Numerator of a rational expression
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numer(f) returns the numerator of the expression
numer regards the input as a rational expression:
non-rational subexpressions such as
are internally replaced by “temporary variables”. The
numerator of this rationalized expression is computed, the temporary
variables are finally replaced by the original subexpressions.
We compute the numerators of some expressions:
numer(x + 1/(2/3*x -2/x))
numer((cos(x)^2 -1)/(cos(x) -1))
numer performs no cancellations if the rational
expression is of the form “numerator/denominator”:
r := (x^2 - 1)/(x^3 - x^2 + x - 1): numer(r)
This numerator has a common factor with the denominator of
cancellation of common factors:
However, automatic normalization occurs if the input expression is a sum:
numer(r + x/(x + 1) + 1/(x + 1) - 1)