Mathcad ignore evaluation in false if statements

Question

I am trying to define a piecewise function in Mathcad to move around singularities, but the program breaks down at the singularities even when they are not called.
I created a program that evaluates one function if "w" is greater than or equal to "r", and another function if "w" is less than "r". The second function has a singularity if "w" is equal to "r" but theoretically it shouldn't need to evaluate that function in that case, as "w" isn't less than "r". The program still returns an error in that case though.
Is there a way to set up the program such that MathCad will not try to evaluate the term in the false if statement
 
Example:
function = if w >= r
                    pi/2
                if w < r
                    atan(1/(w-r))

Werner_E · Accepted Answer

I second what Luc wrote about the worksheet. It should be possible in most cases to narrow down the problem and create and post a worksheet which shows what you are looking after and what fails.

In case of your problem this should be fairly simple! Its still unclear for example if w and r are defined on top of your sheet or if they are provided as function arguments. And you always talk about functions but you don't show any function. So its unclear if you are just sloppy when typing in here the part of the expression or if you misunderstood the meaning of a function in math and confuse it with "term" or "expression". When you write

F2=atan(1/(w-r))

thats not a function but rather the definition of a new variable F2 which Prime tries to evaluate no matter what the values of w an r are. Of course, when the variables w and r are defined above with the same value, this calculation obviously must fail.

If you really insist in splitting this simple and straightforward calculation into a series of single calculations, you may do it with functions like this:

Note that if w and r are defined above, fun must not necessarily be a function but may be a simple variable. F2 has to be a function which is only called when w and r are different.

And here are different approaches without any functions:

Werner_E · Answer

You should attach your worksheet, not just a description what you had done. Its hard to determine what you may have done wrong just from the description. Furthermore you should state which version and which flavor of Mathcad (Prime or real Mathcad) you are using.

You may consider using the "otherwise" (= "else") statement instead of a second "if".

You may also use the if-function (similar syntax as in Excel) instead of the if-programming-statement.

BTW, while I would not suggest doing so, but it works OK even the way you describes it:

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