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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} | -12             0      0 |
     {-2} | -20x-43y        37     0 |
     {-3} | -25x2+23xy+19y2 8x+19y 7 |

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

o3 = | 21053138919    315703659    155735126    2534141178    1061727681   
     | 10384097149420 155715377030 76813661770  1249921366840 523678844959 
     | 53372100504409 800344664860 394806252014 6424335968131 2691600390778
     ------------------------------------------------------------------------
     1116450281    |
     550669822872  |
     2830328405854 |

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

o4 = | 0 0 0 0 8 0 0 0 0 8 |
     | 0 0 0 0 0 0 0 0 0 0 |
     | 0 9 0 0 0 0 2 0 0 6 |

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

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