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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} | 47           0      0  |
     {-2} | -46x+30y     7      0  |
     {-3} | 9x2-15xy+6y2 43x-5y -7 |

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

o3 = | 62782   7501549   127104  1249088  1782537   324697   |
     | 572159  68361604  1158338 11382735 16244781  2958999  |
     | 4767308 569598439 9651433 94842545 135353771 24654792 |

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

o4 = | 0 4 0 0 0 0 0 0 0 0 |
     | 0 0 0 0 0 6 0 0 0 5 |
     | 0 0 0 0 0 0 0 0 0 8 |

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

o5 = | 0 2 0 4 5 3 |
     | 0 0 7 3 7 3 |
     | 0 0 0 1 5 7 |
     | 0 0 0 0 8 2 |
     | 0 0 0 0 0 5 |
     | 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