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docs:Better examples.
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‎docs/Basic-usage.ipynb‎

Lines changed: 90 additions & 32 deletions
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},
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"cell_type": "code",
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"outputs": [],
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},
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{
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"cell_type": "code",
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"outputs": [
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"[\"Root\",[\"Add\",[\"Add\",[\"Multiply\",4,[\"Power\",\"x\",2]],[\"Multiply\",12,\"x\"]],9],2]"
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]
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},
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"cell_type": "code",
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"id": "7a12674f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<table border=\"1\"><thead><tr><th>expr</th><th>Cortex-JS</th><th>LaTeX::Grammar</th></tr></thead><tbody><tr><td align=left>4 x^2 + 12 x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Power&quot;,&quot;4 x&quot;,2],&quot;12 x&quot;],9]</td></tr><tr><td align=left>4 \\times x^2 + 12 \\times x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left>4 * x^2 + 12 * x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left>\\sqrt{4 * x^2 + 12 * x + 9}</td><td align=left>$[&quot;Sqrt&quot;, [&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]]</td><td align=left>[&quot;Root&quot;,[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9],2]</td></tr></tbody></table>"
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"<table border=\"1\"><thead><tr><th>expr</th><th>Cortex-JS</th><th>LaTeX::Grammar</th></tr></thead><tbody><tr><td align=left><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><msup><mi>4 x</mi><mn>2</mn></msup><mo>+</mo><mi>12 x</mi></mrow><mo>+</mo><mn>9</mn></mrow></math></td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Power&quot;,&quot;4 x&quot;,2],&quot;12 x&quot;],9]</td></tr><tr><td align=left><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mrow><mn>4</mn><mo>&#xD7;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow><mn>12</mn><mo>&#xD7;</mo><mi>x</mi></mrow></mrow><mo>+</mo><mn>9</mn></mrow></math></td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mrow><mn>4</mn><mo>&#xD7;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow><mn>12</mn><mo>&#xD7;</mo><mi>x</mi></mrow></mrow><mo>+</mo><mn>9</mn></mrow></math></td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mrow><mrow><msup><mi>4x</mi><mn>2</mn></msup><mo>+</mo><mi>12x</mi></mrow><mo>+</mo><mn>9</mn></mrow></msqrt></math></td><td align=left>$[&quot;Sqrt&quot;, [&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]]</td><td align=left>[&quot;Root&quot;,[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Power&quot;,&quot;4x&quot;,2],&quot;12x&quot;],9],2]</td></tr><tr><td align=left><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mrow><mrow><mrow><mn>4</mn><mo>&#xD7;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow><mn>12</mn><mo>&#xD7;</mo><mi>x</mi></mrow></mrow><mo>+</mo><mn>9</mn></mrow></msqrt></math></td><td align=left>$[&quot;Sqrt&quot;, [&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]]</td><td align=left>[&quot;Root&quot;,[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9],2]</td></tr></tbody></table>"
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" '4 x^2 + 12 x + 9',\n",
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" '4 \\times x^2 + 12 \\times x + 9',\n",
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" '4 * x^2 + 12 * x + 9',\n",
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" '\\sqrt{4 * x^2 + 12 * x + 9}'\n",
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" '\\sqrt{4x^2 + 12x + 9}',\n",
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" '\\sqrt{4 * x^2 + 12 * x + 9}',\n",
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"]\n",
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"andthen $_.map({ %(expr => $_, Cortex-JS => parse-latex($_).raku, 'LaTeX::Grammar' => latex-interpret($_)) })\n",
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"andthen .&to-html(field-names => <expr Cortex-JS LaTeX::Grammar>, align => 'left')"
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"andthen $_.map({ %(expr => \"latex«$_»\", Cortex-JS => parse-latex($_).raku, 'LaTeX::Grammar' => latex-interpret($_)) })\n",
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"andthen .&to-html(field-names => <expr Cortex-JS LaTeX::Grammar>, align => 'left')\n",
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"andthen .subst(/ 'latex«' (.*?) '»' /, { latex-interpret($0.Str, actions => 'MathML')}, :g)"
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"-1"
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"outputs": [
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"a^2+b^2+2ab"
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]
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"$2x^2+3x^2+x+5$ = $5x^2+x+5$"
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]
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},
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"$\\sqrt{5x^2+x+5}$"
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]
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"[3 2]"
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"$3+2\\sqrt{2}, \\: 3-2\\sqrt{2}$"
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"$x+\\frac{1}{x}$"
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"## Calculus"
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{
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"cell_type": "markdown",
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"id": "7a7310a7",
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"metadata": {},
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"source": [
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"Derivate of expression over the variable $x$:"
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"==> to-latex()"
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{
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"source": [
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"Evaluate the undefined integral $\\int x^2 dx$:"
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"==> to-latex()"
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{
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"cell_type": "markdown",
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"id": "d8ffd0d5",
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"metadata": {},
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"source": [
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"Evaluate the defined integral $\\int_{0}^{1} x^2 dx$:"
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"==> to-latex()"
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{
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"cell_type": "markdown",
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"id": "b3c7af81",
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"metadata": {},
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"source": [
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"Evaluate the limit $\\lim_{x \\to 0} \\frac{\\sin(x)}{x}$:"
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]
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"'\\lim_{x \\to 0} \\frac{\\sin(x)}{x}'\n",
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"==> parse-latex()\n",
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"==> evaluate()\n",
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"==> N()"
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]
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},
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"6"
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