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Macaulay2Doc :: random(Module,Module)

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} | 50             0       0  |
     {-2} | -21x+4y        29      0  |
     {-3} | 21x2+32xy-18y2 40x-50y 20 |

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

o3 = | 218727217 12640751 335540839  1686711 52801  33769199  |
     | 684861758 39563322 1050621603 5279110 165232 105736147 |
     | 500506270 28948583 767804119  3862734 120956 77272039  |

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

o4 = | 0 4 0 0 0 2 0 0 0 2 |
     | 0 2 1 0 0 0 0 0 7 0 |
     | 7 0 9 0 0 0 4 0 9 0 |

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

o5 = | 0 4 9 9 5 7 |
     | 0 0 0 0 3 7 |
     | 0 0 0 1 9 6 |
     | 0 0 0 0 5 7 |
     | 0 0 0 0 0 1 |
     | 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