-- -*- M2-comint -*- hash: 6082019841722325855

i1 : R = ZZ/101[x_(0,0)..x_(2,2),y_(0,0)..y_(2,2)]

o1 = R

o1 : PolynomialRing

i2 : M = genericMatrix(R,x_(0,0),3,3)

o2 = | x_(0,0) x_(1,0) x_(2,0) |
     | x_(0,1) x_(1,1) x_(2,1) |
     | x_(0,2) x_(1,2) x_(2,2) |

             3      3
o2 : Matrix R  <-- R

i3 : N = genericMatrix(R,y_(0,0),3,3)

o3 = | y_(0,0) y_(1,0) y_(2,0) |
     | y_(0,1) y_(1,1) y_(2,1) |
     | y_(0,2) y_(1,2) y_(2,2) |

             3      3
o3 : Matrix R  <-- R

i4 : I = ideal flatten(M*N-N*M);

o4 : Ideal of R

i5 : dim I

o5 = 12

i6 : needsPackage "SimplicialComplexes"

o6 = SimplicialComplexes

o6 : Package

i7 : R = QQ[a..d]

o7 = R

o7 : PolynomialRing

i8 : D = simplicialComplex {a*b*c,a*b*d,a*c*d,b*c*d}

o8 = simplicialComplex | bcd acd abd abc |

o8 : SimplicialComplex

i9 : I = monomialIdeal D

o9 = monomialIdeal(a*b*c*d)

o9 : MonomialIdeal of R

i10 : facets D

o10 = {b*c*d, a*c*d, a*b*d, a*b*c}

o10 : List

i11 : dim D

o11 = 2

i12 : dim I

o12 = 3

i13 : 
