2 added 1675 characters in body

# 05AB1E, 18 17 bytes

### Code

0Ev²¹g<Å0«y*NFÁ}+


### Explanation

CodeThe theory behind:

To find the convolution, let's take the example [1, 2, 3], [3, 4, 5]. We position the values of the first array upside down and vertically, like this:

3
2
1


Now, we place the second array like a ladder and multiply it by :

3 ×       [3  4  5]
2 ×    [3  4  5]
1 × [3  4  5]


Resulting into:

        9   12   15
6   8   10
3   4   5


Then, we add them up, resulting into:

        9   12   15
6   8   10
3   4   5

3   10  22  22   15


So, the convolution is [3, 10, 22, 22, 15].

The code itself:

We are going to do this step by step using the [1, 2, 3], [3, 4, 5] as the test case.

0Ev²¹g<Å0«y*NFÁ}+


We first push 0 and then we Evaluate the first input array. We map over each element using v.

So, for each element, we push the second array with ² and then the length of the first array using ¹g and decrease this by 1 (with <). We convert this into a list of zeros with (length 1st array - 1) zeros, using Å0 and append this to our list. Our stack now looks like this for the first item in the input list:

[3, 4, 5, 0, 0]


We multiply this array with the current item, done with y*. After that, we push N, which indicates the index of the current item (zero-indexed) and rotate the array that many times to the right using FÁ}. Finally, we add this to our initial value (0). So, what basically is done is the following:

[0, 0, 9, 12, 15] +
[0, 6, 8, 10, 0] +
[3, 4, 5, 0, 0] =

[3, 10, 22, 22, 15]


Which is then implicitly printed. Uses CP-1252 encoding. Try it online!.

# 05AB1E, 18 17 bytes

Code:

0Ev²¹g<Å0«y*NFÁ}+


Uses CP-1252 encoding. Try it online!

# 05AB1E, 18 17 bytes

### Code

0Ev²¹g<Å0«y*NFÁ}+


### Explanation

The theory behind:

To find the convolution, let's take the example [1, 2, 3], [3, 4, 5]. We position the values of the first array upside down and vertically, like this:

3
2
1


Now, we place the second array like a ladder and multiply it by :

3 ×       [3  4  5]
2 ×    [3  4  5]
1 × [3  4  5]


Resulting into:

        9   12   15
6   8   10
3   4   5


Then, we add them up, resulting into:

        9   12   15
6   8   10
3   4   5

3   10  22  22   15


So, the convolution is [3, 10, 22, 22, 15].

The code itself:

We are going to do this step by step using the [1, 2, 3], [3, 4, 5] as the test case.

0Ev²¹g<Å0«y*NFÁ}+


We first push 0 and then we Evaluate the first input array. We map over each element using v.

So, for each element, we push the second array with ² and then the length of the first array using ¹g and decrease this by 1 (with <). We convert this into a list of zeros with (length 1st array - 1) zeros, using Å0 and append this to our list. Our stack now looks like this for the first item in the input list:

[3, 4, 5, 0, 0]


We multiply this array with the current item, done with y*. After that, we push N, which indicates the index of the current item (zero-indexed) and rotate the array that many times to the right using FÁ}. Finally, we add this to our initial value (0). So, what basically is done is the following:

[0, 0, 9, 12, 15] +
[0, 6, 8, 10, 0] +
[3, 4, 5, 0, 0] =

[3, 10, 22, 22, 15]


Which is then implicitly printed. Uses CP-1252 encoding. Try it online!.

1

# 05AB1E, 18 17 bytes

Code:

0Ev²¹g<Å0«y*NFÁ}+


Uses CP-1252 encoding. Try it online!