```python
from sympy import init_session
init_session()
```


```python
init_printing?
```


```python
# this is for rac[3,1]
a, b, d, k, l0 = symbols('a b d k, l0')
```


```python
f=l0*(k**2 +2*a**2*k + a**4+b**2)*(1+d**2*k)/(a**4 + b**2 + k*(2*a**2 + d**2*(a**4+b**2)))
f
```




$\displaystyle \frac{l_{0} \left(d^{2} k + 1\right) \left(a^{4} + 2 a^{2} k + b^{2} + k^{2}\right)}{a^{4} + b^{2} + k \left(2 a^{2} + d^{2} \left(a^{4} + b^{2}\right)\right)}$




```python
f.factor()
```




$\displaystyle \frac{l_{0} \left(d^{2} k + 1\right) \left(a^{4} + 2 a^{2} k + b^{2} + k^{2}\right)}{a^{4} d^{2} k + a^{4} + 2 a^{2} k + b^{2} d^{2} k + b^{2}}$




```python
diff(f,l0)
```




$\displaystyle \frac{\left(d^{2} k + 1\right) \left(a^{4} + 2 a^{2} k + b^{2} + k^{2}\right)}{a^{4} + b^{2} + k \left(2 a^{2} + d^{2} \left(a^{4} + b^{2}\right)\right)}$




```python
da=diff(f,a)
da.factor()
```




$\displaystyle - \frac{4 a k^{2} l_{0} \left(d^{2} k + 1\right) \left(a^{4} d^{2} + a^{2} d^{2} k + a^{2} - b^{2} d^{2} + k\right)}{\left(a^{4} d^{2} k + a^{4} + 2 a^{2} k + b^{2} d^{2} k + b^{2}\right)^{2}}$




```python
db=diff(f,b)
db.factor()
```




$\displaystyle - \frac{2 b k^{2} l_{0} \left(d^{2} k + 1\right) \left(2 a^{2} d^{2} + d^{2} k + 1\right)}{\left(a^{4} d^{2} k + a^{4} + 2 a^{2} k + b^{2} d^{2} k + b^{2}\right)^{2}}$




```python
dd=diff(f,d)
dd.factor()
```




$\displaystyle \frac{4 a^{2} d k^{2} l_{0} \left(a^{4} + 2 a^{2} k + b^{2} + k^{2}\right)}{\left(a^{4} d^{2} k + a^{4} + 2 a^{2} k + b^{2} d^{2} k + b^{2}\right)^{2}}$




```python
printing.sstrrepr(f.factor())
```




    'l0*(d**2*k + 1)*(a**4 + 2*a**2*k + b**2 + k**2)/(a**4*d**2*k + a**4 + 2*a**2*k + b**2*d**2*k + b**2)'




```python
printing.sstrrepr(diff(f,l0).factor())
```




    '(d**2*k + 1)*(a**4 + 2*a**2*k + b**2 + k**2)/(a**4*d**2*k + a**4 + 2*a**2*k + b**2*d**2*k + b**2)'




```python
printing.sstrrepr(da.factor())
```




    '-4*a*k**2*l0*(d**2*k + 1)*(a**4*d**2 + a**2*d**2*k + a**2 - b**2*d**2 + k)/(a**4*d**2*k + a**4 + 2*a**2*k + b**2*d**2*k + b**2)**2'




```python
printing.sstrrepr(db.factor())
```




    '-2*b*k**2*l0*(d**2*k + 1)*(2*a**2*d**2 + d**2*k + 1)/(a**4*d**2*k + a**4 + 2*a**2*k + b**2*d**2*k + b**2)**2'




```python
printing.sstrrepr(dd.factor())
```




    '4*a**2*d*k**2*l0*(a**4 + 2*a**2*k + b**2 + k**2)/(a**4*d**2*k + a**4 + 2*a**2*k + b**2*d**2*k + b**2)**2'




```python

```

f719e99c690d43871029289fbecaedef5c8a0dfa
ipynb
Jupyter Notebook
notebooks/.ipynb_checkpoints/RAC-31_derivatives-checkpoint.ipynb
tsommerfeld/L2-methods_for_resonances
acba48bfede415afd99c89ff2859346e1eb4f96c
MIT
notebooks/.ipynb_checkpoints/RAC-31_derivatives-checkpoint.ipynb
tsommerfeld/L2-methods_for_resonances
acba48bfede415afd99c89ff2859346e1eb4f96c
MIT
notebooks/.ipynb_checkpoints/RAC-31_derivatives-checkpoint.ipynb
tsommerfeld/L2-methods_for_resonances
acba48bfede415afd99c89ff2859346e1eb4f96c
MIT
Qwen/Qwen-72B
1. YES
2. YES