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random(Module,Module) -- make a random module map

Synopsis

Description

i1 : R = ZZ/101[x,y];
i2 : random(R^{1,2,3},R^{1,2,3})

o2 = {-1} | 11              0        0 |
     {-2} | -11x-18y        -24      0 |
     {-3} | -16x2+19xy+16y2 -29x+40y 6 |

             3       3
o2 : Matrix R  <--- R
i3 : random(ZZ^3,ZZ^6,MaximalRank=>true)

o3 = | 28187616  737478  1036 3696403  6672353  75578  |
     | 194314367 5083883 7148 25481579 45996475 520980 |
     | 1920519   50247   70   251846   454621   5152   |

              3        6
o3 : Matrix ZZ  <--- ZZ
i4 : random(ZZ^3,ZZ^10,Density=>.3)

o4 = | 0 0 1 0 6 0 0 0 0 0 |
     | 0 0 0 0 0 0 2 1 9 0 |
     | 0 0 0 0 4 0 0 0 0 0 |

              3        10
o4 : Matrix ZZ  <--- ZZ
i5 : random(ZZ^6,ZZ^6,UpperTriangular=>true)

o5 = | 0 0 8 5 7 3 |
     | 0 0 6 9 1 6 |
     | 0 0 0 3 9 1 |
     | 0 0 0 0 1 9 |
     | 0 0 0 0 0 7 |
     | 0 0 0 0 0 0 |

              6        6
o5 : Matrix ZZ  <--- ZZ

Caveat

Over a polynomial ring, specifying MaximalRank=>true will yield a non-homogeneous matrix.

See also