-- -*- M2-comint -*- {* hash: 1283043676 *}
i1 : kk = ZZ/101
o1 = kk
o1 : QuotientRing
i2 : A = kk[a,b]
o2 = A
o2 : PolynomialRing
i3 : B = kk[c,d,e]
o3 = B
o3 : PolynomialRing
i4 : describe(A**B)
o4 = kk[a..e, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
{0} {1} {GRevLex => {2:1} }
{Position => Up }
{GRevLex => {3:1} }
i5 : describe tensor(A,B,VariableBaseName=>p)
o5 = kk[p , p , p , p , p , Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
0 1 2 3 4 {0} {1} {GRevLex => {2:1} }
{Position => Up }
{GRevLex => {3:1} }
i6 : describe tensor(A,B,Variables=>{a1,a2,b1,b2,b3})
o6 = kk[a1, a2, b1, b2, b3, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
{0} {1} {GRevLex => {2:1} }
{Position => Up }
{GRevLex => {3:1} }
i7 : describe (C = tensor(A,B,DegreeRank=>1,Degrees=>{5:1}))
o7 = kk[a..e, Degrees => {5:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
{GRevLex => {2:1} }
{Position => Up }
{GRevLex => {3:1} }
i8 : degreeLength C
o8 = 1
i9 : degreesRing C
o9 = ZZ[T]
o9 : PolynomialRing
i10 : describe tensor(A,B,MonomialSize=>8)
o10 = kk[a..e, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 8 }, DegreeRank => 2]
{0} {1} {MonomialSize => 32}
{GRevLex => {2:1} }
{Position => Up }
{GRevLex => {3:1} }
i11 : describe (C = tensor(A,B,MonomialOrder=>Eliminate numgens A))
o11 = kk[a..e, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
{0} {1} {Weights => {2:1} }
{GRevLex => {5:1} }
{Position => Up }
i12 : describe (C = tensor(A,B,MonomialOrder=>GRevLex))
o12 = kk[a..e, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder =>
{0} {1}
-----------------------------------------------------------------------
{MonomialSize => 32}, DegreeRank => 2]
{GRevLex => {5:1} }
{Position => Up }
i13 : As = kk[a,b,SkewCommutative=>true]
o13 = As
o13 : PolynomialRing
i14 : D = kk[c,d,e,SkewCommutative=>true]
o14 = D
o14 : PolynomialRing
i15 : E = tensor(As,D)
o15 = E
o15 : PolynomialRing
i16 : describe E
o16 = kk[a..e, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2, SkewCommutative => {0, 1, 2, 3, 4}]
{0} {1} {GRevLex => {2:1} }
{Position => Up }
{GRevLex => {3:1} }
i17 : c*a
o17 = -a*c
o17 : E
i18 : E = kk[x,Dx,WeylAlgebra=>{x=>Dx}]
o18 = E
o18 : PolynomialRing
i19 : tensor(E,E,Variables=>{x,Dx,y,Dy})
o19 = kk[x, Dx, y, Dy]
o19 : PolynomialRing
i20 : describe oo
o20 = kk[x, Dx, y, Dy, Degrees => {2:{1}, 2:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2, WeylAlgebra => {0 => 1, 2 => 3}]
{0} {1} {GRevLex => {2:1} }
{Position => Up }
{GRevLex => {2:1} }
i21 : A = ZZ/101[a,b]
o21 = A
o21 : PolynomialRing
i22 : B = A[x,y]
o22 = B
o22 : PolynomialRing
i23 : C = tensor(B,B,Variables=>{x1,y1,x2,y2})
o23 = C
o23 : PolynomialRing
i24 : describe C
o24 = A[x1, y1, x2, y2, Degrees => {2:{1}, 2:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
{0} {1} {GRevLex => {2:1} }
{Position => Up }
{GRevLex => {2:1} }
i25 : C.FlatMonoid
o25 = [x1, y1, x2, y2, a..b, Degrees => {2:{1}, 2:{0}, 2:{0}}, Heft => {3:1}, MonomialOrder => {MonomialSize => 32 }, DegreeRank => 3]
{0} {1} {0} {GRevLex => {2:1} }
{0} {0} {1} {Position => Up }
{2:(GRevLex => {1, 1})}
o25 : GeneralOrderedMonoid
i26 :
