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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 = .958295888829664

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

o2 = .637429407931590140701260788693+.154591412559859407564033508243*ii

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

o3 = Tally{-1 => 14}
           -2 => 11
           -3 => 8
           -4 => 8
           -5 => 6
           0 => 9
           1 => 12
           2 => 4
           3 => 13
           4 => 7
           5 => 9

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

      36    33    32    31    30    26    21    20    17    15    14    13  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      8    7    6    4    3
     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     3 2     2 3       4     5
o6 = 5x  + 5x y  + 4x y  + 5x*y  + 3y

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