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34 lines
5.6 KiB
34 lines
5.6 KiB
{ |
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"created_at": 1752150799, |
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"content": "# This is a test file for writing mathematical formulas in #NostrMarkup\n\nThis document covers the rendering of formulas in TeX/LaTeX and AsciiMath notation, or some combination of those within the same page. It is meant to be rendered by clients utilizing MathJax.\n\nIf you want the entire document to be rendered as mathematics, place the entire thing in a back-tick code-block, but know that this makes the document slower to load, it is harder to format the prose, and the result is less legible. It also doesn't increase portability, as it's easy to export markup as LaTeX files, or as PDFs, with the formulas rendered.\n\nThe general idea, is that anything placed within `single back-ticks` is inline code, and inline-code will all be scanned for typical mathematics statements and rendered with best-effort. (For more precise rendering, use AsciiDoc.) We will not render text that is not marked as inline code, as mathematical formulas, as that is prose.\n\nIf you want the TeX to be blended into the surrounding text, wrap the text within single `$`. Otherwise, use double `$$` symbols, for display math, and it will appear on its own line.\n\n## TeX Examples\n\nInline equation: `$\\sqrt{x}$`\n\nSame equation, in the display mode: `$$\\sqrt{x}$$`\n\nSomething more complex, inline: `$\\mathbb{N} = \\{ a \\in \\mathbb{Z} : a > 0 \\}$`\n\nSomething complex, in display mode: `$$P \\left( A=2 \\, \\middle| \\, \\dfrac{A^2}{B}>4 \\right)$$`\n\nAnother example of `$$\\prod_{i=1}^{n} x_i - 1$$` inline formulas.\n\nFunction example: \n`$$\nf(x)=\n\\begin{cases}\n1/d_{ij} & \\quad \\text{when $d_{ij} \\leq 160$}\\\\ \n0 & \\quad \\text{otherwise}\n\\end{cases}\n$$`\n\nAnd a matrix:\n`$$\nM = \n\\begin{bmatrix}\n\\frac{5}{6} & \\frac{1}{6} & 0 \\\\[0.3em]\n\\frac{5}{6} & 0 & \\frac{1}{6} \\\\[0.3em]\n0 & \\frac{5}{6} & \\frac{1}{6}\n\\end{bmatrix}\n$$`\n\nLaTeX ypesetting won't be rendered. Use NostrMarkup delimeter tables for this sort of thing.\n\n`\\\\begin{tabular}{|c|c|c|l|r|}\n\\\\hline\n\\\\multicolumn{3}{|l|}{test} & A & B \\\\\\\\\n\\\\hline\n1 & 2 & 3 & 4 & 5 \\\\\\\\\n\\\\hline\n\\\\end{tabular}`\n\nWe also recognize common LaTeX statements:\n\n`\\[\n\\begin{array}{ccccc}\n1 & 2 & 3 & 4 & 5 \\\\\n\\end{array}\n\\]`\n\n`\\[ x^n + y^n = z^n \\]`\n\n`\\sqrt{x^2+1}`\n\nGreek letters are a snap: `$\\Psi$`, `$\\psi$`, `$\\Phi$`, `$\\phi$`. \n\nEquations within text are easy--- A well known Maxwell thermodynamic relation is `$\\left.{\\partial T \\over \\partial P}\\right|_{s} = \\left.{\\partial v \\over \\partial s}\\right|_{P}$`.\n\nYou can also set aside equations like so: `\\begin{eqnarray} du &=& T\\ ds -P\\ dv, \\qquad \\mbox{first law.}\\label{fl}\\\\ ds &\\ge& {\\delta q \\over T}.\\qquad \\qquad \\mbox{second law.} \\label{sl} \\end {eqnarray}`\n\n## And some good ole Asciimath\n\nAsciimath doesn't use `$` or `$$` delimiters, but we are using it to make mathy stuff easier to find. If you want it inline, include it inline. If you want it on a separate line, put a hard-return before and after.\n\nInline text example here `$E=mc^2$` and another `$1/(x+1)$`; very simple.\n\nDisplaying on a separate line:\n\n`$$sum_(k=1)^n k = 1+2+ cdots +n=(n(n+1))/2$$`\n\n`$$int_0^1 x^2 dx$$`\n\n`$$x = (-6 +- sqrt((-6)^2 - 4 (1)(4)))/(2 xx 1)$$`\n\n`$$|x|= {(x , if x ge 0 text(,)),(-x , if x <0.):}$$`\n\nDisplaying with wider spacing:\n\n`$a=3, \\ \\ \\ b=-3,\\ \\ $` and `$ \\ \\ c=2$`.\n\nThus `$(a+b)(c+b)=0$`.\n\nDisplaying with indentations:\n\nUsing the quadratic formula, the roots of `$x^2-6x+4=0$` are\n\n`$$x = (-6 +- sqrt((-6)^2 - 4 (1)(4)))/(2 xx 1)$$`\n\n`$$ \\ \\ = (-6 +- sqrt(36 - 16))/2$$`\n\n`$$ \\ \\ =(-6 +- sqrt(20))/2$$`\n\n`$$ \\ \\ = -0.8 or 2.2 \\ \\ \\ $$` to 1 decimal place.\n\nAdvanced alignment and matrices looks like this:\n\nA `$3xx3$` matrix, `$$((1,2,3),(4,5,6),(7,8,9))$$` and a `$2xx1$` matrix, or vector, `$$((1),(0))$$`.\n\nThe outer brackets determine the delimiters e.g. `$|(a,b),(c,d)|=ad-bc$`.\n\nA general `$m xx n$` matrix `$$((a_(11), cdots , a_(1n)),(vdots, ddots, vdots),(a_(m1), cdots , a_(mn)))$$`\n\n## Mixed Examples\n\nHere are some examples mixing LaTeX and AsciiMath:\n\n- LaTeX inline: `$\\frac{1}{2}$` vs AsciiMath inline: `$1/2$`\n- LaTeX display: `$$\\sum_{i=1}^n x_i$$` vs AsciiMath display: `$$sum_(i=1)^n x_i$$`\n- LaTeX matrix: `$$\\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$$` vs AsciiMath matrix: `$$((a,b),(c,d))$$`\n\n## Edge Cases\n\n- Empty math: `$$`\n- Just delimiters: `$ $`\n- Dollar signs in text: The price is $10.50\n- Currency: `$19.99`\n- Shell command: `echo \"Price: $100\"`\n- JavaScript template: `const price = \\`$${amount}\\``\n- CSS with dollar signs: `color: $primary-color`\n\nThis document should demonstrate that:\n1. LaTeX is processed within inline code blocks with proper delimiters\n2. AsciiMath is processed within inline code blocks with proper delimiters\n3. Regular code blocks remain unchanged\n4. Mixed content is handled correctly\n5. Edge cases are handled gracefully", |
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