from sympy import *
from convert_formula import *

def xy_to_polar(formula):
    """
    把直角坐标方程转换为极坐标方程
    :param formula: 直角坐标方程
    :return: 极坐标方程
    """
    formula = convert_formula(formula)
    formula = formula.replace('x', '(r*cos(theta))')
    formula = formula.replace('y', '(r*sin(theta))')
    l = formula.split('=')
    r, theta = symbols('r theta')
    left = simplify(sympify(l[0]+'-('+l[1]+')'))
    return left

def polar_to_xy(formula):
    """
    把极坐标方程转换为直角坐标方程
    :param formula: 极坐标方程
    :return: 直角坐标方程
    """
    formula = convert_formula(formula)
    formula = formula.replace('r', 'sqrt(x**2+y**2)')
    formula = formula.replace('theta', 'arctan(y/x)')
    l = formula.split('=')
    x, y = symbols('x y')
    left = simplify(sympify(l[0]+'-('+l[1]+')'))
    return left

def t_to_xy(xf, yf):
    """
    把参数方程转换为直角坐标方程
    :param xf: 参数方程的x坐标
    :param yf: 参数方程的y坐标
    :return: 直角坐标方程
    """
    xf = convert_formula(xf)
    yf = convert_formula(yf)
    xl = xf.split('=')
    x, t = symbols('x t')
    eq = Eq(sympify(xl[0]), sympify(xl[1]))
    tl = solve(eq, t)
    yf = yf.replace('t', str(tl[0]))
    yl = yf.split('=')
    y, t = symbols('y t')
    eq2 = Eq(sympify(yl[0]), sympify(yl[1]))
    return eq2

def xy_to_t(formula):
    """
    把直角坐标方程转换为参数方程
    :param formula: 直角坐标方程
    :return: 参数方程
    """
    formula = convert_formula(formula)
    l = formula.split('=')
    x, y = symbols('x y')
    eq = Eq(sympify(l[0]), sympify(l[1]))
    l2 = solve(eq, y)
    return l2

def t_to_polar(xf, yf):
    """
    把参数方程转换为极坐标方程
    :param xf: 参数方程的x坐标
    :param yf: 参数方程的y坐标
    :return: 极坐标方程
    """
    xy = t_to_xy(xf, yf)
    xy = str(xy).lstrip('Eq(')[:-1].replace(", ","=")
    return xy_to_polar(xy)

def polar_to_t(formula):
    """
    把极坐标方程转换为参数方程
    :param formula: 极坐标方程
    :return: 参数方程
    """
    xy = polar_to_xy(formula)
    xy = str(xy)+'=0'
    return xy_to_t(xy)

def UI():
    while True:
        fr = input("请选择输入方程类型 1.直角坐标方程 2.参数方程 3.极坐标方程 q.退出")
        if fr == "2":
            xin = input("请输入x，格式x=x(t)")
            yin = input("请输入y，格式y=y(t)")
        elif fr == "q":
            break
        else:
            forin = input("请输入方程")
        to = input("请选择输出方程类型 1.直角坐标方程 2.参数方程 3.极坐标方程")
        if fr == to:
            print("输入和输出的方程类型不能相同")
        else:
            if fr == "1":
                if to == "2":
                    print("x = x")
                    print("y = ")
                    pprint(xy_to_t(forin))
                elif to == "3":
                    pprint(Eq(xy_to_polar(forin), 0))
            elif fr == "2":
                if to == "1":
                    pprint(t_to_xy(xin, yin))
                elif to == "3":
                    pprint(Eq(t_to_polar(xin, yin), 0))
            elif fr == "3":
                if to == "1":
                    pprint(Eq(polar_to_xy(forin), 0))
                elif to == "2":
                    print("x = x")
                    print("y = ")
                    pprint(polar_to_t(forin))

if __name__ == '__main__':
    UI()