CoCoA:Randomized

Randomized

randomize the coefficients of a given polynomial

Description

This function with a polynomial argument returns a polynomial

obtained by replacing the coefficients of F with randomly generated

coefficients. The original polynomial, F, is unaffected. With an integer argument, it returns a random integer.

Note: It is possible that some coefficients will be replaced by

zeroes, i.e., some terms from the original polynomial may disappear in

the result.

The similar function <ttref>Randomize</ttref> performs the same operation,

but returns NULL and modifies the argument.

NB: every time you restart CoCoA the sequence of random numbers will

be the same (as in other programming languages). If you want total

randomness read <ttref>Seed</ttref>.

Example

  Use R ::= Q[x];
  F := 1 + x + x^2;
  Randomized(F);
-2917104644x^2 + 3623608766x - 2302822308
-------------------------------
  F;
x^2 + x + 1
-------------------------------
  Randomized(23);
-3997312402
-------------------------------
  Use R ::= Z/(7)[x,y];
  Randomized(x^2 + 3x - 5);
3x^2 + 2x - 2
-------------------------------

Syntax

Randomized(F:POLY or INT):POLY or INT

where V is a variable containing a polynomial.

Rand

Randomize

Seed

   <type>polynomial</type>