# Normal form for rational functions: ratnormal

### 5.12.16 Normal form for rational functions: ratnormal

The ratnormal command rewrites an expression using its irreducible representation. The expression is viewed as a multivariate rational function with coefficients in ℚ (or ℚ[i]). The variables are generalized identifiers which are assumed to be algebraically independent. Unlike with normal, an algebraic extension is considered as a generalized identifier. Therefore ratnormal is faster but might miss some simplifications if the expression contains radicals or algebraically dependent transcendental functions.

- ratnormal takes one argument:
  expr, an expression.
- ratnormal(expr) returns the irreducible representation of expr.

#### Examples.

- Input:
  ratnormal((x^3-1)/(x^2-1))
  Output:

  x2+x+1
  x+1

- Input:
  ratnormal((-2x^3+3x^2+5x-6)/(x^2-2x+1))
  Output:

  −2 x2+x+6
  x−1