# Santa's ELF holomorphing machine (500 points)

## Description

We have intercepted the blueprints and a memory dump for another of Santa's wicked contraptions. What is the old man hiding this time around?

Author: PinkiePie1189

## Solution

The solution is [**here**](https://en.wikipedia.org/wiki/Holomorphic_function)

We just need to draw the plot using the Cauchy-Riemann condition.

```python
import matplotlib.pyplot as plt
import re

data = open('data.txt', 'r')
lines = data.readlines()

x = []
y = []
for line in lines:
parsed = re.findall(r"[-+]?\d*\.?\d+|[-+]?\d+", line)
parsed = list(map(float,parsed))

uOrV = line[0]
firstMult = int(parsed[0])
secondMult = int(parsed[1])
currX = parsed[2]
currY = parsed[3]

zx = 0
zy = 0

if (uOrV == 'u'):
zx = firstMult * currX + secondMult * currY
zy = firstMult * currY - secondMult * currX
else:
zy = firstMult * currX + secondMult * currY
zx = secondMult * currX - firstMult * currY

x.append(zx)
y.append(zy)

plt.plot(x, y, '.')
plt.show()
```


Looks like flag, but we need to flip the plot:

```python
plt.gca().invert_yaxis()
```


Flag: X-MAS{C4uchy_4nd_Ri3m4nn_ar3_c0ming_t0_t0wn}

Original writeup (https://github.com/holypower777/ctf_writeups/tree/main/xmasCTF_2020/holomorphing).