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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} | 21              0      0  |
     {-2} | -10x+41y        18     0  |
     {-3} | -18x2-46xy-48y2 20x-9y 10 |

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

o3 = | 18420067221738 96142961607 1748950465978 291429844198 3498648957507
     | 169539527196   884906223   16097456733   2682339722   32201798342  
     | 2026215974282  10575770559 192385365902  32057418607  384853014963 
     ------------------------------------------------------------------------
     1754571411332 |
     16149192285   |
     193003672509  |

              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 0 0 7 0 0 0 0 0 0 |
     | 0 4 0 0 5 0 0 0 3 7 |

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

o5 = | 0 9 9 5 9 0 |
     | 0 0 1 8 6 8 |
     | 0 0 0 1 5 6 |
     | 0 0 0 0 7 3 |
     | 0 0 0 0 0 2 |
     | 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