Question: why Maple did this automatic simplification on numer and denom?

One thing I always liked about Maple, is that it does not do automatic simplifications or automatic re-write of expressions without the user explicitly asking for it like some other CAS systems do, which I think this is the right way.

So I was surprised when I set up a rational expression of a numerator and denominator, then when I asked for its denom and numer, I found Maple did automatic rewrite (even though on the screen the expression remained as it was originally). This caused a bug in my program (since it assumed as long as no simplifcation is made on the expression, numer and denom will remain as it was orginally placed). Here is an example


So now, one would expect, by looking at the screen, when asking for numer(expr) to obtain back -(1-x/exp(y))  but this is not what happens




So Maple's internal representation of numer and denom, is not what "appears" on the screen for the user. Maple automatically replaced -1+x/exp(y) by (-exp(y)+x)/exp(y) and then moved denominator of this, which is exp(y), down to the denominator of the orginal expression.

I was surprised by this, since as I said, my experence with Maple is that it keeps expressions as entered and will change them only when the user asks for a change.

How common is such behavior in Maple? and why did Maple do this under the cover manipulation in this case? It is probably documented somewhere if I search hard enough.



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