Rating:

We are given 802 lines of data.
Each line contains either a function `u(x,y)` or a function `v(x,y)` and an imaginary number `z=x+y*i`.
The task is to compute the value `f(z)` of an unknown holomorphic function `f: C->C` at the position `z`. We don't know `f`. But we know either the real part `Re(f(z)) = u(x,y)` or the imaginary part `Im(f(z)) = v(x,y)` of `f(z)`.

To solve this challenge we read up on [holomorphic functions](https://en.wikipedia.org/wiki/Holomorphic_function) and the [Cauchy-Riemann equations](https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations).

Since `f` is a holomorphic function, `u(x,y)` and `v(x,y)` fulfill the Cauchy-Riemann equations:
```
du/dx = dv/dy
```
and
```
du/dy = -dv/dx
```

This means that if we know either `u` or `v`, we can compute the other function up to an unknown constant which is introduced when integrating over `x` and `y`.

The following Sage9 script parses the given data. From the given function `u` or `v` it computes the missing second function. To do so, it assumes the constant to be zero. It then computes the value `f(z)` and plots each value to the x-y-plane.
```python3
#!/usr/bin/sage
import matplotlib.pyplot as plt
ll = list()
llx = list()
lly = list()
for _ in range(802):
line = input()
uvs, zs = line.split('; ')
uv, uvt = uvs.split(' =')
zt = zs.split(' = ')[1]
uva, uvb = uvt.split(' + ')
uva, uvb = int(uva.split(' * ')[0]), int(uvb.split(' * ')[0])
zx, zy = zt.split(' + ')
zx, zy = float(zx), float(zy.split('*')[0])
xx, yy = 0, 0
if uv == 'u':
xx = uva * zx + uvb * zy
yy = -uvb * zx + uva * zy
pass
else:
xx = uvb * zx - uva * zy
yy = uva * zx + uvb * zy
pass
yy = 20 - yy
print(xx, yy)
ll.append((xx, -yy))
llx.append(xx)
lly.append(yy)
pass
plt.scatter(llx, lly)
plt.show()
```

The plot prints the flag to the screen. Since it is printed bottom up, we inverted the y-coordinates with `yy = 20 - yy`. The flag is
```
X-MAS{C4uchy_4nd_Ri3m4nn_ar3_c0ming_t0_t0wn}
```