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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 = .566121889121169

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

o2 = .850701382779363563673560195325+.098319758049460821945261853026*ii

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

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

o3 : Tally
i4 : random GF(2,40)
GC Warning: Repeated allocation of very large block (appr. size 1167360):
        May lead to memory leak and poor performance.

      38    37    35    33    30    25    23    22    21    15    14    13  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      12    11    10    8    7    6    5    3
     a   + a   + a   + 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      4     5
o6 = 2x  + 6x y + 5x y  + x*y  + 2y

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

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