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Sandbox Expand a polynomial [FINALIZED]

posted 3y ago by Moshi‭ · edited 3y ago by Moshi‭

Article code-golf math finalized

#4: Post edited by

Moshi‭ · 2021-09-11T02:52:35Z (over 3 years ago)

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~~Expand a polynomial~~

Expand a polynomial [FINALIZED]

code-golf math

code-golf math finalized

#3: Post edited by

Moshi‭ · 2021-09-01T21:27:39Z (over 3 years ago)

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# 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 $r_{1}, r_{2}, \dots, r_{n}$ , find the coefficients of the expansion of $(x - r_{1}) (x - r_{2}) \dots (x - r_{n})$ .~~
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 $r_{1}, r_{2}, \dots, r_{n}$ , find the coefficients of the expansion of $(x - r_{1}) (x - r_{2}) \dots (x - r_{n})$ , 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 (over 3 years ago)

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# 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 $r_{1}, r_{2}, \dots, r_{n}$ , find the coefficients of the expansion of $(x - r_{1}) (x - r_{2}) \dots (x - r_{n})$ .
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 (over 3 years ago)

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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!

code-golf math

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