The Query command sends a query to a large language model, attempting to instruct the model to use both natural language and MathML. Maple tries to split the answer into MathML and non-MathML, parse the MathML, and then print the results on screen. The command does not return anything.

Maple can interface with OpenAI's GPT-4 and ChatGPT models. The default model is GPT-4; you can select ChatGPT by using the $\mathrm{model}=\mathrm{ChatGPT}$ option, or force use of the GPT-4 model by using the $\mathrm{model}=\mathrm{GPT4}$ option. Note that OpenAI may deprecate and disable models, so the set of models supported may change in the future.

Note: Large language models often generate inaccurate statements. Please keep this in mind: this is not technology for building a bridge with.

$\mathrm{with}\left(\mathrm{NaturalLanguage}\right)\:$

$\mathrm{Query}\left(''What\; is\; Pythagoras\text{'}\; Theorem?''\right)$

$''Pythagoras\text{'}\; Theorem\; states\; that\; in\; a\; right-angled\; triangle,\; the\; square\; of\; the\; length\; of\; the\; hypotenuse\; (the\; side\; opposite\; the\; right\; angle)\; is\; equal\; to\; the\; sum\; of\; the\; squares\; of\; the\; lengths\; of\; the\; other\; two\; sides.\; This\; can\; be\; written\; as:\; a²\; +\; b²\; =\; c²\; where\; c\; represents\; the\; length\; of\; the\; hypotenuse,\; and\; a\; and\; b\; represent\; the\; lengths\; of\; the\; other\; two\; sides.\; this\; formula\; can\; be\; represented\; as:''$

$a^2+b^2=c^2$

$\mathrm{Query}\left(''How\; do\; I\; calculate\; the\; Sharpe\; ratio\; for\; financial\; analysis?''\,\mathrm{model}=\mathrm{ChatGPT}\right)$

$To calculate the Sharpe ratio, you need to follow the formula and perform the necessary calculations. Here's an explanation in English and the corresponding MathML representation: 1. Gather the necessary data: Start by obtaining the historical returns of the financial asset or portfolio you want to analyze, as well as the risk-free rate, typically represented by a T-bill or a similar benchmark. 2. Calculate the excess return: Subtract the risk-free rate from the average return of the asset or portfolio. This measures the excess return generated above the risk-free rate. a = Average return of the asset or portfolio b = Risk-free rate Excess return = a - b 3. Calculate the standard deviation of the asset or portfolio: Measure the volatility or risk of the asset or portfolio using the standard deviation of its returns. s = Standard deviation of the asset or portfolio 4. Compute the Sharpe ratio: Divide the excess return by the standard deviation to determine the risk-adjusted return of the asset or portfolio. Sharpe ratio = (a - b) / s The Sharpe ratio provides insights into the risk-adjusted performance of an investment. A higher ratio indicates a better risk-adjusted return, while a lower ratio suggests a lower return relative to the assumed risk. Please note that some of the MathML formulas may not render properly depending on the platform or browser you are using.$

$\mathrm{Query}\left(''What\; is\; the\; volume\; of\; a\; partially\; filled\; sphere?''\right)$

$''The\; volume\; of\; a\; partially\; filled\; sphere,\; also\; known\; as\; a\; spherical\; cap,\; can\; be\; found\; using\; the\; following\; formula:\; V\; =\; (\pi h^2\; /\; 3)*(3r\; -\; h)\; where:\; -\; V\; is\; the\; volume\; of\; the\; spherical\; cap,\; -\; h\; is\; the\; depth\; or\; height\; of\; the\; liquid\; in\; the\; sphere\; (from\; the\; top\; of\; the\; sphere\; to\; the\; surface\; of\; the\; liquid),\; and\; -\; r\; is\; the\; radius\; of\; the\; sphere.\; Note\; that\; r\; and\; h\; must\; be\; in\; the\; same\; units\; (e.g.,\; all\; in\; inches\; or\; all\; in\; centimeters)\; for\; the\; formula\; to\; work.''$

$V=\frac{\mathrm{\pi }{h}^2\left(3r-h\right)}{3}$

$''Remember\; that\; this\; formula\; considers\; that\; the\; sphere\; is\; sitting\; with\; its\; base\; on\; a\; surface\; and\; is\; not\; so\; appropriate\; if\; the\; sphere\; is\; floating\; in\; space.''$

The OpenAI website.

The NaturalLanguage:-Query command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.