Editing Maxima (software) (section)

== Examples of Maxima code ==

=== Basic operations ===

==== Arbitrary-precision arithmetic ====
<syntaxhighlight lang="maxima">
bfloat(sqrt(2)), fpprec=40;
</syntaxhighlight><math>1.41421356237309504880168872420969807857 \cdot 10^0</math>

==== Function ====
<syntaxhighlight lang="maxima" line="1">
f(x):=x^3$
f(4);
</syntaxhighlight><math>64</math>

==== Expand ====
<syntaxhighlight lang="maxima">
expand((a-b)^3);
</syntaxhighlight><math>-b^3+3 ab^2-3a^2b+a^3</math>

==== Factor ====
<syntaxhighlight lang="maxima">
factor(x^2-1);
</syntaxhighlight><math>(x-1)(x+1)</math>

=== Solving equations ===
<math>x^2+a \ x + 1=0</math><syntaxhighlight lang="maxima">
solve(x^2 + a*x + 1, x);
</syntaxhighlight><math>[x=-\Biggl(\frac{\sqrt{a^2-4}+a}{2}\Biggr),x=\frac{\sqrt{a^2-4}-a}{2}]</math>

=== Solving equations numerically ===
<math>\cos x = x</math><syntaxhighlight lang="maxima">
find_root(cos(x) = x, x, 0, 1);
</syntaxhighlight><math>0.7390851332151607</math><syntaxhighlight lang="maxima">
bf_find_root(cos(x) = x, x, 0, 1), fpprec = 50;
</syntaxhighlight><math>7.3908513321516064165531208767387340401341175890076 \cdot 10^{-1}</math>

=== Indefinite integral ===
<math>\int x^2+\cos x\ d x</math><syntaxhighlight lang="maxima">
integrate(x^2 + cos(x), x);
</syntaxhighlight><math>\sin x + \frac{x^3}{3}</math>

=== Definite integral ===
<math>\int_{0}^{1}\frac{1}{x^3+1}\, dx</math><syntaxhighlight lang="maxima">
integrate(1/(x^3 + 1), x, 0, 1), ratsimp;
</syntaxhighlight><math>\frac{\sqrt3 \log2+\pi}{3^{\frac{3}{2}}}</math>

=== Numerical integral ===
<math>\int_{0}^{2} \sin(\sin (x)) \, dx</math><syntaxhighlight lang="maxima">
quad_qags(sin(sin(x)), x, 0, 2)[1];
</syntaxhighlight><math>1.247056058244003</math>

=== Derivative ===
<math>{d^3 \over d x^3} \cos^2 x</math><syntaxhighlight lang="maxima">
diff(cos(x)^2, x, 3);
</syntaxhighlight><math>8 \cos{x}\sin{x}</math>

=== Limit ===
<math>\lim_{x \to \infty} \frac{1+\sinh{x}}{e^{x}}</math><syntaxhighlight lang="maxima">
limit((1+sinh(x))/exp(x), x, inf);
</syntaxhighlight><math>\frac{1}{2}</math>

=== Number theory ===
<syntaxhighlight lang="maxima">
primes(10, 20);
</syntaxhighlight><math>[11,13,17,19]</math><syntaxhighlight lang="maxima">
fib(10);
</syntaxhighlight><math>55</math>

=== Series ===
<math>\sum_{x=1}^\infty \frac{1}{x^2} </math><syntaxhighlight lang="maxima">
sum(1/x^2, x, 1, inf), simpsum;
</syntaxhighlight><math>\frac{\pi^2}{6}</math>

=== Series expansion ===
<syntaxhighlight lang="maxima">
taylor(sin(x), x, 0, 9);
</syntaxhighlight><math>x-\frac{x^3}{6}+\frac{x^5}{120}-\frac{x^7}{5040}+\frac{x^9}{362880}</math><syntaxhighlight lang="maxima">
niceindices(powerseries(cos(x), x, 0));
</syntaxhighlight><math>\sum_{i=0}^\infty \frac{(-1)^ix^{2i}}{(2i)!}</math>

=== Special functions ===
<syntaxhighlight lang="maxima">
bessel_j(0, 4.5);
</syntaxhighlight><math>-0.3205425089851214</math><syntaxhighlight lang="maxima">
airy_ai(1.5);
</syntaxhighlight><math>0.07174949700810543</math>