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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} | 7               0        0  |
     {-2} | 26y             -25      0  |
     {-3} | -37x2-20xy-42y2 -23x+46y 50 |

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

o3 = | 175767497  54030554   7964622093   228931336  1591789051  459467597  
     | 744050909  228721049  33715473291  969107568  6738288494  1945009150 
     | 4706840837 1446878670 213282941026 6130529062 42626184527 12304036574
     ------------------------------------------------------------------------
     |
     |
     |

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

o4 = | 0 0 2 2 0 0 4 0 0 0 |
     | 0 0 0 0 0 6 9 5 0 0 |
     | 8 0 2 0 6 2 0 3 0 0 |

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

o5 = | 0 1 6 1 2 3 |
     | 0 0 7 0 7 6 |
     | 0 0 0 2 3 0 |
     | 0 0 0 0 3 4 |
     | 0 0 0 0 0 9 |
     | 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