next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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} | -29             0     0  |
     {-2} | 48x+8y          21    0  |
     {-3} | -11x2+24xy-49y2 x-13y 12 |

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

o3 = | 75462947198  693573519177  1578177960 68790252085  84387863564 
     | 24882637389  228694200312  520377645  22682428343  27825478393 
     | 302585473075 2781037306197 6328055599 275829817629 338371910505
     ------------------------------------------------------------------------
     412862485  |
     136134468  |
     1655463982 |

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

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

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

o5 = | 0 0 9 4 8 4 |
     | 0 0 6 2 1 0 |
     | 0 0 0 9 3 8 |
     | 0 0 0 0 8 0 |
     | 0 0 0 0 0 7 |
     | 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