Software to visualise multivariable functions $f:Z^2\rightarrow Z^2$ I want to visualize the division algorithm as a function $f:Z^2\rightarrow Z^2$ . That is, given a unique value of (dividend, divisor) [$Z^2$ - domain], it will give a unique value of (quotient, remainder) [$Z^2$ - range] as is stated in the definition of the division algorithm.
I want to visualize this as a mapping from a plane with all integer points to another plane with all integer points (a 2-dimensional integer lattice, also called a square or grid lattice) . Can you suggest me any program for PC where I can do this and any source on how to do this?
 A: See WolframAlpha which is powered by Mathematica: https://www.wolframalpha.com/examples/mathematics/plotting-and-graphics/
You may want to probably use ListPointPlot3D function to plot points on a 3D space.
https://reference.wolfram.com/language/ref/ListPointPlot3D.html
You need to derive a parameter $t$ as a function of two variables (one from the domain and another from the range). Then you can form a 3D coordinate and then you can use the 3D plots in Mathematica/WolframAlpha. This is one possible visualization. The link for ListPointPlot3D has some nice examples.
If you want to map a point to another and visualize it using colors, then derive a parametric function $c: Z^2 \rightarrow Z$ that maps a point to an integer in a color space (eg: RGB colorspace) and draw an integer lattice where the lattice points are colored based on $c(x,y)$. For this you can use the ListPlot function. The link shows an example for varying the size and color of the points plotted (See example for Use individual colors for each point).
