Posing a prompt that gets a useful result currently requires some consideration. Below are some possible tasks for LLMs, along with additional context for the LLM.
Convert Latex to SymPy
TODO :
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: SymPy is an open-source Python library for symbolic computation. SymPy provides a computer algebra system. SymPy can convert Latex math to SymPy, and SymPy can render a mathematical expression as Latex.
Question: What is the SymPy representation for the Latex expression $x^2 + y^2 = 1$ ?
Answer:
Right response :
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: SymPy is an open-source Python library for symbolic computation. SymPy provides a computer algebra system. SymPy can convert Latex math to SymPy, and SymPy can render a mathematical expression as Latex.
Question: What is the SymPy representation for the Latex expression $\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}$ ?
Answer:
Right response :
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: SymPy is an open-source Python library for symbolic computation. SymPy provides a computer algebra system. SymPy can convert Latex math to SymPy, and SymPy can render a mathematical expression as Latex.
Question: What is the SymPy representation for the Latex expression $x = \langle\psi_{\alpha}| \hat{A} |\psi_{\beta}\rangle$ ?
Answer:
Right response :
Specify the mathematical relation between period and frequency as an equation in Latex
TODO :
Caveat : the page https://en.wikipedia.org/wiki/Frequency includes the statement that
"period is the reciprocal of the frequency: f = 1/T."
Use the context below to produce a result. Keep the response short and concise. Respond "Unsure about answer" if not sure about the answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: Period (symbol T) is the interval of time between events. Frequency (symbol f) is the number of occurrences of a repeating event per unit of time
Specify the mathematical relation between period and frequency as an equation in Latex.
Find arxiv papers with derivations
TODO :
Explain arxiv
define what I mean by a derivation
Provide example citations
Provide citations based on the context below.
Context: arxiv is an open-access repository of electronic preprints
Context: a derivation in mathematical Physics consists of a sequence of steps. Each step relates mathematical expressions to an inference rule. An expression is comprised of symbols and operators. An inference rule typically transforms input expressions into output expressions.
Cite three papers from arxiv that contain mathematical derivations with more than four steps.
Identify derivation steps between physics equations
TODO :
define what I mean by a derivation
Provide example steps
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer. Let's work this out in a step by step way to be sure we have the right answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: a derivation in mathematical Physics consists of a sequence of steps. Each step relates mathematical expressions to an inference rule. An expression is comprised of symbols and operators. An inference rule typically transforms input expressions into output expressions.
Question: What mathematical steps relate the Latex math expression $i x = log(y)$ and $\exp(i x) = y$ ?
Answer:
Right answer : Raise both sides as the power of $\exp$
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer. Let's work this out in a step by step way to be sure we have the right answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: a derivation in mathematical Physics consists of a sequence of steps. Each step relates mathematical expressions to an inference rule. An expression is comprised of symbols and operators. An inference rule typically transforms input expressions into output expressions.
Question: What is the derivative of $y = \cos(x) + i \sin(x)$ with respect to $x$ ?
Answer:
Right answer : $\frac{d}{dx} y = -\sin(x) + i\cos(x)$
Derive the wave function for a quantum particle in a 1D box
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer. Let's work this out in a step by step way to be sure we have the right answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Context: a derivation in mathematical Physics consists of a sequence of steps. Each step relates mathematical expressions to an inference rule. An expression is comprised of symbols and operators. An inference rule typically transforms input expressions into output expressions.
Question: derive the wave function for a quantum particle in a 1D box
Answer:
Right answer: see https://derivationmap.net/review_derivation/000010/
Derive Newton's Law of Universal Gravitation
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer. Let's work this out in a step by step way to be sure we have the right answer.
Context: a derivation in mathematical Physics consists of a sequence of steps. Each step relates mathematical expressions to an inference rule. An expression is comprised of symbols and operators. An inference rule typically transforms input expressions into output expressions.
provide a derivation of Newton's Law of Universal Gravitation
See https://physicsderivationgraph.blogspot.com/2023/06/finding-derivations-of-newtons-law-of.html
Convert derivation steps to a proof in Lean
TODO :
define what I mean by a derivation
Explain lean
Provide example
Emphasize correctness and precision
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer. Let's work this out in a step by step way to be sure we have the right answer.
Context: Lean is a proof assistant and programming language. Lean is based on the calculus of constructions with inductive types.
`a=b` is a proposition. The variable `a` is Real valued and `b` is Real valued. Prove in Lean that `(a=b) -> (a+2=b+2)`
Identify symbols in latex arxiv papers
TODO :
Provide example
Emphasize correctness and precision
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Question: What mathematical expressions are present in the following Latex?
```
\begin{equation}
a = b + c
\end{equation}
Assuming you know $b$, then
\begin{equation}
b*c = f
\end{equation}
```
Answer:
Answer the question based on the context below. Keep the answer short and concise. Respond "Unsure about answer" if not sure about the answer.
Context: Latex is software for document preparation to generate PDF files. Mathematical equations can be expressed in Latex using markup syntax.
Question: What variables are present in the following Latex?
```
\begin{equation}
a = b + c
\end{equation}
Assuming you know $b$, then
\begin{equation}
b*c = f
\end{equation}
```
Answer:
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