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from sympy import *
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from matplotlib.pyplot import *
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from convert_formula import *
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def basic_caculate(formula):
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return eval(convert_formula(formula).replace('*j', 'j'))
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def solve_formula(formula, independent_variable=1):
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"""
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求解方程
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:param formula: 方程列表
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:param independent_variable: 变量个数
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:return: 方程解
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"""
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llist = []
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x, y, z = symbols('x y z')
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for i in formula:
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l = i.split('=')
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left = l[0] + '-(' + l[1] + ')'
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llist.append(sympify(convert_formula(left)))
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if independent_variable == 1:
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return solve(llist[0], x)
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elif independent_variable == 2:
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return solve((llist[0], llist[1]), (x, y))
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elif independent_variable == 3:
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return solve((llist[0], llist[1], llist[2]), (x, y, z))
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def plot_function(formula, length):
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"""
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绘制函数图像
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:param formula: 函数表达式
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:param length: 自变量取值范围
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:return: 图像
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"""
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x = np.linspace(length[0], length[1], 1000)
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independent, formula = split_function(convert_formula(formula))
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y = eval('lambda %s: %s' % (independent, formula)) # 使用eval直接生成lambda函数
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plot(x, y(x))
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show()
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def plot_implicit_function(formula, x_range=(-5, 5), y_range=(-5, 5), density=200):
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'''
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绘制隐函数图像（如 x²+y²=1）
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:param formula: 隐函数表达式（字符串，如 "x**2 + y**2 - 1"）
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:param x_range: x轴取值范围（元组，如 (-5,5)）
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:param y_range: y轴取值范围（元组，如 (-5,5)）
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:param density: 网格点密度（数值越大越平滑）
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'''
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# 生成x和y的网格点
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x = np.linspace(x_range[0], x_range[1], density)
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y = np.linspace(y_range[0], y_range[1], density)
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X, Y = np.meshgrid(x, y)
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# 转换表达式（复用现有convert_formula处理符号）
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formula = convert_formula(formula)
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l = formula.split('=')
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formula = l[0]+'-('+l[1]+')'
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# 计算网格点的函数值F(x,y)
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try:
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F = eval(formula.replace('x', 'X').replace('y', 'Y')) # 将表达式中的x/y替换为二维网格X/Y
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except Exception as e:
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raise ValueError(f"表达式错误：{e}")
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# 绘制F(x,y)=0的等高线（即隐函数图像）
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contour(X, Y, F, levels=[0], colors='blue')
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grid(True)
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show()
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def UI():
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while True:
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command = input('请选择功能：1.基本计算 2.解方程 3.绘制函数图像 4.绘制平面解析几何图像 5.退出\n')
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if command == '1':
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formula = input('请输入算式：')
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print(basic_caculate(formula))
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elif command == '2':
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independent_variable = input('请输入方程未知量个数：')
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formula = input('请输入方程组（方程之间用英文逗号分隔）：')
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print(solve_formula(formula.split(','), int(independent_variable)))
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elif command == '3':
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formula = input('请输入函数表达式（如 f(x)=x^2）：')
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length = input('请输入自变量取值范围（区间形式，不支持半开半闭区间）：')
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plot_function(formula, eval(length))
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elif command == '4':
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formula = input('请输入隐函数表达式（如 x^2+y^2=1）：')
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plot_implicit_function(formula)
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elif command == '5':
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print('谢谢使用！')
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break
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else:
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print('输入错误，请重新输入！')
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if __name__ == '__main__':
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UI() |
