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')
    expr = sympify(l[0] + '-(' + l[1] + ')', evaluate=False)
    left = trigsimp(radsimp(expand_trig(expr)))
    return factor(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', 'atan2(y,x)')  # 使用atan2替代arctan以处理全象限
    l = formula.split('=')
    x, y = symbols('x y')
    expr = sympify(l[0] + '-(' + l[1] + ')', evaluate=False)
    left = trigsimp(radsimp(expr.rewrite(sin)))  # 重写为sin以优化三角表达式
    return factor(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, domain=S.Reals)
    if not tl:
        raise ValueError("无法消去参数t")
    # 选择最简单的解
    t_solution = tl[0] if len(tl) == 1 else min(tl, key=lambda sol: len(str(sol)))
    yf = yf.replace('t', str(t_solution))
    yl = yf.split('=')
    y = symbols('y')
    eq2 = Eq(sympify(yl[0]), sympify(yl[1]))
    return simplify(factor(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, domain=S.Reals)
    if not l2:
        raise ValueError("无法求解y")
    # 选择最简单的解
    y_solution = l2[0] if len(l2) == 1 else min(l2, key=lambda sol: len(str(sol)))
    return Eq(y, factor(simplify(y_solution)))

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 == "q":
            break
        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): ")
        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:
            try:
                if fr == "1":
                    if to == "2":
                        print("x = t")
                        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 = t")
                        print("y =")
                        pprint(polar_to_t(forin))
            except Exception as e:
                print(f"错误: {e}")

if __name__ == '__main__':
    UI()