10.1.2 Normal form
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
expr, an expression.
- normal(expr) returns the expanded irreducible
representation of expr. (See also ratnormal,
Section 10.1.5, for pure rational function or
simplify, Section 10.1.3, if the transcendental
functions are not algebraically independent.)
Examples
normal((1-sin(x))*(1+sin(x)) |
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.