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from sympy import *
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from convert_formula import *
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def xy_to_polar(formula):
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"""
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把直角坐标方程转换为极坐标方程
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:param formula: 直角坐标方程
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:return: 极坐标方程
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"""
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formula = convert_formula(formula)
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formula = formula.replace('x', '(r*cos(theta))')
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formula = formula.replace('y', '(r*sin(theta))')
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l = formula.split('=')
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r, theta = symbols('r theta')
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expr = sympify(l[0] + '-(' + l[1] + ')', evaluate=False)
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left = trigsimp(radsimp(expand_trig(expr)))
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return factor(left)
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def polar_to_xy(formula):
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"""
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把极坐标方程转换为直角坐标方程
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:param formula: 极坐标方程
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:return: 直角坐标方程
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"""
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formula = convert_formula(formula)
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formula = formula.replace('r', 'sqrt(x**2+y**2)')
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formula = formula.replace('theta', 'atan2(y,x)') # 使用atan2替代arctan以处理全象限
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l = formula.split('=')
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x, y = symbols('x y')
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expr = sympify(l[0] + '-(' + l[1] + ')', evaluate=False)
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left = trigsimp(radsimp(expr.rewrite(sin))) # 重写为sin以优化三角表达式
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return factor(left)
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def t_to_xy(xf, yf):
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"""
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把参数方程转换为直角坐标方程
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:param xf: 参数方程的x坐标
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:param yf: 参数方程的y坐标
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:return: 直角坐标方程
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"""
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xf = convert_formula(xf)
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yf = convert_formula(yf)
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xl = xf.split('=')
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x, t = symbols('x t')
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eq = Eq(sympify(xl[0]), sympify(xl[1]))
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tl = solve(eq, t, domain=S.Reals)
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if not tl:
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raise ValueError("无法消去参数t")
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# 选择最简单的解
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t_solution = tl[0] if len(tl) == 1 else min(tl, key=lambda sol: len(str(sol)))
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yf = yf.replace('t', str(t_solution))
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yl = yf.split('=')
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y = symbols('y')
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eq2 = Eq(sympify(yl[0]), sympify(yl[1]))
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return simplify(factor(eq2))
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def xy_to_t(formula):
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"""
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把直角坐标方程转换为参数方程
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:param formula: 直角坐标方程
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:return: 参数方程
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"""
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formula = convert_formula(formula)
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l = formula.split('=')
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x, y = symbols('x y')
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eq = Eq(sympify(l[0]), sympify(l[1]))
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l2 = solve(eq, y, domain=S.Reals)
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if not l2:
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raise ValueError("无法求解y")
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# 选择最简单的解
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y_solution = l2[0] if len(l2) == 1 else min(l2, key=lambda sol: len(str(sol)))
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return Eq(y, factor(simplify(y_solution)))
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def t_to_polar(xf, yf):
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"""
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把参数方程转换为极坐标方程
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:param xf: 参数方程的x坐标
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:param yf: 参数方程的y坐标
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:return: 极坐标方程
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"""
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xy = t_to_xy(xf, yf)
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xy = str(xy).lstrip('Eq(')[:-1].replace(", ","=")
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return xy_to_polar(xy)
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def polar_to_t(formula):
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"""
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把极坐标方程转换为参数方程
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:param formula: 极坐标方程
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:return: 参数方程
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"""
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xy = polar_to_xy(formula)
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xy = str(xy) + '=0'
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return xy_to_t(xy)
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def UI():
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while True:
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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: ")
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if fr == "q":
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break
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if fr == "2":
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xin = input("请输入x，格式x=x(t): ")
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yin = input("请输入y，格式y=y(t): ")
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else:
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forin = input("请输入方程: ")
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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: ")
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if fr == to:
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print("输入和输出的方程类型不能相同")
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else:
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try:
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if fr == "1":
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if to == "2":
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print("x = t")
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print("y =")
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pprint(xy_to_t(forin))
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elif to == "3":
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pprint(Eq(xy_to_polar(forin), 0))
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elif fr == "2":
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if to == "1":
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pprint(t_to_xy(xin, yin))
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elif to == "3":
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pprint(Eq(t_to_polar(xin, yin), 0))
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elif fr == "3":
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if to == "1":
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pprint(Eq(polar_to_xy(forin), 0))
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elif to == "2":
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print("x = t")
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print("y =")
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pprint(polar_to_t(forin))
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except Exception as e:
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print(f"错误: {e}")
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if __name__ == '__main__':
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UI() |
