求推荐支持多变量函数操作的免费数学软件

Great question! If you're looking for free alternatives to Maple that cover all the features you mentioned—fixing variables in multivariable functions and simplifying, computing partial derivatives, and doing definite integrals (with analytical solutions preferred, numerical when needed)—here are some solid options:

SymPy (Python Library) #

SymPy is a fully open-source, free symbolic mathematics library for Python, perfect if you don't mind a bit of coding. It handles all your required tasks smoothly:

• Fix variables & simplify: Define your function, substitute the fixed variable value, then simplify the result. Example code:

  from sympy import symbols, simplify, diff, integrate
  
  # Define variables and function
  x, y = symbols('x y')
  f = x**2 + x*y + y**2
  
  # Fix y=3 and simplify
  simplified_f = simplify(f.subs(y, 3))
  # Output: x² + 3x + 9
  

• Partial derivatives: Use the diff() function to compute partial derivatives with respect to any variable:

  partial_x = diff(f, x)  # Output: 2x + y
  partial_y = diff(f, y)  # Output: x + 2y
  

• Region integration: Prioritizes analytical solutions for definite integrals; if no closed-form exists, you can pair it with SciPy's numerical integration tools for approximate results:

  # Analytical double integral over x=0→1, y=0→2
  analytical_integral = integrate(f, (x, 0, 1), (y, 0, 2))
  # Output: 13/3 ≈ 4.333
  

Wolfram Alpha (Free Web Version) #

Wolfram Alpha's free tier is a no-code option that's incredibly user-friendly, though it has daily query limits. It supports all your use cases with natural language input:

• Fix variables & simplify: Type something like x² + xy + y² where y=3, simplify and it will return the simplified single-variable function.
• Partial derivatives: Input partial derivative of x² + xy + y² with respect to x to get the result instantly.
• Region integration: Enter integrate x² + xy + y² from x=0 to 1, y=0 to 2—it will first try to return an analytical solution, and switch to numerical results if the integral can't be solved symbolically.

Maxima (Open-Source CAS) #

Maxima is a classic, free computer algebra system (similar in style to Maple) that runs on desktop or via web interfaces like wxMaxima. It's great if you prefer a traditional CAS workflow:

• Fix variables & simplify: Use substitution and simplification commands:

  f: x^2 + x*y + y^2;
  ratsimp(substitute(f, y=3));  /* Output: x² + 3x + 9 */
  

• Partial derivatives: Compute partial derivatives with the diff() function:

  diff(f, x);  /* Output: 2x + y */
  diff(f, y);  /* Output: x + 2y */
  

• Region integration: Supports analytical definite integrals, and can fall back to numerical methods when needed:

  integrate(f, x, 0, 1, y, 0, 2);  /* Output: 13/3 */
  

All these tools are completely free and should cover every requirement you listed!

内容的提问来源于stack exchange，提问作者steviekm3