default format for [polynomials]

Question

Some languages do not have native ways of representing polynomials, others do. Many times a list of coefficients (in one or the other order) works well. In order to avoid explicitly specifying this over and over again in all polynomials challenge, I'd like add that to the tag info.

Please add your suggestions for default representations.

Answer 1

List of coefficients

A list of coefficients

• in ascending order [a(0),a(1),a(2),...,a(n)] OR
• in descending order [a(n),a(n-1),...,a(0)]

If the degree is known, it may be zero padded as

[a(0),...,a(n),0,...,0]

or

[0,...,0,a(n),...,a(0)]

Answer 2

Default representation in [language]

Many langauges, especially ones that include a CAS have native ways of representing polynomials.

Answer 3

A function that takes \$k\$ as input and outputs the coefficient of \$x^k\$

For example, \$24 x^4 + 96 x^3 + 72 x^2 + 16 x + 1\$ can be represented as

f(k) = 24 if k = 4
     = 96 if k = 3
     = 72 if k = 2
     = 16 if k = 1
     = 1  if k = 0
     = 0  otherwise

This is different from the "function representation" in @xnor's answer.

If the challenge requires outputting a polynomial, we can also take \$k\$ as an additional input and output the coefficient of \$x^k\$.

For multivariable polynomials, we can take a list of inputs \$[k_1, k_2, \ldots, k_n]\$ and output the coefficient of \$x_1^{k_1} x_2^{k_2} \cdots x_n^{k_n}\$.

Answer 4

The function and k

The pure function doesn't give an upperbound of k so it needs extra provided

Seems to trivialize some question but anyway list here

Answer 5

Beware function representations

Be careful about allowing a polynomial to be represented by a function that computes it, in languages where functions are objects. For example, in Python the polynomial 3*x^2+2 could be represented by the function object lambda x:3*x*x+2.

Take the challenge to compose polynomials. One could submit

Haskell, 3 bytes

(.)

where . is Haskell's function composition operator: if f and g are functions, then f.g is a function that takes x to f(g(x)). This would cut off the possibility for a much more interesting answer in the coefficient list representation.

Even a wordy language like Python could do better with

lambda f,g:lambda x:f(g(x))