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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 = .222294441097916

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

o2 = .183560091803780935561424260039+.15763645901454326316158297604*ii

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

o3 = Tally{-1 => 1}
           -1 => 1
           -1 => 1
           -1 => 1
           -1 => 1
           -1 => 1
           -1 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           1 => 1
           1 => 1
           1 => 1
           1 => 1
           1 => 1
           1 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1

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

      39    38    36    33    31    27    26    24    22    19    17    15  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      13    11    8    7    6    5    4    3    2
     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
o6 = 8x  + 9x y + 7x y  + 9x 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 = {x  - 2x y + 2a*x*y  + 2a*y                           }
     {        3     2                 2            3       }
     {(a + 2)x  - 2x y + (- 2a + 2)x*y  + (2a - 1)y        }
     {     3              2                 2            3 }
     {- a*x  + (- 2a + 1)x y + (- 2a + 1)x*y  + (2a - 2)y  }
     {          3            2               2      3      }
     {(- a - 2)x  + (2a + 1)x y + (2a - 1)x*y  - a*y       }
     {   3             2                2       3          }
     {- x  + (- a + 1)x y + (- a + 1)x*y  - 2a*y           }
     {         3             2                2           3}
     {(2a + 1)x  + (- a + 2)x y + (- a - 1)x*y  + (a - 2)y }
     {          3     2              2    3                }
     {(- a - 1)x  - 2x y + (a + 1)x*y  + y                 }

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

See also