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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} | 41             0        0 |
     {-2} | -9x-18y        35       0 |
     {-3} | 17x2-37xy+39y2 -49x-36y 8 |

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

o3 = | 10234796479 28887529183 9374509155 439476 480620491 9469997744 |
     | 3633391864  10255183258 3327986576 156016 170622111 3361885390 |
     | 9028006437  25481385970 8269156027 387658 423950285 8353385508 |

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

o4 = | 4 0 0 3 8 0 0 0 0 0 |
     | 0 3 8 8 7 0 8 4 5 0 |
     | 0 0 0 0 0 0 0 0 0 0 |

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

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