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random(Type) -- random element of a type

Synopsis

Description

Synopsis

  • Usage:
    random T
  • Inputs:
  • Outputs:
    • a random instance of the type T. If the Height option specifies a number h and T is ZZ and , then the integers returned are in the range 0 .. h-1; for QQ the numerator and denominator are in the range 1 .. h.
i1 : random RR

o1 = .388425276654073

o1 : RR (of precision 53)
i2 : random CC_100

o2 = .400669994638748181422770322982+.18355848645362627467507443061*ii

o2 : CC (of precision 100)
i3 : tally for i to 100 list random GF 11

o3 = Tally{-1 => 5 }
           -2 => 11
           -3 => 11
           -4 => 10
           -5 => 7
           0 => 9
           1 => 7
           2 => 7
           3 => 12
           4 => 11
           5 => 11

o3 : Tally
i4 : random GF(2,40)

      39    38    37    36    32    29    26    23    21    19    13    10  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      9    7    5    3    2
     a  + a  + a  + a  + a

o4 : GF 1099511627776

Synopsis

  • Usage:
    random(d,R)
  • Inputs:
  • Outputs:
    • a random homogeneous element of the ring R of degree d
i5 : R = ZZ[x,y];
i6 : random(5,R)

       5    4     3 2     2 3       4     5
o6 = 8x  + x y + x y  + 5x y  + 3x*y  + 7y

o6 : R
i7 : R = GF(25,Variable=>a)[x,y];
i8 : VerticalList for i to 6 list random(3,R)

     {          2         2      3                     }
o8 = {(- a + 1)x y + a*x*y  + a*y                      }
     {          3              2              2       3}
     {(- a - 1)x  + (- 2a - 1)x y + (a + 2)x*y  + 2a*y }
     {         2                 2     3               }
     {(2a - 1)x y + (- 2a - 1)x*y  - 2y                }
     {         3      2               2       3        }
     {(2a + 2)x  + a*x y + (2a + 2)x*y  - 2a*y         }
     {        3           2          2           3     }
     {(a - 2)x  + (a - 1)x y + 2a*x*y  + (a - 1)y      }
     {     2       2      3                            }
     {- a*x y + x*y  - a*y                             }
     {   3           2               2      3          }
     {a*x  + (a + 2)x y + (2a - 2)x*y  - a*y           }

o8 : VerticalList
The length of d, if it's a list, should be the same as degreeLength R.

See also