Group Project 2, Problem 17

%matplotlib inline
import matplotlib.pyplot as plt
from sympy import *
init_printing()

x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
L = Symbol("L")
U= Symbol("U")

A=solve([y-z,1-x*y,y**2 +z**2 -1,1/2 -L],[x,y,z,L])
B=solve([-y-z,1-x*y,-y**2 -z**2 +1,-1/2 -L],[x,y,z,L])
A[1][0],A[1][1],A[1][2],A[1][3]
B[1][0],B[1][1],B[1][2],B[1][3]
(A[1][0])*(A[1][1])
(B[1][0])*(B[1][1])
(A[1][1])**2 +(A[1][2])**2
(B[1][1])**2 +(A[1][2])**2
(A[1][1])*((A[1][0])+(A[1][3]))
(B[1][1])*((B[1][0])+(B[1][3]))