6.12.13 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 6.12.16, for pure rational function or
simplify, Section 6.12.14, if the transcendental
functions are not algebraically independent.)
Examples.
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.