random(Module,Module) -- get a random map of module

Synopsis

• Function: random

• Usage:

  f = random(F, G)

• Inputs:
  • F, a module,
  • G, a module,
• Optional inputs:
  • Density => a real number, default value 1, the proportion of entries to set
  • MaximalRank => a Boolean value, default value false, whether to ensure that the resulting map has maximal rank: designed mostly for use with matrices of numbers: for polynomial rings, returns inhomogeneous results
  • UpperTriangular => a Boolean value, default value false, whether to set just entries strictly above the diagonal
  • Height => ..., default value 10, get a random homogeneous element from a graded ring
• Outputs:
  • f, a matrix, a random, graded, degree 0 map $f: G \to F$

Description

i1 : R = ZZ/101[x,y];

i2 : random(R^{1,2,3}, R^{1,2,3})

o2 = {-1} | 24             0       0   |
     {-2} | -29x+19y       -36     0   |
     {-3} | -29x2-8xy-22y2 19x-10y -30 |

             3      3
o2 : Matrix R  <-- R

i3 : random(ZZ^3, ZZ^10, Density => .3)

o3 = | 8 0 0 0 2 3 0 0 8 0 |
     | 0 5 7 5 0 6 0 3 6 0 |
     | 0 0 8 0 0 0 0 6 9 0 |

              3       10
o3 : Matrix ZZ  <-- ZZ

i4 : random(ZZ^3, ZZ^6, MaximalRank => true)

o4 = | 257597387 5266934 883667254 241 1289732 36905796 |
     | 7597733   155353  26062295  8   38041   1088577  |
     | 64155081  1311739 220078904 60  321210  9191452  |

              3       6
o4 : Matrix ZZ  <-- ZZ

i5 : random(ZZ^6, ZZ^6, UpperTriangular => true)

o5 = | 0 0 7 2 3 0 |
     | 0 0 9 5 0 2 |
     | 0 0 0 7 1 7 |
     | 0 0 0 0 7 5 |
     | 0 0 0 0 0 8 |
     | 0 0 0 0 0 0 |

              6       6
o5 : Matrix ZZ  <-- ZZ

Caveat

See also

• random(Module) -- get a random vector in the module
• setRandomSeed -- set starting point for random number generator