This page provides a list of the algorithms used by MathCore to perform some of its math tasks. The following are not intended to be rigorous proofs, since I am not a math-teacher and the math involved is not too difficult.
The mcPolynomial::math_RaiseTo function implements the algorithm used by MathCore to raise to the n-th power (where n is an integer value) a generic m-terms polynomial.
Which formula does it use ? Consider the classical Newton's binomial formula:
This formula is the formal rule used to raise a binomial to a power n.
Since we want to have the explicit formula for a generic polynomial, we can think b as being the sum of two other monomials c and d:
Since (c+d)^k is another binomial, we can apply Newton's formula on it again using another iterator j, obtaining:
If we try to substitute to d the sum of e and f, we get:
Performing such type of substitution for all members of our polynomial, we get:
where m is the number of the monomials contained in the polynomial to raise and all the k are the iterators required.
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