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These are questions asked by mzh

Dear Maple Users

I wonder if and how I can use Maple to calculate the difference of two sums algebraically, meaning if I dont have an explicit expression for the range of the sum. Rather, I want to calculate

Sum(i, i=0..N) - Sum(i, i=0..N, i!=k);

which should, obviously return k.

Is it possible to evaluate such an expression, and more advanced cases, using Maple?
Thanks for hints.


Dear Maple Users

Let the density of electronic states be denoted

Dear Forum

Lets say, I use the simplify function to process some expression and it returns x*x. On the paper, I find x^2. How can I use Maple to verify that x*x==x^2?


Thanks for any hints.

Dear Forum

I'm trying to evaluate the following expression:

Int(Int(Int(N*exp(-alpha*r^2)*N*exp(-alpha*r^2)*r^2,r=0..infinity) *sin(t), t=0..Pi),p=0..2*Pi)

The value of the integral should equal 1 and from that the value of the normalization constant N can be obtained. It should equal sqrt...


I'm new in Mapleprimes and I'm looking forward to interesting discussions.

I was just wondering if and how it would be possible to use Maple for something like proving invariance of trace under unitary transformation.


tr(\Omega) = tr(U^{+} O U)


U^{+}U = I

After a number of reformulations, one arrives at an expression tr(O) = tr(U \Omega U^{+}).

Another example would be to show that (AB)^{-1} = B^{-1}A^{-1}....

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