Editing Maple (software) (section)

==Examples of Maple code==
The following code, which computes the factorial of a nonnegative integer, is an example of an [[imperative programming]] construct within Maple:

<syntaxhighlight lang="maple">
myfac := proc(n::nonnegint)
   local out, i;
   out := 1;
   for i from 2 to n do
       out := out * i
   end do;
   out
end proc;
</syntaxhighlight>
Simple functions can also be defined using the "maps to" arrow notation:
<syntaxhighlight lang="maple">
 myfac := n -> product(i, i = 1..n);
</syntaxhighlight>

===Integration===
Find
:<math>\int\cos\left(\frac{x}{a}\right)dx</math>.
<syntaxhighlight lang="maple">
 int(cos(x/a), x);
</syntaxhighlight>
Output:
:<math>a \sin\left(\frac{x}{a}\right)</math>

===Determinant===
Compute the determinant of a matrix.
<syntaxhighlight lang="maple">
 M := Matrix([[1,2,3], [a,b,c], [x,y,z]]);  # example Matrix
</syntaxhighlight>
: <math>
  \begin{bmatrix}
    1 & 2 & 3 \\
    a & b & c \\
    x & y & z
  \end{bmatrix}
</math>
 LinearAlgebra:-Determinant(M);
: <math>bz-cy+3ay-2az+2xc-3xb</math>

===Series expansion===
<syntaxhighlight lang="maple">
series(tanh(x), x = 0, 15)
</syntaxhighlight>
:<math>x-\frac{1}{3}\,x^3+\frac{2}{15}\,x^5-\frac{17}{315}\,x^7</math>
:<math>{}+\frac{62}{2835}\,x^9-\frac{1382}{155925}\,x^{11}+\frac{21844}{6081075}\,x^{13}+\mathcal{O}\left(x^{15}\right)</math>

===Solve equations numerically===
The following code numerically calculates the roots of a high-order polynomial:
<syntaxhighlight lang="maple">
 f := x^53-88*x^5-3*x-5 = 0

 fsolve(f)

 -1.097486315, -.5226535640, 1.099074017
</syntaxhighlight>

The same command can also solve systems of equations:
<syntaxhighlight lang="maple">
 f := (cos(x+y))^2 + exp(x)*y+cot(x-y)+cosh(z+x) = 0:

 g := x^5 - 8*y = 2:

 h := x+3*y-77*z=55;
                    
 fsolve( {f,g,h} );

 {x = -2.080507182, y = -5.122547821, z = -0.9408850733}
</syntaxhighlight>

===Plotting of function of single variable===
Plot <math>x \sin(x)</math> with {{mvar|x}} ranging from -10 to 10:
<syntaxhighlight lang="maple">
 plot(x*sin(x), x = -10..10);
</syntaxhighlight>
[[Image:Maple1DPlot.PNG|thumb|center|300px]]

===Plotting of function of two variables===
Plot <math>x^2+y^2</math> with {{mvar|x}} and {{mvar|y}} ranging from -1 to 1:
<syntaxhighlight lang="maple">
plot3d(x^2+y^2, x = -1..1, y = -1..1);
</syntaxhighlight>
[[Image:Maple163DPlot.jpg|thumb|center|300px]]

===Animation of functions===
* Animation of function of two variables
:<math>f := \frac{2k^2}{\cosh^2\left(x k - 4 k^3 t\right)}</math>
<syntaxhighlight lang="maple">
plots:-animate(subs(k = 0.5, f), x=-30..30, t=-10..10, numpoints=200, frames=50, color=red, thickness=3);
</syntaxhighlight>
[[File:Bellsoliton2.gif|thumb|center|300px|2D bell solution]]

* Animation of functions of three variables
<syntaxhighlight lang="maple">
plots:-animate3d(cos(t*x)*sin(3*t*y), x=-Pi..Pi, y=-Pi..Pi, t=1..2);
</syntaxhighlight>
[[File:3dsincos animation.gif|thumb|center|300px|3D animation of function]]

* Fly-through animation of 3-D plots.<ref>[http://www.maplesoft.com/applications/view.aspx?SID=33073&view=html Using the New Fly-through Feature in Maple 13] Maplesoft</ref>
<syntaxhighlight lang="maple">
 M := Matrix([[400,400,200], [100,100,-400], [1,1,1]], datatype=float[8]):
 plot3d(1, x=0..2*Pi, y=0..Pi, axes=none, coords=spherical, viewpoint=[path=M]);
</syntaxhighlight>
[[File:Maple plot3D flythrough.gif|thumb|center|300px|Maple plot3D fly-through]]

===Laplace transform===
* [[Laplace transform]]
<syntaxhighlight lang="maple">
f := (1+A*t+B*t^2)*exp(c*t);
</syntaxhighlight>
:<math> \left(1 + A \, t + B \, t^2\right) e^{c t}</math>
<syntaxhighlight lang="maple">
 inttrans:-laplace(f, t, s);
</syntaxhighlight>
:<math>\frac{1}{s-c}+\frac{A}{(s-c)^2}+\frac{2B}{(s-c)^3}</math>

* inverse Laplace transform
<syntaxhighlight lang="maple">
inttrans:-invlaplace(1/(s-a), s, x);
</syntaxhighlight>
: <math>e^{ax}</math>

===Fourier transform===
* [[Fourier transform]]
<syntaxhighlight lang="maple">
 inttrans:-fourier(sin(x), x, w)
</syntaxhighlight>
:<math>\mathrm{I}\pi\,(\mathrm{Dirac}(w+1)-\mathrm{Dirac}(w-1))</math>

===Integral equations===
Find functions {{mvar|f}} that satisfy the [[integral equation]]
:<math>f(x)-3\int_{-1}^1(xy+x^2y^2)f(y)dy = h(x)</math>.
<syntaxhighlight lang="maple">
eqn:= f(x)-3*Int((x*y+x^2*y^2)*f(y), y=-1..1) = h(x):
intsolve(eqn,f(x));
</syntaxhighlight>
:<math>f \left( x \right) =\int _{-1}^{1}\! \left( -15\,{x}^{2}{y}^{2}-3\,xy \right) h \left( y \right) {dy}+h \left( x \right)
</math>