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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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left = simplify(sympify(l[0]+'-('+l[1]+')'))
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return 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', 'arctan(y/x)')
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l = formula.split('=')
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x, y = symbols('x y')
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left = simplify(sympify(l[0]+'-('+l[1]+')'))
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return 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)
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yf = yf.replace('t', str(tl[0]))
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yl = yf.split('=')
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y, t = symbols('y t')
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eq2 = Eq(sympify(yl[0]), sympify(yl[1]))
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return 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)
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return l2
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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 == "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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elif fr == "q":
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break
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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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if fr == "1":
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if to == "2":
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print("x = x")
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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 = x")
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print("y = ")
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pprint(polar_to_t(forin))
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if __name__ == '__main__':
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UI() |
