# Software for algebraic computation with geometric objects?

Recently I started to get interested in the a certain kind of geometry, where a body is described based on a set of functions, which are based on irrational numbers.

For example consider this cuboid:
length: $\bg_white \pi$
width: $\bg_white \dpi{110} \inline \pi\cdot3^{-1}$
height: $\bg_white \inline \pi\cdot3^{-1}+3^{-1}$

Is there a software, where you can define such a body in a way that lets you algebraically compute its volume (e.g. $\bg_white \dpi{110} \inline (\pi^3+\pi^2)\cdot3^{-2}$) or any other property?

Numerically (e.g 4.54176...) you could do it with CAD software like OnShape, but that's not what I'm looking for.

Mostly I use (Fedora) Linux, so an open source solution would be the nicest, but I can work with windows 10 and a payed software too, as long as it is personal use and not a company license with the price of a small car.

Since I have a bit of programming experience (Python, R, Java) even a library would work for me.

• Welcome Someone! If you have an OS preference (or preferences) and a price range (or gratis), please add them (and the appropriate tags) to your post. Also, the images you posted have black foregrounds with transparent backgrounds, which means they will be invisible to everyone using a dark theme. You can reference a QA like this one to learn how to enter mathematical entities. Thanks, and again, welcome! Sep 1 '21 at 22:30

The best open source calculator I know so far is the windows calculator. Yes it is an open source project but the main problem is that it is designed for windows users.

But you can install it in linux using uno platform.

in linux if you have snap installed then try this command.

``````sudo snap install uno-calculator
``````

or if you dont have snap installed try this:

``````sudo dnf install snapd

sudo ln -s /var/lib/snapd/snap /snap

sudo snap install uno-calculato
``````

Not sure if it helps but these software seem interesting. Don't know if they work with irrational numbers and a sphere.

# polymake

polymake is open source software for research in polyhedral geometry. It deals with polytopes, polyhedra and fans as well as simplicial complexes, matroids, graphs, tropical hypersurfaces, and other objects. Supported platforms include various flavors of Linux, FreeBSD and Mac OS.

# PORTA

PORTA is a collection of routines for analyzing polytopes and polyhedra.

# Qhull

Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. The source code runs in 2-d, 3-d, 4-d, and higher dimensions. Qhull implements the Quickhull algorithm for computing the convex hull. It handles roundoff errors from floating point arithmetic. It computes volumes, surface areas, and approximations to the convex hull.