tensor

tensor(M,N) -- tensor product of rings or monoids.

This method allows all of the options available for monoids, see monoid for details. This routine essentially combines the variables of M and N into one monoid.

For rings, the rings should be quotient rings of polynomial rings over the same base ring.

Here is an example with monoids.

i1 : M = monoid[a..d, MonomialOrder => Eliminate 1]



o1 = M



o1 : GeneralOrderedMonoid

i2 : N = monoid[e,f,g, Degrees => {1,2,3}]



o2 = N



o2 : GeneralOrderedMonoid

i3 : P = tensor(M,N,MonomialOrder => GRevLex)



o3 = P



o3 : GeneralOrderedMonoid

i4 : describe P



o4 = [a,b,c,d,e,f,g,Degrees => {{1}, {1}, {1}, {1}, {1}, {2}, {3}},MonomialOrder => GRevLex]



o4 : String

i5 : tensor(M,M,Variables => {t_0 .. t_7}, MonomialOrder => ProductOrder{4,4})



o5 = [t ,t ,t ,t ,t ,t ,t ,t ,MonomialOrder => ProductOrder {4, 4}]

       0  1  2  3  4  5  6  7



o5 : GeneralOrderedMonoid

i6 : describe oo



o6 = [t_0,t_1,t_2,t_3,t_4,t_5,t_6,t_7,MonomialOrder => new ProductOrder from {4, 4}]



o6 : String

Here is a similar example with rings.

i7 : tensor(ZZ/101[x,y], ZZ/101[r,s], MonomialOrder => Eliminate 2)



      ZZ

o7 = ---[x,y,r,s,MonomialOrder => Eliminate 2]

     101



o7 : PolynomialRing