Denominator of a rational expression
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denom(f) returns the denominator of the expression
denom regards the input as a rational expression:
non-rational subexpressions such as
are internally replaced by “temporary variables”. The
denominator of this rationalized expression is computed, the temporary
variables are finally replaced by the original subexpressions.
We compute the denominators of some expressions:
denom(x + 1/(2/3*x -2/x))
denom((cos(x)^2 -1)/(cos(x) -1))
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
cancellation of common factors:
However, automatic normalization occurs if the input expression is a sum:
denom(r + x/(x + 1) + 1/(x + 1) - 1)