### 5.12.13 Normal form : normal

normal takes as argument an expression. The expression is considered as a rational fraction with respect to generalized identifiers (either true identifiers or transcendental functions replaced by a temporary identifiers) with coefficients in ℚ or ℚ[i] or in an algebraic extension (e.g. ℚ[√2]). normal returns the expanded irreducible representation of this rational fraction. See also ratnormal for pure rational fractions or simplify if the transcendental functions are not algebraically independent.
Input :

normal((x-1)*(x+1))

Output :

x`^`2-1

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.