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Macaulay2Doc :: Matrix ** Module

Matrix ** Module -- tensor product

Synopsis

Description

i1 : R = ZZ/101[x,y];
i2 : R^2 ** vars R

o2 = | x y 0 0 |
     | 0 0 x y |

             2       4
o2 : Matrix R  <--- R
i3 : (vars R) ** R^2

o3 = | x 0 y 0 |
     | 0 x 0 y |

             2       4
o3 : Matrix R  <--- R
When N is a free module of rank 1 the net effect of the operation is to shift the degrees of f.
i4 : R = ZZ/101[t];
i5 : f = matrix {{t}}

o5 = | t |

             1       1
o5 : Matrix R  <--- R
i6 : degrees source f

o6 = {{1}}

o6 : List
i7 : degrees source (f ** R^{-3})

o7 = {{4}}

o7 : List

See also