Perm and Comb are calculated incorrectly about ncalc

[axkr]

Version 3.4.1 in IDE mode you can input the functions like this

    Binomial(17,13)

    Factorial(0.75)

Can you give some examples of your calculations which go wrong.

[lwchkg]

Please refer to the screenshot below. I've seen all the ceiling operators, and that's the mistake.

The correct way to calculate Comb(n, r) is n!/(r!(n-r)!), non-negative integers or not. There should not be any rounding up or rounding down. So don't round off the inputs.

Similarly, we have Perm(n, r) = n!/r! for all numbers.

If you wonder what is n! for non-integer n, then take n! = Gamma(n+1). (You have already done this correctly.) The Gamma function works for complex numbers, so if your program support complex numbers you should also check your factorials against complex numbers.

Again, refer to the Wolfram article if you need any help. It has specifically defined nCr defined for non-integers with gamma function.

BTW, if you wonder what are the use of non-integers for nCr, consider the binomial expansion of (1+x)^n (where n is not an integer). I don't know for any use of non-integer r, but the web says that some people do use it.

[axkr]

You mean file CustomFunctions.java where the definitions should be:

    Comb(n_, k_):=Binomial(n,k)
    Perm(n_, k_):=Gamma(n+1)/Gamma(k+1)

BTW in you screenshot the input Comb(2.5,) is parsed as Comb(2.5, Null)

[lwchkg]

Yes.

BTW, I don't understand why the second string is named BINOMIAL, which is supposed to be a synonym of "combination". I guess you should name that PERMUTATION instead.

Anyway, parsing Comb(2.5,) is parsed as Comb(2.5, Null) is okay to me. With invalid input anything other than crashing is okay. I gave you the screenshot just because it exposes the wrong formula.

[axkr]

Fixed with 3.4.3-beta