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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 = .0428096155793165

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

o2 = .286136192893119057122617238017+.357723389746025012848977245156*ii

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

o3 = Tally{-1 => 7 }
           -2 => 9
           -3 => 7
           -4 => 7
           -5 => 10
           0 => 9
           1 => 11
           2 => 6
           3 => 9
           4 => 15
           5 => 11

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

      38    37    34    30    29    26    23    22    21    13    12    11  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      10    7    6    4    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
o6 = 7x  + 8x y + 3x y  + x y  + 2x*y

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

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

See also