def solve(eq, var=('x', 'y')):
""" Solve a system of simultaneous equation in
two variables of the form
2*x + 5*y=c1; 3*x - 5*y=c2
Example: solve('12*x - 3*y = 21; 9*x - 18*y=0')
Should work for negative constants as well.
Example: solve('3*x - 5*y=-11; 12*x + 3*y=48')
Returns a two tuple of (x, y) values.
NOTE: Won't denegarate to the special case
of solving for only one variable.
"""
var_re = re.compile(r'(\+|\-)\s*(\d*)\s*\*?\s*(x|y)')
const_re = re.compile(r'(\+|\-)\s*(\-?\d+)$')
constants, eqns, coeffs, default = [],[], {'x': [], 'y': []}, {'': '1'}
for e in eq.split(';'):
eq1 = e.replace("="," - ").strip()
if not eq1.startswith('-'):
eq1 = '+' + eq1
eqns.append(eq1)
var_eq1, var_eq2 = map(var_re.findall, eqns)
constants = [-1*int(x[0][1]) for x in map(const_re.findall, eqns)]
[coeffs[x[2]].append(int((x[0]+ default.get(x[1], x[1])).strip())) for x in (var_eq1 + var_eq2)]
ycoeff = coeffs['y']
xcoeff = coeffs['x']
# Adjust equations to take out y and solve for x
if ycoeff[0]*ycoeff[1] > 0:
ycoeff[1] *= -1
xcoeff[0] *= ycoeff[1]
constants[0] *= -1*ycoeff[1]
else:
xcoeff[0] *= -1*ycoeff[1]
constants[0] *= ycoeff[1]
xcoeff[1] *= ycoeff[0]
constants[1] *= -1*ycoeff[0]
# Obtain x
xval = sum(constants)*1.0/sum(xcoeff)
# Now solve for y using value of x
z = eval(eqns[0],{'x': xval, 'y': 1j})
yval = -z.real*1.0/z.imag
return (xval, yval)
