assignment-13

################
# Problem 1
################

import sympy as sp
from sympy import symbols

x, y, r = symbols('x y r')
# Solution with just unknown variables swapped
sol = [{r: sp.sqrt(x ** 2 + y ** 2), y: 2 * x + 0.5}] * 2


################
# Problem 2
################


from sympy.abc import y, x
from sympy import plot_implicit, Eq

pl1 = plot_implicit(Eq(x ** 2 + y ** 2, 4), (x, -3, 3), (y, -3, 3), aspect_ratio=(2, 2),
                    title="Plotting Ellipsis",xlabel='X axis', ylabel='Y axis', line_color='#323353', show=False,
                    markers=[{'args': [-1 / 4, 0], 'color': 'green', 'marker': 'o'},
                             {'args': [-3 / 20, 1 / 5], 'color': 'green', 'marker': 'o'}],
                    annotations=[
                        {'xy': (1, 2.1), 'text': "2y = 4x + 1", 'ha': 'left', 'va': 'bottom', 'color': '#0b5e65'}])
pl2 = plot_implicit(Eq(2 * y - 4 * x - 1, 0), line_color='#0b5e65', show=False)
pl1.append(pl2[0])
backend = pl1.backend(pl1)
backend.process_series()
backend.fig.savefig('Problem2.pdf', dpi=150)
pl1.show()

################
# Problem 3
################

import sympy as sp
from sympy.abc import x

def canonical_representation(fractional, irrational=sp.sqrt(2)):
    sqrt_2_exp = fractional(irrational).simplify()
    return sqrt_2_exp.subs(irrational, 0), sqrt_2_exp.coeff(irrational)

################
# Problem 4
################

import sympy as sp
from sympy.abc import x, a, b, c, d


def canonical_representation(fractional, irrational=sp.sqrt(2)):
    decomposition = fractional.apart()(irrational)
    sqrt_2_coefficient = decomposition.coeff(irrational)
    return decomposition - irrational * sqrt_2_coefficient, sqrt_2_coefficient