Suppose I have two polynomials f(x) and g(x) and I somehow represent their coeff

Question

Suppose I have two polynomials f(x) and g(x) and I somehow represent their coefficients. I have a couple of ways to hold a polynomial depending on how many significant coefficients the polynomial has. I want to determine the amount of significant coefficients in the results of f(x)+g(x) ,f(x)?g(x) , f(x)?g(x) etc. .

But I'd like to do it before I create the object that holds them, is there some efficient way of doing this without calculating the result twice?

I can assume that I know the current rank and number of elements in f(x) and g(x)

If this is not possible knowing that the new polynomial's non-trivial coefficients will be at least half of the rank will suffice, but I'm unsure how to do it as well.

I did try to apply various heuristics but didn't come up with something consistent and fast.

Explanation / Answer

If F is the number of terms in f(x) and G is the number of terms in g(x) then the number of terms in f(x)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.