikestillman]

@antonleykin @mahrud (not sure who I should tag on this) The following code in the documentation (DOC/basics.m2:150) purports to create a chain complex (OldChainComplexes):

     needsPackage "WeylAlgebras"
      makeWA(QQ[x,y])
      C = chainComplex{matrix{{x*dx, y^2+dx}},matrix{{dx*dy},{y^2*dy^3}}}

But this C isn't a chain complex. Is it supposed to be?

I found this when trying to get this package to use Complexes, rather than OldChainComplexes.

[mikestillman]

Here is the output under M2 version 1.25.11.

i1 : needsPackage "WeylAlgebras";

i2 : makeWA(QQ[x,y])

o2 = QQ[x..y, dx, dy]

o2 : PolynomialRing, 2 differential variable(s)

i3 :  C = chainComplex{matrix{{x*dx, y^2+dx}},matrix{{dx*dy},{y^2*dy^3}}}

                       1                       2                       1
o3 = (QQ[x..y, dx, dy])  <-- (QQ[x..y, dx, dy])  <-- (QQ[x..y, dx, dy])
                                                      
     0                       1                       2

o3 : ChainComplex

i4 : C.dd^2 == 0

o4 = false