Problem 44260. Multivariate polynomials  convert monomial form to array
In Problem 44259 I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles onevariable polynomials. However, that representation has at least two problems:
 Defining a polynomial is an indexing headache, with a high probability of errors.
 Polynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.
Here, we will represent a polynomial as a sum of monomials. For example, the polynomial p(x,y) = 2*x^5*y + 3*x*y^5 is the sum of two monomials in x and y. We will represent this by exponents, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector coefficients for the coefficient of each monomial. For p(x,y), these are
exponents = [5 1; 1 5]; coefficients = [2; 3];
Let's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function
function c = coeffArray(exponents,coefficients)
that inputs the exponents and coefficients and returns an array as defined in Problem 44259.
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5 Comments
What is the matrix form for, say, A*x^2+B*x*y+C*y^2+D*x+E*y+F?
Tim, it is
exponents = [2 0; 1 1; 0 2; 1 0; 0 1; 0 0];
coefficients = [A B C D E F]';
What I meant to ask was, what is the correct output from coeffArray for that case?
@Tim The correct output from coeffArray for A*x^2+B*x*y+C*y^2+D*x+E*y+F should be [0 0 A;0 B D;C E F]
Shouldn't the single variable case be a row vector? "a matrix of integers with each row representing the exponents of one monomial" The test suite is representing it as a column. I guess you meant a matrix of integers with each row representing an exponent of one variable or with each row of size n representing the exponents of n variables.
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