tensorModule -- Constructor for making modules whose elements are tensors

i1 : R=QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : M=tensorModule(R,{4,3,2})

      24
o2 = R  {4x3x2}

o2 : Free R-TensorModule of order 3, dimensions {4, 3, 2}

i3 : M_(2,0,1) -- same as M_13

     +------+------+------+
o3 = |{0, 0}|{0, 0}|{0, 0}|
     +------+------+------+
     |{0, 0}|{0, 0}|{0, 0}|
     +------+------+------+
     |{0, 1}|{0, 0}|{0, 0}|
     +------+------+------+
     |{0, 0}|{0, 0}|{0, 0}|
     +------+------+------+

      24
o3 : R  {4x3x2}

i4 : M.factors

       4   3   2
o4 = {R , R , R }

o4 : List

i5 : M.dimensions

o5 = {4, 3, 2}

o5 : List

i6 : I = ideal(x*y)

o6 = ideal(x*y)

o6 : Ideal of R

i7 : M=R^4/I

o7 = cokernel | xy 0  0  0  |
              | 0  xy 0  0  |
              | 0  0  xy 0  |
              | 0  0  0  xy |

                            4
o7 : R-module, quotient of R

i8 : N=tensorModule(M,{2,2})

o8 = cokernel | xy 0  0  0  |
              | 0  xy 0  0  |
              | 0  0  xy 0  |
              | 0  0  0  xy |

                                                                4
o8 : R-TensorModule of order 2, dimensions {2, 2}, quotient of R

i9 : N_(0,0)

     +-+-+
o9 = |1|0|
     +-+-+
     |0|0|
     +-+-+

o9 : cokernel | xy 0  0  0  |
              | 0  xy 0  0  |
              | 0  0  xy 0  |
              | 0  0  0  xy |

i10 : oo*x*y==0_N

o10 = true