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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} | 28            0        0  |
     {-2} | 14x+14y       -39      0  |
     {-3} | 20x2-17xy-9y2 -30x+47y -7 |

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

o3 = | 95389347 633012767704 674279482 867181834 1872392999 76728848527 |
     | 3107131  20619233031  21963420  28246827  60989815   2499301892  |
     | 11641175 77251943147  82288072  105829590 228504076  9363875338  |

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

o4 = | 0 0 1 0 0 0 0 0 0 0 |
     | 0 2 0 2 0 0 8 0 5 0 |
     | 0 3 0 3 4 3 7 0 0 0 |

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

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