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 = | bcd acd abd abc | o8 : SimplicialComplex |
i9 : I = monomialIdeal D o9 = monomialIdeal(a*b*c*d) o9 : MonomialIdeal of R |
i10 : facets D o10 = | bcd acd abd abc | 1 4 o10 : Matrix R <--- R |
i11 : dim D o11 = 2 |
i12 : dim I o12 = 3 |