\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{gloo13}
\pdfinfo{
  /Title (sympy.pdf)
  /Creator (Cheatography)
  /Author (gloo13)
  /Subject (Sympy Cheat Sheet)
}

% Lengths and widths
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\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
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\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{A3A3A3}
\definecolor{LightBackground}{HTML}{F3F3F3}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Sympy Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{gloo13} via \textcolor{DarkBackground}{\uline{cheatography.com/185324/cs/39863/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}gloo13 \\
  \uline{cheatography.com/gloo13} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 13th August, 2023.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Basic Operations}}  \tn
% Row 0
\SetRowColor{LightBackground}
expr.subs({[}(x, 2), (y, 4), (z, 0){]}) & substitute x with 2 etc. \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
sympify(str\_expr) & convert strings into SymPy expressions \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
expr.evalf(15, chop=True) & evaluate a numerical expression into a floating point number \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
lambdify(x, expr, "numpy") & converts the SymPy names to the names of the given numerical library \tn 
% Row Count 11 (+ 4)
% Row 4
\SetRowColor{LightBackground}
init\_printing() & This will automatically enable the best printer available in your environment. \tn 
% Row Count 15 (+ 4)
% Row 5
\SetRowColor{white}
simplify(expr) & simplify mathematical expressions \tn 
% Row Count 17 (+ 2)
% Row 6
\SetRowColor{LightBackground}
expand(expr) & expand polynomial expressions \tn 
% Row Count 19 (+ 2)
% Row 7
\SetRowColor{white}
factor(expr) & takes a polynomial and factors it into irreducible factors over the rational numbers \tn 
% Row Count 23 (+ 4)
% Row 8
\SetRowColor{LightBackground}
factor\_list(expr) & returns a list with the factors. More structured. \tn 
% Row Count 26 (+ 3)
% Row 9
\SetRowColor{white}
collect(expr, x) & collects common powers of a term in an expression \tn 
% Row Count 29 (+ 3)
% Row 10
\SetRowColor{LightBackground}
cancel(expr) & take any rational function and put it into the standard canonical form \tn 
% Row Count 33 (+ 4)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Basic Operations (cont)}}  \tn
% Row 11
\SetRowColor{LightBackground}
apart(expr) & performs a partial fraction decomposition on a rational function \tn 
% Row Count 4 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.23965 cm} x{2.73735 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Matrices}}  \tn
% Row 0
\SetRowColor{LightBackground}
Matrix({[}1, 2, 3{]}) & matrix constructor(mutable matrix) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
shape(expr) & shape of matrix \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
M.row(0) & get the first row \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
M.col(-1) & get the last column \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
M.col\_del(0) & delete first column \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
M.row\_del(1) & delete second row \tn 
% Row Count 7 (+ 1)
% Row 6
\SetRowColor{LightBackground}
M.row\_insert(1, Matrix({[}{[}0, 4{]}{]})) & insert a row \tn 
% Row Count 9 (+ 2)
% Row 7
\SetRowColor{white}
M.col\_insert(0, Matrix({[}1, -2{]})) & insert a column \tn 
% Row Count 11 (+ 2)
% Row 8
\SetRowColor{LightBackground}
M**-1 & inverse of M \tn 
% Row Count 12 (+ 1)
% Row 9
\SetRowColor{white}
M.T & transpose of M \tn 
% Row Count 13 (+ 1)
% Row 10
\SetRowColor{LightBackground}
eye(n) & create a nxn identity matrix \tn 
% Row Count 15 (+ 2)
% Row 11
\SetRowColor{white}
zeros(n,m) & creates a nxm matrix of zeroes \tn 
% Row Count 17 (+ 2)
% Row 12
\SetRowColor{LightBackground}
ones(n,m) & creates a nxm matrix of ones \tn 
% Row Count 19 (+ 2)
% Row 13
\SetRowColor{white}
diag(expr) & creates a matrix with expr in the diagonal \tn 
% Row Count 21 (+ 2)
% Row 14
\SetRowColor{LightBackground}
M.det() & computes the determinant of M \tn 
% Row Count 23 (+ 2)
% Row 15
\SetRowColor{white}
M.rref() & put a matrix into reduced row echelon form \tn 
% Row Count 25 (+ 2)
% Row 16
\SetRowColor{LightBackground}
M.nullspace() & returns a list of column vectors that span the nullspace of the matrix \tn 
% Row Count 29 (+ 4)
% Row 17
\SetRowColor{white}
M.columnspace() & returns a list of column vectors that span the columnspace of the matrix \tn 
% Row Count 33 (+ 4)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{2.23965 cm} x{2.73735 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Matrices (cont)}}  \tn
% Row 18
\SetRowColor{LightBackground}
M.eigenvals() & eigenvals returns a dictionary of eigenvalue: \seqsplit{algebraic\_multiplicity} pairs \tn 
% Row Count 4 (+ 4)
% Row 19
\SetRowColor{white}
M.eigenvects() & returns a list of tuples of the form (eigenvalue, \seqsplit{algebraic\_multiplicity}, {[}eigenvectors{]}) \tn 
% Row Count 9 (+ 5)
% Row 20
\SetRowColor{LightBackground}
M.diagonalize() & returns a tuple (P, D), where D is diagonal and M = P DP **−1 \tn 
