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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 = .49172932285074

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

o2 = .658124620704750277782619310253+.0870612852333047230876293016173*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
           -1 => 1
           -1 => 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
           -4 => 1
           -4 => 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
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           1 => 1
           1 => 1
           1 => 1
           1 => 1
           1 => 1
           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
           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
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1

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

      39    37    36    35    30    29    27    26    25    24    19    17  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      16    15    13    12    10    6    5    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     5
o6 = 6x  + 2x y + 6x y  + 4x y  + 8x*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*x  + (- 2a - 2)x y - x*y  + (- a + 1)y          }
     {           3            2       2           3      }
     {(- 2a + 2)x  + (2a + 1)x y - x*y  + (a - 2)y       }
     {     2                 2             3             }
     {- a*x y + (- 2a - 1)x*y  + (- a + 2)y              }
     {          3       2          2           3         }
     {(- a - 2)x  + 2a*x y - 2a*x*y  + (a + 1)y          }
     {          3            2              2           3}
     {(- a - 2)x  + (2a + 1)x y + (a - 1)x*y  + (a + 1)y }
     {      3           2                 2            3 }
     {- 2a*x  + (a + 1)x y + (- 2a - 1)x*y  + (2a + 1)y  }
     {        3           2               2            3 }
     {(a - 1)x  + (a - 1)x y + (2a + 1)x*y  + (2a + 2)y  }

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

See also