{ "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 10.2.rc1, Release Date: 2023-11-10'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "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 0x7f749fe78df0>" ] }, "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 0x7f749fe78370>" ] }, "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 0x7f749fe796f0>\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|0x7f749fea4c10>|\$" ], "text/latex": [ "$\\displaystyle \\verb|<__main__.NativeDisplay|\\verb| |\\verb|object|\\verb| |\\verb|at|\\verb| |\\verb|0x7f749fea4c10>|$" ], "text/plain": [ "<__main__.NativeDisplay object at 0x7f749fea4c10>" ] }, "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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\n", "text/plain": [ "