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Macaulay2Doc :: random(Type)

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 = .956639699110817

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

o2 = .0403422376537764068174651934937+.00588011582063891489699076963611*ii

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

o3 = Tally{-1 => 10}
           -2 => 12
           -3 => 8
           -4 => 11
           -5 => 6
           0 => 6
           1 => 9
           2 => 11
           3 => 10
           4 => 8
           5 => 10

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

      38    37    36    35    33    30    28    27    26    25    24    23  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      20    19    17    16    14    12    10    6    5    4    3
     a   + a   + a   + a   + a   + a   + 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 = 5x  + 6x y + 7x y  + 9x y  + 3x*y  + 4y

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

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

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

See also