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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} | -29          0       0  |
     {-2} | 25x+32y      46      0  |
     {-3} | 24x2-27xy+y2 14x-24y 14 |

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

o3 = | 20   14030   12667   1  1736   4   |
     | 161  111874  101298  3  13843  37  |
     | 1794 1247806 1129519 39 154400 407 |

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

o4 = | 0 0 0 0 0 0 0 0 0 0 |
     | 0 6 0 0 4 0 0 4 0 0 |
     | 0 0 0 0 0 0 4 6 5 0 |

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

o5 = | 0 6 5 3 9 4 |
     | 0 0 3 8 4 3 |
     | 0 0 0 2 4 1 |
     | 0 0 0 0 5 2 |
     | 0 0 0 0 0 8 |
     | 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