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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 = .593037951593035

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

o2 = .742590581025393417581541180971+.967439786059538717396331506993*ii

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

o3 = Tally{-1 => 10}
           -2 => 11
           -3 => 10
           -4 => 11
           -5 => 2
           0 => 14
           1 => 10
           2 => 8
           3 => 5
           4 => 13
           5 => 7

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

      38    37    34    32    28    24    22    19    13    12    10    9  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a  +
     ------------------------------------------------------------------------
      7    5    3    2
     a  + a  + a  + a  + a + 1

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 = 2x  + 2x y + 9x y  + 9x y  + 9x*y  + 2y

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

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

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

See also