-- -*- M2-comint -*- hash: 13668604610970724378

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}]
                            {0}    {1}                                   {GRevLex => {2:1}  }
                                                                         {Position => Up    }
                                                                         {GRevLex => {3:1}  }

i5 : describe tensor(A, B, VariableBaseName => p)

o5 = kk[p ..p , Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}]
         0   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}]
                                          {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}]
                                                              {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 }]
                             {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}]
                             {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}]
                             {0}    {1}

i13 : As = kk[a, b, SkewCommutative => true]

o13 = As

o13 : PolynomialRing, 2 skew commutative variable(s)

i14 : D  = kk[c, d, e, SkewCommutative => true]

o14 = D

o14 : PolynomialRing, 3 skew commutative variable(s)

i15 : E = tensor(As, D)

o15 = E

o15 : PolynomialRing, 5 skew commutative variable(s)

i16 : describe E

o16 = kk[a..e, Degrees => {2:{1}, 3:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, SkewCommutative => {0..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, 1 differential variable(s)

i19 : tensor(E, E, Variables => {x, Dx, y, Dy})

o19 = kk[x, Dx, y, Dy]

o19 : PolynomialRing, 2 differential variable(s)

i20 : describe oo

o20 = kk[x, Dx, y, Dy, Degrees => {2:{1}, 2:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, WeylAlgebra => {{x, Dx}, {y, Dy}}]
                                     {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}]
                                      {0}    {1}                                   {GRevLex => {2:1}  }
                                                                                   {Position => Up    }
                                                                                   {GRevLex => {2:1}  }

i25 : C.FlatMonoid

o25 = monoid[x1, y1, x2, y2, a..b, Degrees => {2:{1}, 2:{0}, 2:{0}}, Heft => {3:1}, MonomialOrder => {MonomialSize => 32   }]
                                                 {0}    {1}    {0}                                   {GRevLex => {2:1}     }
                                                 {0}    {0}    {1}                                   {Position => Up       }
                                                                                                     {2:(GRevLex => {1, 1})}

o25 : GeneralOrderedMonoid

i26 : 
