for_freya.py

import sympy
sympy.init_printing()

sympy.var('c d P0 P1 P2 P3 v a b k0 k1 k2 k3 u')
R = c+(v-a)*(d-c)/(b-a)
A0 = R.subs({a:k0, b:k1, c:P0, d:P1, v:u})
A1 = R.subs({a:k1, b:k2, c:P1, d:P2, v:u})
A2 = R.subs({a:k2, b:k3, c:P2, d:P3, v:u})
B0 = R.subs({a:k0, b:k2, c:A0, d:A1, v:u})
B1 = R.subs({a:k1, b:k3, c:A1, d:A2, v:u})
P = R.subs({a:k1, b:k3, c:B0, d:B1, v:u})
res = [var*P.diff(var).simplify() for var in [P0,P1,P2,P3]]
for itm in res:
  display(itm)
pass