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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} | 42             0        0  |
     {-2} | -41x-y         -9       0  |
     {-3} | -8x2+45xy+12y2 -44x-16y 32 |

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

o3 = | 1872875  5592954  234100  300781  395186  475109  |
     | 16747530 50013022 2093357 2689112 3533953 4248262 |
     | 17144367 51198102 2142960 2753282 3617568 4349130 |

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

o4 = | 0 9 0 0 0 0 0 0 0 0 |
     | 0 0 7 0 0 0 0 0 0 4 |
     | 0 4 0 4 0 0 0 0 0 0 |

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

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