6.12.9  Separation of variables: split

The split command tries to factor an expression involving two variables into the product of two expressions, each of which depends on only one of the variables.

• split takes two arguments:
  • expr, an expression depending on two variables x and y.
  • [x,y], the list of these two variables.
• split(expr,[x,y]) returns a list [factor₁,factor₂], if such a list exists, where expr=factor₁·factor₂, factor₁ only depends on x and factor₂ only depends on y. If such a factorization doesn’t exist, the list [0] is returned.

Examples.

• Input:
  split((x+1)*(y-2),[x,y])
  or:
  split(x*y-2*x+y-2,[x,y])
  Output:

  ⎡ ⎣

  x+1,y−2

  ⎤ ⎦

• Input:
  split((x^2*y^2-1,[x,y])
  Output:

  ⎡ ⎣

  0

  ⎤ ⎦