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\begin{document}
\begin{center}\huge{\textbf{SymPy Cheatsheet (http://sympy.org)}}\end{center}
\begin{multicols*}{3}


\tikzstyle{mybox} = [draw=black, fill=white, very thick,
    rectangle, rounded corners, inner sep=10pt, inner ysep=10pt]
\tikzstyle{fancytitle} =[fill=black, text=white, font=\bfseries]

\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
    		%Sympy packages:& \verb|from sympy import some_package |\\
		Sympy help: & \verb|help(function)|\\
		Declare symbol:& \verb|x = Symbol('x')|\\
		Substitution:& \verb|expr.subs(old, new)|\\
		Numerical evaluation:& \verb|expr.evalf()|\\
		Expanding:& \verb|expr.expand()|\\
		Common denominator:& \verb|ratsimp(expr)|\\
		Simplify expression:&\verb|simplify(expr)|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Basics};
\end{tikzpicture}

\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.075\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		$\pi$: &\verb|pi|\\
		$e$: &\verb|E|\\
		$\infty$:&\verb|oo|\\
		$i$:&\verb|I|
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Constants};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.195\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
    		Integers ($\mathbb{Z}$): &\verb|Integer(x)|\\
    		Rationals ($\mathbb{Q}$): &\verb|Rational(p, q)|\\
    		Reals ($\mathbb{R}$): &\verb|Float(x)|\\
    		\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Numbers types};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		Trigonometric: &\verb|sin cos tan cot|\\
		Cyclometric: &\verb|asin acos atan acot|\\
		Hyperbolic: &\verb|sinh cosh tanh coth|\\
		Area hyperbolic: &\verb|asinh acosh atanh acoth|\\
		Exponential: &\verb|exp(x)|\\
		Square root: &\verb|sqrt(x)|\\
		Logarithm ($\log_ba$): &\verb|log(a, b)|\\
		Natural logarithm: &\verb|log(a)|\\
		Gamma ($\Gamma(x)$): &\verb|gamma(x)|\\
		Absolute value: &\verb|abs(x)|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Basic functions};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		$\displaystyle\lim_{x\to a} f(x)$: &\verb|limit(f, x, a)|\\
		$\displaystyle\lim_{x\to a_-} f(x)$: &\verb|limit(f, x, a, dir='-')|\\
		$\displaystyle\lim_{x\to a_+} f(x)$: &\verb|limit(f, x, a, dir='+')|\\
		$\frac{d}{dx}f(x)$: &\verb|diff(f, x)|\\
		$\frac{\partial}{\partial x} f(x,y)$: &\verb|diff(f, x)|\\
		$\int f(x) \, dx:$& \verb|integrate(f, x)|\\
		$\int_a^b f(x) \, dx:$& \verb|integrate(f, (x, a, b))|\\
		Taylor series (at $a$, deg $n$)& \verb|f.series(x, a, n)|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Calculus};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		Equation $f(x)=0$: &\verb|solve(f, x)|\\
		System of equations: &\verb|solve([f, g], [x, y])|\\
		Differential equation: &\verb|dsolve(equation, f(x))|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Equations};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		Points: & \verb|a = Point(xcoord, ycoord)|\\
		Lines: &\verb|l = Line(pointA, pointB)|\\
		Circles: &\verb|c = Circle(center, radius)|\\
		Triangles: &\verb|t = Triangle(a, b, c)|\\
		Area: &\verb|object.area|\\
		Intersection: &\verb|intersection(a, b)|\\
		Checking tangency: &\verb|c.is_tangent(l)|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Geometry};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		Plot: &\verb|Plot(f, [a, b])|\\
		Zoom: $+/-$: &\verb|R/F or PgUp/PgDn or Numpad +/-|\\
		Rotate X,Y axis: &\verb|Arrow Keys or WASD|\\
		Rotate Z axis: &\verb| Q and E or Numpad 7 and 9|\\
		View XY: &\verb|F1|\\
		View XZ: &\verb|F2|\\
		View YZ: &\verb|F3|\\
