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Expand a polynomial [FINALIZED]
#4: Post edited
by
Moshi
·
2021-09-11T02:52:35Z (about 3 years ago)
Expand a polynomial
- Expand a polynomial [FINALIZED]
#3: Post edited
by
Moshi
·
2021-09-01T21:27:39Z (about 3 years ago)
- # Challenge
- Given the roots of a polynomial (that is, the $x$ values where the polynomial evaluates to zero), as an array of real numbers, return the polynomial's coefficients.
That is, given real roots $r_1, r_2, \cdots , r_n$, find the coefficients of the expansion of $(x-r_1)(x-r_2)\cdots(x-r_n)$.- You may use either lowest power first or highest power first order for the resulting list of coefficients.
- ## Tests
- ```
- [] -> [1]
- [1] -> [-1, 1] // (x - 1) = -1 + 1x
- [1, 2] -> [2, -3, 1] // (x - 1)(x - 2) = 2 - 3x + 1x^2
- [1, 1] -> [1, -2, 1] // (x - 1)^2 = 1 -2x + 1x^2
- [1, 2, 3] -> [-6, 11, -6, 1] // (x - 1)(x - 2)(x - 3) = -6 + 11x - 6x^2 + x^3
- ```
- This is code golf, so the shortest answer in bytes wins!
- # Challenge
- Given the roots of a polynomial (that is, the $x$ values where the polynomial evaluates to zero), as an array of real numbers, return the polynomial's coefficients.
- That is, given real roots $r_1, r_2, \cdots , r_n$, find the coefficients of the expansion of $(x-r_1)(x-r_2)\cdots(x-r_n)$, or any non-zero scalar multiple of it.
- You may use either lowest power first or highest power first order for the resulting list of coefficients.
- ## Tests
- ```
- // Note that any non-zero scalar multiple of these results is valid
- [] -> [1]
- [1] -> [-1, 1] // (x - 1) = -1 + 1x
- [1, 2] -> [2, -3, 1] // (x - 1)(x - 2) = 2 - 3x + 1x^2
- [1, 1] -> [1, -2, 1] // (x - 1)^2 = 1 -2x + 1x^2
- [1, 2, 3] -> [-6, 11, -6, 1] // (x - 1)(x - 2)(x - 3) = -6 + 11x - 6x^2 + x^3
- ```
- This is code golf, so the shortest answer in bytes wins!
#2: Post edited
by
Moshi
·
2021-08-31T23:08:17Z (about 3 years ago)
- # Challenge
Given the roots of a polynomial, as an array of numbers, return the polynomial's coefficients. You may use either lowest power first or highest power first order.- ## Tests
- ```
- [] -> [1]
- [1] -> [-1, 1] // (x - 1) = -1 + 1x
- [1, 2] -> [2, -3, 1] // (x - 1)(x - 2) = 2 - 3x + 1x^2
- [1, 1] -> [1, -2, 1] // (x - 1)^2 = 1 -2x + 1x^2
- [1, 2, 3] -> [-6, 11, -6, 1] // (x - 1)(x - 2)(x - 3) = -6 + 11x - 6x^2 + x^3
- ```
- This is code golf, so the shortest answer in bytes wins!
- # Challenge
- Given the roots of a polynomial (that is, the $x$ values where the polynomial evaluates to zero), as an array of real numbers, return the polynomial's coefficients.
- That is, given real roots $r_1, r_2, \cdots , r_n$, find the coefficients of the expansion of $(x-r_1)(x-r_2)\cdots(x-r_n)$.
- You may use either lowest power first or highest power first order for the resulting list of coefficients.
- ## Tests
- ```
- [] -> [1]
- [1] -> [-1, 1] // (x - 1) = -1 + 1x
- [1, 2] -> [2, -3, 1] // (x - 1)(x - 2) = 2 - 3x + 1x^2
- [1, 1] -> [1, -2, 1] // (x - 1)^2 = 1 -2x + 1x^2
- [1, 2, 3] -> [-6, 11, -6, 1] // (x - 1)(x - 2)(x - 3) = -6 + 11x - 6x^2 + x^3
- ```
- This is code golf, so the shortest answer in bytes wins!
#1: Initial revision
by
Moshi
·
2021-08-31T22:15:31Z (about 3 years ago)
Expand a polynomial
# Challenge Given the roots of a polynomial, as an array of numbers, return the polynomial's coefficients. You may use either lowest power first or highest power first order. ## Tests ``` [] -> [1] [1] -> [-1, 1] // (x - 1) = -1 + 1x [1, 2] -> [2, -3, 1] // (x - 1)(x - 2) = 2 - 3x + 1x^2 [1, 1] -> [1, -2, 1] // (x - 1)^2 = 1 -2x + 1x^2 [1, 2, 3] -> [-6, 11, -6, 1] // (x - 1)(x - 2)(x - 3) = -6 + 11x - 6x^2 + x^3 ``` This is code golf, so the shortest answer in bytes wins!