![]() ![]() ![]() The lesson I learned, though, was to never use Mathematica for anything beyond basic symbolic calculations-integrals, that sort of thing. (Honestly, I feel pretty stupid for having even tried to do it in Mathematica in the first place.) Now, this is in part about the problem domain: I wasn't doing any symbolic manipulation, though (IIRC) I was comparing my results with those from some symbolic calculations. That was a rather more pleasant experience. Ultimately I re-wrote it in Julia, which was a much better fit for the problem (exact diagonalization of a one-particle tight-binding Hamiltonian). Moreover, I never figured out how to do iterations quickly even once I got the thing working, it was prohibitively slow. (I find my eyes glazing over almost immediately when I try to read the Wolfram blog: it's so very hard for me to see the structure of the code.) Perhaps once you become happy with the core principles of the language all of this gets better, but I spent quite a lot of time thinking it and never really got there. The jungle of function-definition-like expressions and the scoping constructs were particularly bad, but I also found that the language & the culture made it far too difficult to write readable code. ![]() Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people-spanning all professions and education levels.I found that "just using it as a lisp" was a huge pain: the fact that Mathematica is, as you say, "actually a rule rewriting engine" kept causing it to behave in ways that looked absolutely bonkers if you were trying to think Lisp. To cross check using Wolfram derivative of 2-(2/t) - Wolfram|Alpha For more complex functions, additional rules (like for exponentiation, trigonometric functions, etc.) would need to be added. This Prolog program is a basic implementation and works for the given function. In Prolog, you would query this as: ?- derivative(2 - (2 / t), t, Result).Īnd the expected output should be: Result = 2 / t^2. The derivative of 2 - (2/t) is 0 - (-2 / t^2), which simplifies to 2 / t^2.2 is a constant, so its derivative is 0.df/dt = derivative of 2 and dg/dt = derivative of 2/t.Now, let’s calculate the derivative of 2 - (2/t) step by step: Let’s define these rules in Prolog: % Derivative of a constant is 0ĭerivative(U / V, t, (V * DU - U * DV) / (V * V)) :. Derivative of Division: The derivative of u/v is (v * du/dt - u * dv/dt) / v^2, where du/dt is the derivative of u with respect to t, and dv/dt is the derivative of v with respect to t.Derivative of Subtraction: The derivative of f - g is the derivative of f minus the derivative of g.Derivative of a Variable (like t): The derivative of t with respect to t is 1.Derivative of a Constant: The derivative of a constant is zero.We need rules for constants, subtraction, and division. In Prolog, we can define rules for the derivative of constants, power functions, addition, subtraction, multiplication, division, and more complex functions as needed.įor the task at hand, let’s focus on the necessary rules to differentiate the function 2 - (2/t). Don’t be so fast to shoot ChatGPT down or LLMs for that matter.Ĭreate the rules of calculus derivatives for Prolog then show step by step how to calculate the derivative of 2-(2/t)Ĭreating a Prolog program to handle calculus derivatives involves defining rules that capture the basic principles of differentiation. ![]()
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