# Wolfram Alpha

Wolfram Alpha is an online query system to answer any question. I only use it sometimes to query for simple mathematical objects without having to resort to the paid Mathematica software.

• Plot: The `plot` query can be used to plot functions of one and two variables as 2D and 3D graphs respectively. For example, `plot sin x` plots a 2D graph of that function. Similarly, `plot sin x cos y` plots the 3D graph of that function. The 3D graphs are quite beautifully plotted with colors and contour lines, but are only shown from two views (angled and top). If you need to interactively move it around to observe it, you need to pay for a Pro version.

# GeoGebra

GeoGebra is a graphing calculator software that works on many operating systems and platforms.

• An older 4.x version of GeoGebra can be installed easily from Ubuntu repositories:
```\$ sudo apt install geogebra
```
• I highly recommend installing the newer 5.x version of GeoGebra by downloading the Debian package from its website. The 5.x version has major improvements including a 3D graphing mode.

• 2D graphing: Any function of one variable that you type in the input at the bottom is graphed. Older functions can be removed from the list by right-clicking and choosing Delete.

• 3D graphing: This is available only in 5.x versions of GeoGebra. To get this view choose View -> 3D Graphics. Type any function in two variables x and y in the input and its 3D graph is plotted. To rotate the graph, press and hold down the right mouse button and move the mouse.

Tried with: GeoGebra 5.0.307 and Ubuntu 16.04

# KAlgebra

KAlgebra is a simple computer algebra system and graphing calculator for Linux. The 2D and 3D plotting is excellent and a replacement to using an actual graphing calculator. I find it useful to plot functions instead of using SageMath, which can be an overkill for just plotting.

• It can be installed easily from Ubuntu repositories:
```\$ sudo apt install kalgebra
```
• You can see 4 tabs in KAlgebra: calculator, 2D graph, 3D graph and dictionary.

• Calculator: Type any function here to simplify or solve it. For functions with one variable, KAlgebra gives a Plot 2D link after you press Enter. Clicking it takes you to the 2D Graph tab which renders the 2D plot of the function. Similarly, if you enter a function with two variables, it gives a Plot 3D link that takes you to rendering of its 3D plot in the 3D Graph tab.

• 2D Graph: Type a function of one variable here and KAlgebra plots its 2D graph. It checks if the expression is correct as you type and indicates error as tooltip. If expression is correct, then it shows the graph preview right below. If you press Enter after the expression, it is plotted in the main 2D plot window. More functions can be added by clicking the Add tab in the bottom-right corner. As you move the mouse inside the 2D plot window, KAlgebra shows the X and Y coordinate values in the bottom-left corner. It also shows the tangent to the curve as you move your mouse along the curve.

• 3D Graph: Type a function of two variables here and KAlgebra plots its 3D graph. I found that KAlgebra plots 3D graph only for the first function. Any subsequent functions you type will not be plotted. This glaring bug is documented here.

• Dictionary: This lists and describes the 64 functions that can be used in KAlgebra. It shows the function name, its input parameters and description.

Tried with: KAlgebra 15.12.3 and Ubuntu 16.04