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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} | 16           0       0 |
     {-2} | -5x-44y      -33     0 |
     {-3} | -4x2-xy+24y2 -43x-4y 6 |

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

o3 = | 560426502 10609258 59283514 21674321 376498895 69339271 |
     | 62967974  1192027  6660932  2435267  42302379  7790769  |
     | 68990928  1306042  7298053  2668195  46348515  8535964  |

              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 0 2 0 0 0 7 0 |
     | 0 2 0 0 0 0 0 0 0 9 |

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

o5 = | 0 8 6 9 7 0 |
     | 0 0 8 0 0 4 |
     | 0 0 0 5 6 3 |
     | 0 0 0 0 8 5 |
     | 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