% Row Count 12 (+ 3)
% Row 21
\SetRowColor{white}
M.charpoly(lamda) & return the characteristic polynomial \tn 
% Row Count 14 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.4931 cm} x{3.4839 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Trigonometric Simplification}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{trigsimp(expr)} & simplify expressions using trigonometric identities \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{expand\_trig(expr)} & expand trigonometric functions \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{3.33459 cm} x{1.64241 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Powers}}  \tn
% Row 0
\SetRowColor{LightBackground}
powsimp(expr) & use power identities \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
expand\_power\_exp(x**(a + b)) & x**a * x**b \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
expand\_power\_base((x{\emph{y)}}*a) & x**a * y**a \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
powdenest((x{\bf{a)}}b)powdenest((x{\bf{a)}}b) & x**(a*b) \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Exponentials and logarithms}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{expand\_log(expr)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{logcombine(expr)} \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.74195 cm} x{3.23505 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Special Functions}}  \tn
% Row 0
\SetRowColor{LightBackground}
factorial(n) & return the factorial of n \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
binomial(n, k) & return the binomial coefficient of n and k \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
gamma(z) & return the gamma function \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\seqsplit{expr.rewrite(function)} & rewrite expr in terms of function \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\seqsplit{expand\_func(expr)} & expand special functions \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
\seqsplit{hyperexpand(expr)} & rewrite hyper in terms of more standard functions \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\seqsplit{combsimp(expr)} & simplify combinatorial expressions \tn 
% Row Count 12 (+ 2)
% Row 7
\SetRowColor{white}
\seqsplit{gammasimp(expr)} & simplify expressions with gamma functions or combinatorial functions \tn 
% Row Count 15 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.4931 cm} x{3.4839 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Assumptions}}  \tn
% Row 0
\SetRowColor{LightBackground}
positive & negative \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
real & complex \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{integer} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\seqsplit{expr.assumptions0} & The full set of known predicates for a symbol \tn 
% Row Count 5 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\seqsplit{posify(expr)} & replace all symbols in an expression with symbols that have the assumption positive=True \tn 
% Row Count 9 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Calculus}}  \tn
% Row 0
\SetRowColor{LightBackground}
diff(expr, x, n) & nth order derivative of expr in terms of x \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Derivative(expr, x, n) & create an unevaluated derivative \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
deriv.doit() & evaluate an unevaluated derivative \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
integrate(expr, x, a, b) & integrate expr from a to b \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Integral(expr, x, n) & create an unevaluated integral \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
limit(expr, x, xo) & limit of expr to xo \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Limit(expr, x, xo) & create an unevaluated limit \tn 
% Row Count 14 (+ 2)
% Row 7
\SetRowColor{white}
expr.series(x, x0, n) & nth order series expansion of expr around x0 \tn 
% Row Count 16 (+ 2)
% Row 8
\SetRowColor{LightBackground}
expr.series(x, x0, n).removeO() & remove O notation \tn 
% Row Count 18 (+ 2)
% Row 9
\SetRowColor{white}
\seqsplit{differentiate\_finite(expr)} & differentiate using finite differences \tn 
% Row Count 20 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\seqsplit{expr.as\_finite\_difference()} & generate approximations of the derivative to arbitrary order \tn 
% Row Count 23 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Solvers}}  \tn
% Row 0
\SetRowColor{LightBackground}
solveset(expr, x, domain=S.Complexes, dict=False) & solve expr=0 \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
linsolve({[}expr1, expr2, ...{]}, (x, y, ...)) & solve a linear system of equations \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
nonlinsolve({[}expr1, expr2, ...{]}, {[}x, y, ...{]}) & solve a non linear system of equations \tn 
% Row Count 9 (+ 3)
% Row 3
\SetRowColor{white}
dsolve(diffeq, f(x)) & soves differential equation diffeq \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
roots(expr, x) & o get the solutions of a polynomial including multiplicity \tn 
% Row Count 14 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}