## substitution and assuming...

The attached file demonstrates that a substitution into a piecewise function appears (sometimes) to execute the wrong half of the function.

If I use "assuming" instead of substitution, the assumption appears to get through to the piecewise function, but only sometimes.

I don't understand why this happens. Can anyone clarify what is going on? See below.

Thank you.

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## How to find product...

Maple does not find the product
product((k+a)*(k+b)/((k+c)*(k+d)), k = 1 .. infinity) assuming a > 0, b > 0, c > 0, d > 0, a+b = c+d;

GAMMA(c) GAMMA(d) infinity
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## Really real discontinuities....

Hello,

is it possible to search for only real discontinuities? There is a discont command and you can see in the help that it finds discontinuities over the reals. But it searches also over the complex domain. Can I restrict the command only for the real domain? I tried to use "assuming real", "RealDomain", but nothing works.

You can try the following example function: f := x-> 3/(1-exp(1/x)):

The only real discontinuity is in 0,...

## isdifferentiable bug?...

Compare the results of isdifferentiable on 3 piecewise defined expressions f, g, and h.

The first time the order of the asking is f, g, h. The second time (after a restart) the order is h,g,f.

The results are remarkably different! What is going on?

isdifferentiable was first brought to my attention within the last week or so, maybe it is not reliable?

If you remove all the lines with 'assuming' then the inconsistency remains.

restart;

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