# &app; User Manual

Thomas
Führinger
Sam
Tygier
2005
Thomas Führinger
Sam Tygier
2006-09-12

Sam Tygier

2005-10-11

Thomas Führinger

&app; is a simple mathematical function graph plotter.

## Using &app;

Enter functions in Python syntax with `x` as the dependent variable. Press the Plot button to see the graph.

### &app; Window

Shows &app; main window displaying 3 graphs.

Constants and functions of the `math` module are available.

Examples:

    x**3 - 2 * x
    2 * cos(x)
    e ** (x / -5) * sin(x)

xMin, xMax, yMin, yMax define the boundaries of the range on the abszissa and ordinate to be displayed.

To zoom in, activate the Zoom In tool button. It divides the range boundaries by half. Zoom out does the opposite. To closer inspect a specific section, drag the mouse cursor over an area. After release of the button the area thus marked will be displayed.

The scale automatically adjusts as you zoom in and out. To switch between decimal and radian styles, use Graph Scale Style Decimal or Graph Scale Style Radians

.

If you wish to use a custom scale select Graph Scale Style Custom. You can then use the

xScale, yScale entries to input the intervals at which marks are displayed on the respective axis. They can also be stated as expressions. Examples:

    xMin = pi * -2
    xMax = pi * 2
    xScale = pi / 2

To save the graph in PNG format choose File Save.

Using Graph Evaluate you get a dialog box that allows input of an `x` value and calculates `y` values.

## Accelerator Keys

Accelerator | Function
--- | ---
Ctrl L | Plot graph
Ctrl+ | Zoom in
Ctrl- | Zoom out
Ctrl R | Reset zoom
Ctrl S | Save graph
Ctrl E | Evaluate functions
Ctrl Q | Quit &app;

## Operators and Functions

Expressions are entered in python syntax. The following operators can be used. Note: multiplication is not implied (use "2*x" not "2x")

Operator | Description
--- | ---
+,-,*,/ | Plus, minus, multiply, divide
// | Integer divide. (eg 3/2 = 1)
**, ^ | Raise to the power of
% | Remainder

Lybniz has all the math functions of the python standard library available.

- acos()

- asin()

- atan()

- atan2()

- ceil()

- cos()

- cosh()

- degrees()

- exp()

- fabs()

- floor()

- fmod()

- frexp()

- hypot()

- ldexp()

- log()

- log10()

- modf()

- pow()

- radians()

- sin()

- sinh()

- sqrt()

- tan()

- tanh()

These are documented at Python Library Reference - Math.

There are also a few extra functions that may be useful.

Function | Description
--- | ---
fac(x) | Factorial of x (or x!). Note: only works with positive integers.
sinc(x) | sin(x)/x.

The constants pi and e can be used.

Some special functions are provided by scipy (if installed).

Function | Description
--- | ---
j0(x) | Bessel function of the first kind of order 0.
j1(x) | Bessel function of the first kind of order 1.
bessel_y0(x) | Bessel function of the second kind of order 0.
bessel_y1(x) | Bessel function of the second kind of order 1.
i0(x) | Modified Bessel function of order 0.
i1(x) | Modified Bessel function of order 1.
k0(x) | Modified Bessel function of the second kind of order 0, K0.
k1(x) | Modified Bessel function of the second kind of order 1, K1(x).
gamma(x) | Gamma function.
digamma(x) | The digamma function.
erf(x) | The error function.
erfc(x) | Complementary error function, 1 - erf(x).
erfinv(x) | Inverse of the error function erf.
erfcinv(x) | Inverse of the complementary error function erfc.
zeta(x) | Riemann zeta function.

## About &app;

&app; was written by Thomas Führinger and extended by Sam Tygier.

To get the latest version please visit the &app; Web page.

This program is distributed under the revised BSD license.