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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} | 12           0       0   |
     {-2} | 30x+y        30      0   |
     {-3} | 46x2+9xy+5y2 44x+36y -32 |

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

o3 = | 149259373 3196725553 10890459 1595711466 28771425832 2208401 |
     | 11120026  238160169  811355   118882559  2143508264  164528  |
     | 5878644   125904245  428926   62847700   1133173489  86978   |

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

o4 = | 0 0 0 0 0 4 0 0 4 0 |
     | 0 0 7 0 0 0 0 0 6 0 |
     | 2 0 0 3 7 1 0 3 0 7 |

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

o5 = | 0 7 0 1 4 8 |
     | 0 0 0 2 8 2 |
     | 0 0 0 6 1 2 |
     | 0 0 0 0 4 5 |
     | 0 0 0 0 0 3 |
     | 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