{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sage test display notebook\n", "\n", "This is to test various displays in the **Jupyter Notebook** (classic) or **JupyterLab**: LaTeX, interactive widgets, 2d and 3d plots, animated 3d plots, Matplotlib interface, etc., especially in the scope of `%display latex`. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 10.7, Release Date: 2025-08-09'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sage.version.banner" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\sin\\left(x^{2}\\right)\$" ], "text/latex": [ "$\\displaystyle \\sin\\left(x^{2}\\right)$" ], "text/plain": [ "sin(x^2)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(x^2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that long outputs are wrapped (cf. this [comment in #36129](https://github.com/sagemath/sage/pull/36129#issuecomment-1711714578)):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle x^{20} + 20 \\, x^{19} + 190 \\, x^{18} + 1140 \\, x^{17} + 4845 \\, x^{16} + 15504 \\, x^{15} + 38760 \\, x^{14} + 77520 \\, x^{13} + 125970 \\, x^{12} + 167960 \\, x^{11} + 184756 \\, x^{10} + 167960 \\, x^{9} + 125970 \\, x^{8} + 77520 \\, x^{7} + 38760 \\, x^{6} + 15504 \\, x^{5} + 4845 \\, x^{4} + 1140 \\, x^{3} + 190 \\, x^{2} + 20 \\, x + 1\$" ], "text/latex": [ "$\\displaystyle x^{20} + 20 \\, x^{19} + 190 \\, x^{18} + 1140 \\, x^{17} + 4845 \\, x^{16} + 15504 \\, x^{15} + 38760 \\, x^{14} + 77520 \\, x^{13} + 125970 \\, x^{12} + 167960 \\, x^{11} + 184756 \\, x^{10} + 167960 \\, x^{9} + 125970 \\, x^{8} + 77520 \\, x^{7} + 38760 \\, x^{6} + 15504 \\, x^{5} + 4845 \\, x^{4} + 1140 \\, x^{3} + 190 \\, x^{2} + 20 \\, x + 1$" ], "text/plain": [ "x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((1+x)^20).expand()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Miscellaneous outputs in the scope of `%display latex`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check that [#32859](https://github.com/sagemath/sage/issues/32859) is fixed (output of `type()`)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\verb|<class|\\verb| |\\verb|'sage.symbolic.expression.Expression'>|\$" ], "text/latex": [ "$\\displaystyle \\verb||$" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check that [#32208](https://github.com/sagemath/sage/issues/32208) is fixed" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\verb|{1,|\\verb| |\\verb|2}|\$" ], "text/latex": [ "$\\displaystyle \\verb|{1,|\\verb| |\\verb|2}|$" ], "text/plain": [ "{1, 2}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set([1,2])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\begin{array}{l}\n", "\\verb| |\\verb|┌──────────────┐|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|1|\\verb| |\\verb|2|\\verb| |\\verb|3|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|4|\\verb| |\\verb|top|\\verb| |\\verb|5|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|6|\\verb| |\\verb|7|\\verb| |\\verb|8|\\verb| |\\verb|│|\\\\\n", "\\verb|┌────────────┼──────────────┼─────────────┬────────────┐|\\\\\n", "\\verb|│|\\verb| |\\verb|9|\\verb| |\\verb|10|\\verb| |\\verb|11|\\verb| |\\verb|│|\\verb| |\\verb|17|\\verb| |\\verb|18|\\verb| |\\verb|19|\\verb| |\\verb|│|\\verb| |\\verb|25|\\verb| |\\verb|26|\\verb| |\\verb|27|\\verb| |\\verb|│|\\verb| |\\verb|33|\\verb| |\\verb|34|\\verb| |\\verb|35|\\verb| |\\verb|│|\\\\\n", "\\verb|│|\\verb| |\\verb|12|\\verb| |\\verb|left|\\verb| |\\verb|13|\\verb| |\\verb|│|\\verb| |\\verb|20|\\verb| |\\verb|front|\\verb| |\\verb|21|\\verb| |\\verb|│|\\verb| |\\verb|28|\\verb| |\\verb|right|\\verb| |\\verb|29|\\verb| |\\verb|│|\\verb| |\\verb|36|\\verb| |\\verb|rear|\\verb| |\\verb|37|\\verb| |\\verb|│|\\\\\n", "\\verb|│|\\verb| |\\verb|14|\\verb| |\\verb|15|\\verb| |\\verb|16|\\verb| |\\verb|│|\\verb| |\\verb|22|\\verb| |\\verb|23|\\verb| |\\verb|24|\\verb| |\\verb|│|\\verb| |\\verb|30|\\verb| |\\verb|31|\\verb| |\\verb|32|\\verb| |\\verb|│|\\verb| |\\verb|38|\\verb| |\\verb|39|\\verb| |\\verb|40|\\verb| |\\verb|│|\\\\\n", "\\verb|└────────────┼──────────────┼─────────────┴────────────┘|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|41|\\verb| |\\verb|42|\\verb| |\\verb|43|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|44|\\verb| |\\verb|bottom|\\verb| |\\verb|45|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|46|\\verb| |\\verb|47|\\verb| |\\verb|48|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|└──────────────┘|\\\\\n", "\n", "\\end{array}\\)" ], "text/latex": [ "$\\displaystyle \\begin{array}{l}\n", "\\verb| |\\verb|┌──────────────┐|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|1|\\verb| |\\verb|2|\\verb| |\\verb|3|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|4|\\verb| |\\verb|top|\\verb| |\\verb|5|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|6|\\verb| |\\verb|7|\\verb| |\\verb|8|\\verb| |\\verb|│|\\\\\n", "\\verb|┌────────────┼──────────────┼─────────────┬────────────┐|\\\\\n", "\\verb|│|\\verb| |\\verb|9|\\verb| |\\verb|10|\\verb| |\\verb|11|\\verb| |\\verb|│|\\verb| |\\verb|17|\\verb| |\\verb|18|\\verb| |\\verb|19|\\verb| |\\verb|│|\\verb| |\\verb|25|\\verb| |\\verb|26|\\verb| |\\verb|27|\\verb| |\\verb|│|\\verb| |\\verb|33|\\verb| |\\verb|34|\\verb| |\\verb|35|\\verb| |\\verb|│|\\\\\n", "\\verb|│|\\verb| |\\verb|12|\\verb| |\\verb|left|\\verb| |\\verb|13|\\verb| |\\verb|│|\\verb| |\\verb|20|\\verb| |\\verb|front|\\verb| |\\verb|21|\\verb| |\\verb|│|\\verb| |\\verb|28|\\verb| |\\verb|right|\\verb| |\\verb|29|\\verb| |\\verb|│|\\verb| |\\verb|36|\\verb| |\\verb|rear|\\verb| |\\verb|37|\\verb| |\\verb|│|\\\\\n", "\\verb|│|\\verb| |\\verb|14|\\verb| |\\verb|15|\\verb| |\\verb|16|\\verb| |\\verb|│|\\verb| |\\verb|22|\\verb| |\\verb|23|\\verb| |\\verb|24|\\verb| |\\verb|│|\\verb| |\\verb|30|\\verb| |\\verb|31|\\verb| |\\verb|32|\\verb| |\\verb|│|\\verb| |\\verb|38|\\verb| |\\verb|39|\\verb| |\\verb|40|\\verb| |\\verb|│|\\\\\n", "\\verb|└────────────┼──────────────┼─────────────┴────────────┘|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|41|\\verb| |\\verb|42|\\verb| |\\verb|43|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|44|\\verb| |\\verb|bottom|\\verb| |\\verb|45|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|│|\\verb| |\\verb|46|\\verb| |\\verb|47|\\verb| |\\verb|48|\\verb| |\\verb|│|\\\\\n", "\\verb| |\\verb|└──────────────┘|\\\\\n", "\n", "\\end{array}$" ], "text/plain": [ " ┌──────────────┐\n", " │ 1 2 3 │\n", " │ 4 top 5 │\n", " │ 6 7 8 │\n", "┌────────────┼──────────────┼─────────────┬────────────┐\n", "│ 9 10 11 │ 17 18 19 │ 25 26 27 │ 33 34 35 │\n", "│ 12 left 13 │ 20 front 21 │ 28 right 29 │ 36 rear 37 │\n", "│ 14 15 16 │ 22 23 24 │ 30 31 32 │ 38 39 40 │\n", "└────────────┼──────────────┼─────────────┴────────────┘\n", " │ 41 42 43 │\n", " │ 44 bottom 45 │\n", " │ 46 47 48 │\n", " └──────────────┘\n" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "RubiksCube()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check that [#33729](https://github.com/sagemath/sage/issues/33729) is fixed" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\newcommand{\\ZZ}{\\Bold{Z}}\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ZZ/6\\ZZ\$" ], "text/latex": [ "$\\displaystyle \\newcommand{\\ZZ}{\\Bold{Z}}\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ZZ/6\\ZZ$" ], "text/plain": [ "Ring of integers modulo 6" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IntegerModRing(6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test of IPython native LaTeX display via `_repr_latex_`\n", "\n", "IPython implements LaTeX display of all objects that are endowed with a method `_repr_latex_`, cf. IPyhton's [rich display documentation](https://ipython.readthedocs.io/en/stable/config/integrating.html)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "%display plain" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sin(x^2)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = sin(x^2)\n", "s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the plain text mode, the only way to get the LaTeX display of some object is via the function `view`, which generates a pdf file:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "view(s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us test the `_repr_latex_` mechanism of IPython via the method `_latex_` of Sage objects:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'\\\\sin\\\\left(x^{2}\\\\right)'" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s._latex_()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "class NativeDisplay(SageObject):\n", "\n", " def __init__(self, data):\n", " self._data = data\n", "\n", " def _repr_latex_(self):\n", " try:\n", " return '$' + self._data._latex_() + '$'\n", " except (AttributeError, NotImplementedError): \n", " return None # if None is returned, plain text is used\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get a LaTeX display, even if we are the scope of `%display plain`:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sin(x^2)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\sin\\left(x^{2}\\right)$" ], "text/plain": [ "<__main__.NativeDisplay object at 0x7e816e0b1940>" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "NativeDisplay(s)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<__main__.NativeDisplay object at 0x7e816e0b1910>" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "NativeDisplay([s, s])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "<__main__.NativeDisplay object at 0x7e816e7ad850>\n" ] } ], "source": [ "g = plot(s)\n", "print(NativeDisplay(g))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Test of IPython native LaTeX display in the scope of `%display latex`\n", "**(this fails in Sage 9.6.rc2 and Sage 10.2.rc1)**:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\verb|<__main__.NativeDisplay|\\verb| |\\verb|object|\\verb| |\\verb|at|\\verb| |\\verb|0x7e816e0840e0>|\$" ], "text/latex": [ "$\\displaystyle \\verb|<__main__.NativeDisplay|\\verb| |\\verb|object|\\verb| |\\verb|at|\\verb| |\\verb|0x7e816e0840e0>|$" ], "text/plain": [ "<__main__.NativeDisplay object at 0x7e816e0840e0>" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "\n", "NativeDisplay(s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test of matplotlib.pyplot\n", "\n", "### Check that [#32882](https://github.com/sagemath/sage/issues/32882) is fixed:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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