How to solve a polynomial with decimal degrees in Scilab?

Question

I'm trying to program in Scilab a polynomial with decimals degrees like this : 3x^2.5 + 5x^7.5;

It is easy to write a polynomial with integers degrees in Scilab. The method is the following : v =[-2-5*%x+%x^2]; disp("Result is " + pol2str(v)); // it writes : -2 -5*x + x^2";

But if I write this code, it doesn't work anymore: v =[-2-5*%x^1.5+%x^2.5]; // I have an error in the console of Scilab, and I don't get this result expected : -2 -5*x^1.5 + x^2.5.

I have tried to write a polynomial by multplying with a sqrt, but I have some difficulties.

My question is how can we define a polynomial with decimals degrees in Scilab ?

Thank you in advance.

Answer 1

Here is how to find the roots for your example. Just adapt the values of coefficients in a and exponents in expo for other cases:

a = [3 5];
expo = [2.5,7.5];
[n,d] = rat(expo);
q = lcm(d);
coef(expo*q+1) = a;
P = poly(coef,'X','coeff');
theRoots = roots(P).^q;

// eval the function at roots
for i = 1:length(theRoots)
    disp(abs(sum(a.*theRoots(i).^expo)))
end

see also https://math.stackexchange.com/questions/1291208/number-of-roots-of-a-polynomial-of-non-integer-degree