		View Perspective: &\verb|F4|\\
		Axes Visibility: &\verb|F5|\\
		Axes Colors: &\verb|F6|\\
		Screenshot: &\verb|F8|\\
		Exit plot: &\verb|ESC|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Plotting};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		Factorial ($n!$): &\verb|factorial(n)|\\
		Binomial coefficient $n\choose k$: &\verb|binomial(n, k)|\\
		Sum ($\sum_{n=a}^b expr$): &\verb|summation(expr, (n, a, b))|\\
		Product ($\prod_{n=a}^b expr$): &\verb|product(expr, (n, a, b))|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Discrete math};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		Matrix definition: &\verb|m = Matrix([[a, b], [c, d]])|\\
		Determinant: &\verb|m.det()|\\
		Inverse: &\verb|m.inv()|\\
		Identity matrix $n\times n$: &\verb|eye(n)|\\
		Zero matrix $n\times n$: &\verb|zeros(n)|\\
		Ones matrix $n\times n$: &\verb|ones(n)|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Linear algebra};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\begin{center}\small{\begin{tabular}{l r}
		\LaTeX{} print: &\verb|print latex()|\\
		Python print: &\verb|print python()|\\
		Pretty print: &\verb|pprint()|\\
	\end{tabular}}\end{center}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Printing};
\end{tikzpicture}
\begin{tikzpicture}
\node [mybox] (box){%
    \begin{minipage}{0.3\textwidth}
	\small{
		Find 100 digits of $\pi^e$:\\
		\verb|(pi**E).n(100)|\\
		\\
		Expand $(x+y)^2(x-y)(x^2+y)$:\\
		\verb|((x + y)**2 * (x - y) * (x**2 + y)).expand()|\\
		\\
		Simplify $\displaystyle\frac{1}{x} + \frac{x\sin x -1}{x^2-1}$:\\
		\verb|simplify((1/x) + (x * sin(x) - 1)/(x**2 - 1))|\\
		\\
		Check if line passing through points $(0,1)$ and $(1,1)$\\
		is tangent to circle with center at $(5,5)$ and radius $3$:\\
		\verb|Circle(Point(5,5), 3).is_tangent(|\\\verb|Line(Point(0,1), Point(1,1)))|\\
		\\
		Find roots of $x^4-4x^3+2x^2-x=0$:\\
		\verb|solve(x**4 - 4*x**3 + 2*x**2 - x, x)|\\
		\\
		Solve the equations system: $x+y=4$, $xy=3$:\\
		\verb|solve([x + y - 4, x*y - 3], [x, y])|\\
		\\
		Calculate limit of the sequence $\sqrt[n]{n}$:\\
		\verb|limit(n**(1/n), n, oo)|\\
		\\
		Calculate left-sided limit of the function $\frac{|x|}{x}$ in 0:\\
		\verb|limit(abs(x)/x, x, 0, dir='-')|\\
		\\
		Calculate the sum $\sum_{n=0}^{100} n^2$:\\
		\verb|summation(n**2, (n, 0, 100))|\\
		\\
		Calculate the sum $\sum_{n=0}^{\infty} \frac{1}{n^2}$:\\
		\verb|summation(1/n**2, (n, 0, oo))|\\
		\\
		Calculate the integral $\int \cos^3 x \, dx$:\\
		\verb|integrate(cos(x)**3, x)|\\
		\\
		Calculate the integral $\int_1^{\infty} \frac{dx}{x^2}$:\\
		\verb|integrate(1/x**2, (x, 1, oo))|\\
		\\
		Find 10 terms of series expansion of $\frac{1}{1-2x}$ at $0$:\\
		\verb|(1/(1 - 2*x)).series(x, 0, 10)|\\
		\\
		Solve the differential equation $f^{''}(x)+9f(x)=1$:\\
		\verb|dsolve(f(x).diff(x, x) + 9*f(x) - 1, f(x))|\\
	}
    \end{minipage}
};
\node[fancytitle, right=10pt] at (box.north west) {Examples};
\end{tikzpicture}
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%	\end{tabular}}\end{center}
%    \end{minipage}
%};
%\node[fancytitle, right=10pt] at (box.north west) {Numbers types};
%\end{tikzpicture}
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%\node [mybox] (box){%
%    \begin{minipage}{0.3\textwidth}
%	\begin{center}\small{\begin{tabular}{l r}
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%	\end{tabular}}\end{center}
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%};
%\node[fancytitle, right=10pt] at (box.north west) {Numbers types};
%\end{tikzpicture}
\end{multicols*}
\end{document}
