Question

# Prototype of N-R for a system of two non-linear equations
#evaluating  functions of two variables
# f(x,y)=1.6 * x ** 2 + 3.6 * x * y - 7.8 * x - 2.6 * y + 5.2
# g(x,y)=0.9 * y ** 2 + 3.1 * x **2 - 6.2 * x + 6.2 * y

# x = 0.5
# y =0.4

from math import *

eq1 = raw_input('Enter the equation 1: ')
eq2 = raw_input('Enter the equation 2: ')
x0 = float(input('Enter x: '))
y0 = float(input('Enter y: '))

def f(x,y):
    return eval(eq1)

def g(x,y):
    return eval(eq2)

Ea_X = 1
x = x0
y = y0

for n in range(1, 8):

    a = (f(x + 1e-06, y) - f(x,y)) / 1e-06   #in this one start the trouble
    b = (f(x, y + 1e-06) - f(x,y)) / 1e-06
    c = 0 - f(x,y)
    d = (g(x + 1e-06, y) - g(x,y)) / 1e-06
    eE = (g(x, y + 1e-06) - g(x,y)) / 1e-06
    f = 0 - g(x,y)


    print "f(x, y)= ", eq1
    print "g(x, y)= ", eq2
    print """x   y """
    print x, y
    print """a   b   c   d   e   f """
    print a, b, c, d, e, f

    print """
    a * x + b * y = c
    d * x + e * y = f
    """

    print a," * x  +  ",b," * y  =  ",c
    print d," * x  +  ",eE," * y  =  ",f

    _Sy = (c - a * f / d) / (b - a * eE / d)
    _Sx = (f / d) - (eE / d) * _Sy

    Ea_X = (_Sx ** 2 + _Sy ** 2)**0.5


    x = x + _Sx
    y = y + _Sy

    print "Sx = ", _Sx
    print "Sy = ", _Sy

    print "x = ", x
    print "y = ", y

    print "|X_1 - X_0| = ", Ea_X

I’ve been testing the Newton-Rapson method for two non-linear equations,
the prototype code works but then I was thinking in making it more
useful, because the prototype is about the input of the 2 equations
and the first guesses, and it would be good to implement a for loop
instead of starting the process like 6 or 10 to resolve just one
of the so many equations that I’m working with

# Prototype of N-R for a system of two non-linear equations
# f(x,y)=1.6 * x ** 2 + 3.6 * x * y - 7.8 * x - 2.6 * y + 5.2
# g(x,y)=0.9 * y ** 2 + 3.1 * x **2 - 6.2 * x + 6.2 * y

# x = 0.5
# y =0.4


# evaluating  functions of two variables

from math import *


eq1 = raw_input('Enter the equation 1: ')
eq2 = raw_input('Enter the equation 2: ')
x0 = float(input('Enter x: '))
y0 = float(input('Enter y: '))

def f(x,y):
    return eval(eq1)

def g(x,y):
    return eval(eq2)

Ea_X = 1
x = x0
y = y0

a = (f(x + 1e-06, y) - f(x,y)) / 1e-06
b = (f(x, y + 1e-06) - f(x,y)) / 1e-06
c = 0 - f(x,y)
d = (g(x + 1e-06, y) - g(x,y)) / 1e-06
eE = (g(x, y + 1e-06) - g(x,y)) / 1e-06
f = 0 - g(x,y)


print "f(x, y)= ", eq1
print "g(x, y)= ", eq2
print """x   y """
print x, y
print """a   b   c   d   e   f """
print a, b, c, d, e, f

print """
a * x + b * y = c
d * x + e * y = f
"""

print a," * x  +  ",b," * y  =  ",c
print d," * x  +  ",eE," * y  =  ",f

_Sy = (c - a * f / d) / (b - a * eE / d)
_Sx = (f / d) - (eE / d) * _Sy

Ea_X = (_Sx ** 2 + _Sy ** 2)**0.5


x = x + _Sx
y = y + _Sy

print "Sx = ", _Sx
print "Sy = ", _Sy

print "x = ", x
print "y = ", y

print "|X_1 - X_0| = ", Ea_X

Answer 1

In the line

f = 0 - g(x,y)

you assign a number to the name f. Since functions and other variables share a namespace in Python (a function is just a callable object, bound to any variable), this makes future iterations fail. Pick another name for the value you’re assigning in the above line.