M

#### minmax

##### Guest

Code:

`-8*F_p + 8*Omega*u + 6*alpha*u*(u**2 + v**2) - 5*beta*u*(u**4 + 2*u**2*v**2 + v**4) - 8*gamma*omega*v`

So it ends up like

Code:

`-8*F_p + 8*Omega*u + 6*alpha*u*r**2 - 5*beta*u*r**4 - 8*gamma*omega*v`

with

`r**2=u**2+v**2`

It is not working though, but when I use

Code:

`factor(u**4 + 2*u**2*v**2 + v**4).subs(u**2+v**2, r**2)`

The output I get is r**4 as expected. Unfortunately, I don't get this simplification when I try this with the first expression. I wonder if there is a way to tell sympy to factor only the expressions inside the innermost parentheses.

Here is the full code

Code:

```
from sympy import symbols
u, v, r = symbols('u v r')
# parameters
alpha = symbols('alpha', positive=True)
beta = symbols('beta', positive=True)
F_p = symbols('F_p', positive=True)
gamma = symbols('gamma', positive=True)
omega = symbols('omega', positive=True)
Omega = symbols('Omega', positive=True)
f=-8*F_p + 8*Omega*u + 6*alpha*u**3 + 6*alpha*u*v*v - 5*beta*u**5 - 10*beta*u**3*v**2 - 5*beta*u*v**4 - 8*gamma*omega*v
print(f)
f = collect(f, [alpha, beta])
print(simplify(f))
# Substitute u^2 + v^2 = r^2
subs_dict = {u**2 + v**2: r**2}
# Simplify the expression
simplified_expr = simplify(f.subs(subs_dict))
print(simplified_expr)
print(factor(u**4 + 2*u**2*v**2 + v**4).subs(u**2+v**2, r**2))
```

<pre><code>-8*F_p + 8*Omega*u + 6*alpha*u*(u**2 + v**2) - 5*beta*u*(u**4 + 2*u**2*v**2 + v**4) - 8*gamma*omega*v

</code></pre>

<p>So it ends up like</p>

<pre><code>-8*F_p + 8*Omega*u + 6*alpha*u*r**2 - 5*beta*u*r**4 - 8*gamma*omega*v

</code></pre>

<p>with <code>r**2=u**2+v**2</code></p>

<p>It is not working though, but when I use</p>

<pre><code>factor(u**4 + 2*u**2*v**2 + v**4).subs(u**2+v**2, r**2)

</code></pre>

<p>The output I get is r**4 as expected. Unfortunately, I don't get this simplification when I try this with the first expression. I wonder if there is a way to tell sympy to factor only the expressions inside the innermost parentheses.</p>

<p>Here is the full code</p>

<pre><code>from sympy import symbols

u, v, r = symbols('u v r')

# parameters

alpha = symbols('alpha', positive=True)

beta = symbols('beta', positive=True)

F_p = symbols('F_p', positive=True)

gamma = symbols('gamma', positive=True)

omega = symbols('omega', positive=True)

Omega = symbols('Omega', positive=True)

f=-8*F_p + 8*Omega*u + 6*alpha*u**3 + 6*alpha*u*v*v - 5*beta*u**5 - 10*beta*u**3*v**2 - 5*beta*u*v**4 - 8*gamma*omega*v

print(f)

f = collect(f, [alpha, beta])

print(simplify(f))

# Substitute u^2 + v^2 = r^2

subs_dict = {u**2 + v**2: r**2}

# Simplify the expression

simplified_expr = simplify(f.subs(subs_dict))

print(simplified_expr)

print(factor(u**4 + 2*u**2*v**2 + v**4).subs(u**2+v**2, r**2))

</code></pre>