How do you represent a polynomial number in a computer system?

In a computer system, a polynomial is typically represented as an array or list of coefficients.

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. For example, the polynomial 3x^2 + 2x + 1 has three coefficients: 3, 2, and 1. In a computer system, this polynomial can be represented as an array or list of these coefficients. The index of each coefficient in the array corresponds to the power of the variable that the coefficient is multiplied by. So, for the polynomial 3x^2 + 2x + 1, the array would be [1, 2, 3].

This representation is efficient and convenient for many operations on polynomials. For example, to evaluate the polynomial at a specific value of x, you can simply iterate over the array, multiplying each coefficient by the corresponding power of x and adding the results. Similarly, to add two polynomials, you can simply add the corresponding coefficients in their arrays.

However, this representation assumes that the polynomial is dense, i.e., that it has a coefficient for every power of the variable up to the highest one. If the polynomial is sparse, i.e., if it has many powers with a coefficient of zero, then this representation can be wasteful of space. In such cases, it may be more efficient to represent the polynomial as a list of pairs of coefficients and powers, or to use a data structure like a dictionary or map that can efficiently represent sparse data.

In addition to arrays and lists, other data structures can also be used to represent polynomials, depending on the specific requirements of the problem at hand. For example, if the coefficients are large numbers, it may be more efficient to use a data structure like a linked list that can handle large numbers efficiently. Similarly, if the polynomial is a multivariate one, i.e., it involves more than one variable, then a more complex data structure like a multidimensional array or a tree might be needed.