## Question:

I am relatively new to programming and as a personal project I decided to make a calculator of basic operations of polynomials (Addition, Multiplication, Subtraction and Division) without the help of libraries in Python, currently I am stuck in the final step for Multiplication; simplification. The "L1" represents the exponent of the "x" and the "L2" represents the coefficient of the "x".

```
L1 = [4,3,2,3,2,1,2,1,0]
L2 = [2,3,2,4,6,4,6,9,6]
```

The expected result for this example would be to end up with the following lists:

```
L4 = [4,3,2,1,0]
L5 = [2,7,14,13,6]
```

What I need is to find a method to add each element of L2 that corresponds to each element of L1 repeated, that is, in the case of exponents 2:

```
L6 = [2,2,2]
L7 = [2,6,6]
```

An apology if my question is not very clear, it is the first post I make in a forum. Thanks

## Answer:

A simple solution. You match the lists `L1`

and `L2`

(which must be the same length) with the `zip()`

function in order to take pairs of values (one from each list). The first value in each pair would be the exponent and the second would be the coefficient. You use the exponent as a dictionary key to add the coefficient to what is already in that dictionary key.

If you also use the `defaultdict(int)`

(a dictionary whose values are created with the default zero value at the moment they are accessed for the first time, if they don't already exist), the thing is very simple:

```
from collections import defaultdict
p = defaultdict(int)
for exp, coef in zip(L1, L2):
p[exp] += coef
```

The result in `p`

is a dictionary in which each key is each of the processed exponents, and each value is the result of adding the coefficients. In your example this dictionary would have:

```
{0: 6, 1: 13, 2: 14, 3: 7, 4: 2}
```

If you want to have it in two separate lists (one for exponents and one for coefficients), from highest to lowest exponent, you can separate them like this:

```
L4 = list(sorted(p, reverse=True))
L5 = [p[exp] for exp in L4]
```

And you get:

```
L4: [4, 3, 2, 1, 0]
L5: [2, 7, 14, 13, 6]
```

## Without using defaultdict

The code is a bit longer because you have to verify that the key exists in the dictionary (and if not create it before accessing it):

```
p = {}
for exp, coef in zip(L1, L2):
if not exp in p:
p[exp] = 0
p[exp]+=coef
```

The way to separate the result into two lists would be the same.