Documentation

# denom

Denominator of a rational expression

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denom(f)

## Description

denom(f) returns the denominator of the expression f.

denom regards the input as a rational expression: non-rational subexpressions such as sin(x), x^(1/2) etc. are internally replaced by “temporary variables”. The denominator of this rationalized expression is computed, the temporary variables are finally replaced by the original subexpressions.

### Note

Numerator and denominator are not necessarily cancelled: the denominator returned by denom may have a non-trivial gcd with the numerator returned by numer. Pre-process the expression by normal to enforce cancellation of common factors. Cf. Example 2.

## Examples

### Example 1

We compute the denominators of some expressions:

denom(-3/4)

denom(x + 1/(2/3*x -2/x))

denom((cos(x)^2 -1)/(cos(x) -1))

### Example 2

denom performs no cancellations if the rational expression is of the form “numerator/denominator”:

r := (x^2 - 1)/(x^3 - x^2 + x - 1): denom(r)

This denominator has a common factor with the numerator of r; normal enforces cancellation of common factors:

denom(normal(r))

However, automatic normalization occurs if the input expression is a sum:

denom(r + x/(x + 1) + 1/(x + 1) - 1)

delete r:

 f

## Return Values

Arithmetical expression.