# Normal form: normal

### 5.12.13 Normal form: normal

The normal command takes an expression and considers it to be a rational function with respect to generalized identifiers (which are either true identifiers or transcendental functions replaced by temporary identifiers) with coefficients in ℚ or ℚ[i] or in an algebraic extension (such as ℚ[√2] and finds its expanded irreducible representation.

- normal takes one argument:
  expr, an expression.
- normal(expr) returns the expanded irreducible representation of expr. (See also ratnormal, Section 5.12.16, for pure rational function or simplify, Section 5.12.14, if the transcendental functions are not algebraically independent.)

#### Examples.

- Input:
  normal((x-1)*(x+1))
  Output:

  x2−1

- Input:
  normal((1-sin(x))*(1+sin(x))
  Output:

  −sin2x+1

Remarks.

- Unlike simplify, normal does not try to find algebraic relations between transcendental functions like cos(x)2+sin(x)2=1.
- It is sometimes necessary to run the normal command twice to get a fully irreducible representation of an expression containing algebraic extensions.