```python


import sympy as sp
```


```python
op, os, oc,oo = sp.symbols('op os oc oo')
b0, b1, b2, b3,b4 = sp.symbols('b0 b1 b2 b3 b4')
```


```python
op = 2*os - oc
```


```python
bp = b0 + b1 * (op - oo) + (1/2)*b2 *(op - oo)**2 + (1/6) * b3 (op - oo)**3 + (1/24)*b4 (op - oo)**4
```


```python
bs = b0 + b1 * (os - oo) + (1/2)*b2 *(os - oo)**2 + (1/6) * b3 (os - oo)**3 + (1/24)*b4 (os - oo)**4
```


```python
bc = b0 + b1 * (oc - oo) + (1/2)*b2 *(oc - oo)**2 + (1/6) * b3 (oc - oo)**3 + (1/24)*b4 (oc - oo)**4
```


```python
db = sp.expand(bp) + sp.expand(bc) -2*sp.expand(bs)
```


```python
db
```




    1.0*b2*oc**2 - 2.0*b2*oc*os + 1.0*b2*os**2




```python
sp.simplify(db)
```




    b2*(1.0*oc**2 - 2.0*oc*os + 1.0*os**2)




```python
sp.__version__
```




    '1.0'




```python
import numpy as np
l = np.arange(1.48,1.49,0.005)
```


```python
10**(-l/10)
```




    array([ 0.71121351,  0.71039517,  0.70957777])




```python
import numpy as np
import matplotlib.pyplot as plt

l = np.linspace(0,4, 512)
y1 = np.sin(l)**2
y2 = np.cos(l)**2


```


```python
import matplotlib
font = {'size'   : 16}

matplotlib.rc('font', **font)
```


```python
fig = plt.figure(figsize=(5, 3))
plt.plot(l, y1*100, label = 'p3')
plt.plot(l,y2*100, label = 'p4')
plt.xlabel('f')
plt.ylabel('% of p1 power')
plt.xticks([])
plt.legend()
plt.savefig('sin_cos_wdm.png', bbox_inches = 'tight')
plt.show()
```


```python

```

ef70cfc0303c636a504d1445abc980b1dfcba1d0
ipynb
Jupyter Notebook
Research_logs_and_notebooks/Stable_logs/dispersion_analytic.ipynb
ibegleris/w-fopo
e44b83b8ec54d01bb34b89805378a2b0659dfe6f
BSD-3-Clause
Research_logs_and_notebooks/Stable_logs/dispersion_analytic.ipynb
ibegleris/w-fopo
e44b83b8ec54d01bb34b89805378a2b0659dfe6f
BSD-3-Clause
Research_logs_and_notebooks/Stable_logs/dispersion_analytic.ipynb
ibegleris/w-fopo
e44b83b8ec54d01bb34b89805378a2b0659dfe6f
BSD-3-Clause
Qwen/Qwen-72B
1. YES
2. YES