tensor -- tensor product

tensor -- tensor product

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}}]

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

       0   1   2   3   4   5   6   7

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

See also:

** -- a binary operator, usually used for tensor product

Ways to use tensor :

tensor(CoherentSheaf,CoherentSheaf)

tensor(Module,Module)

tensor(Monoid,Monoid)

tensor(PolynomialRing,PolynomialRing)

tensor(PolynomialRing,QuotientRing)

tensor(QuotientRing,PolynomialRing)

tensor(QuotientRing,QuotientRing)

tensor(Ring,Ring)

Optional arguments :