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normal -- normalize an expression

Introduction

normal(f) returns the normal form of the rational expression f. This is a rational expression with expanded numerator and denominator whose greatest common divisor is 1.

normal(object) replaces the operands of object by their normalized form.

Call(s)

normal(f)
normal(object)

Parameters

f - an arithmetical expression
object - a polynomial of type DOM_POLY, a list, a set, a table, an array, an equation, an inequality, or a range

Returns

an object of the same type as the input object.

Overloadable:

object

Further Documentation

Chapter ``Manipulating Expressions'' of the Tutorial.

Related Functions

collect, combine, denom, expand, factor, gcd, indets, numer, partfrac, rationalize, rectform, rewrite, simplify

Details

Example 1

We compute the normal form of some rational expressions:

>> normal(x^2 - (x + 1)*(x - 1))
                                     1
>> normal((x^2 - 1)/(x + 1))
                                   x - 1
>> normal(1/(x + 1) + 1/(y - 1))
                                   x + y
                              ---------------
                              y - x + x y - 1

The following expression should be regarded as a rational expression in the ``indeterminates'' y and sin(x):

>> normal(1/sin(x)^2 + y/sin(x))
                               y sin(x) + 1
                               ------------
                                       2
                                 sin(x)

Example 2

In the following, we give examples of non-rational expressions as argument. First, we normalize the entries of a list:

>> [(x^2 - 1)/(x + 1), x^2 - (x + 1)*(x - 1)]
                    --  2                           --
                    |  x  - 1   2                    |
                    |  ------, x  - (x - 1) (x + 1)  |
                    -- x + 1                        --
>> normal(%)
                                [x - 1, 1]

The coefficients of polynomials are normalized:

>> poly((x^2-1)/(x+1)*Y^2 + (x^2-(x+1)*(x-1))*Y - 1, [Y])
             / /  2     \                                        \
             | | x  - 1 |  2     2                               |
         poly| | ------ | Y  + (x  - (x - 1) (x + 1)) Y - 1, [Y] |
             \ \ x + 1  /                                        /
>> normal(%)
                                     2
                       poly((x - 1) Y  + Y - 1, [Y])

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