how to do symbolic type negation ?

How can one do symbolic type negation ? (Advanced methods permitted!!)

For example

syms x n m
y = symsum(1/(x-n),n,1,m)

y = 

Notice the -- that is, if x is an integer. That leads to the question: how can you set an assumption such that x is known to be a non-integer ?

You can use assume() to set x to be integer, but assume() does not support negation. It is not obvious to me that the internal MuPAD routine assume does either; you can read the code for it by using

regexprep(char(evalin(symengine, 'expose(assume)')),'\\n','\n')

You can appear to construct an appropriate type at the MuPAD level:

S1 = evalin(symengine, 'Dom::Real and not Dom::Integer')

S1 = 

S2 = evalin(symengine, '~(x in integer)')

S2 = 

but how could you associate that type with a symbolic variable?

I know that in this particular case you could use children() to extract the third branch of the piecewise() and proceed from there, skipping around the problem: but what if you wanted MATLAB to be able to reason about the fact that a variable is a non-integer ?

Answer 1

[Paul]

Accoding to the doc page for assume(), maybe

assume(~in(x,'integer'))

will do what you want? I couldn't test it because my version (2019a) only returns

psi(1 - x) - psi(m - x + 1)

as the ouput of that symsum, without any conditions.

[Walter Roberson]

Oh, well done!