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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} | -20            0        0   |
     {-2} | -49x-36y       43       0   |
     {-3} | 42x2+20xy-45y2 -47x+39y -47 |

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

o3 = | 29609413654  1230873967  245004465  158991493  9869615405   48693947 
     | 323197573236 13435439249 2674313232 1735450242 107730459809 531512220
     | 9434239883   392184738   78064044   50658341   3144686361   15515009 
     ------------------------------------------------------------------------
     |
     |
     |

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

o4 = | 0 0 0 0 0 0 0 0 6 8 |
     | 0 0 0 0 8 9 9 0 0 1 |
     | 0 0 0 0 0 0 2 0 0 4 |

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

o5 = | 0 6 0 6 6 6 |
     | 0 0 8 0 2 7 |
     | 0 0 0 1 2 6 |
     | 0 0 0 0 0 8 |
     | 0 0 0 0 0 0 |
     | 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