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# Module ^** ZZ -- tensor power

- Operator: ^**
- Usage:
    `M^**i`
- Inputs:
  - M, a module
  - i, an integer
- Outputs:
  - a module, the i-th tensor power of M

## Description

The second symmetric power of the canonical module of the rational quartic:

    i1 : R = QQ[a..d];

    i2 : I = monomialCurveIdeal(R,{1,3,4})

                            3      2     2    2    3    2
    o2 = ideal (b*c - a*d, c  - b*d , a*c  - b d, b  - a c)

    o2 : Ideal of R

    i3 : M = Ext^1(I,R^{-4})

    o3 = cokernel {1} | c 0 -d 0 -b |
                  {1} | b c 0  a 0  |
                  {1} | 0 d c  b a  |

                                3
    o3 : R-module, quotient of R

    i4 : M^**2

    o4 = cokernel {2} | c 0 -d 0 -b 0 0 0  0 0  0 0 0  0 0  c 0 -d 0 -b 0 0 0  0 0  0 0 0  0 0  |
                  {2} | b c 0  a 0  0 0 0  0 0  0 0 0  0 0  0 0 0  0 0  c 0 -d 0 -b 0 0 0  0 0  |
                  {2} | 0 d c  b a  0 0 0  0 0  0 0 0  0 0  0 0 0  0 0  0 0 0  0 0  c 0 -d 0 -b |
                  {2} | 0 0 0  0 0  c 0 -d 0 -b 0 0 0  0 0  b c 0  a 0  0 0 0  0 0  0 0 0  0 0  |
                  {2} | 0 0 0  0 0  b c 0  a 0  0 0 0  0 0  0 0 0  0 0  b c 0  a 0  0 0 0  0 0  |
                  {2} | 0 0 0  0 0  0 d c  b a  0 0 0  0 0  0 0 0  0 0  0 0 0  0 0  b c 0  a 0  |
                  {2} | 0 0 0  0 0  0 0 0  0 0  c 0 -d 0 -b 0 d c  b a  0 0 0  0 0  0 0 0  0 0  |
                  {2} | 0 0 0  0 0  0 0 0  0 0  b c 0  a 0  0 0 0  0 0  0 d c  b a  0 0 0  0 0  |
                  {2} | 0 0 0  0 0  0 0 0  0 0  0 d c  b a  0 0 0  0 0  0 0 0  0 0  0 d c  b a  |

                                9
    o4 : R-module, quotient of R

## Ways to use this method:

- Module ^** ZZ -- tensor power

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/tensor-doc.m2:444:0.