[General Topics] Skyica:
Graphing Tools

GeoGebra​

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This app stands out with exceptional 3D graphing (however there are problems with implicit surfaces).

2D graphing is also good, but tracing is missing.

It may also be used as a “general-purpose calculator”, however the keys are quite small on phones for quick calculations.

Numeric and symbolic calculation seems to be very well in general, but there are problems with simplification, and statistics, scientific constants, and unit conversion are missing.

The user interface is sophisticated and intuitive to use. However, a complete user guide is missing, and some things are not obvious.

Note that GeoGebra consists of several apps (mainly Graphing Calculator, 3D Calculator, CAS Calculator, and Geometry), that are available as a suite or singly.

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Numeric and symbolic calculation​

Symbolic computation essentials:

Bad Some simple expressions are not simplified automatically, e.g., e^pi/e^(2pi), or e^x/e^(2x). The Simplify function does simplify them however.

Feature Factorization, expansion, substitution

Feature Domain constraints

Equation solving

Equation solving seems to be quite powerful in general, but there are some problems, e.g., sin(x)=x can only be solved numerically

Feature Equation systems

Feature Inequalities

Differentiation and integration

Good Symbolic integration is powerful, quite complicated elementary and nonelementary Integrals can be solved.

However there are sometimes problems with the simplification. (E.g., for the integral of x/(1+sin(x)), a very complicated expression is shown while the solution can be written much simpler. When differentiating the retuned solution, an even more complicated expression is shown, not the originally integrated expression)

Other calculus and analysis

Feature Taylor expansion

Feature First and second order ordinary differential equations solving, numeric and symbolic.

Matrices and vectors

Bad Matrices must be entered in linear form

Statistics and probability

Missing No statistics

Missing No regression

Feature Probability distribution calculator with graphical UI

Missing No base-n calculation

Missing No scientific constants and unit conversion

2D and 3D Graphing​

Graph types

Feature Implicit plots, however it does not draw more complicated implicit surfaces like 4*(x^2+y^2+z^2)+16*x*y*z = 1 (Cayley surface)

Feature Slope field plots for differential equations

Display

Feature 2D: Customizable grid with major and minor lines

Feature 3D: optional semitransparent x-y-plane and x-y-grid

Feature 3D: variable transparency and wireframe surfaces

Feature 3D: Orthographic and perspective projection

Feature Animation of parameter variables with sliders

Navigation

Feature 3D: Automatic (continued) rotation, parameters can be changed while the graph is rotating

Feature 3D: Augmented reality navigation

Analysis

Missing Tracing

Environment and user Interface​

Variables and functions:

Feature Custom-named variables for storing values and for use in symbolic computation

Feature User-defined functions that can be used in numeric and symbolic calculations

Feature Piecewise functions

Input and output:

Missing Parts of expressions cannot be selected and copied, only the whole input or result can be copied.

Feature Automatic calculation without tapping enter key

Feature GeoGebra is also available for iOS, Windows, macOS, Linux, and as web interface. Documents from one device can be saved to the cloud and opened on another.

Adaption and customization:

Bad The keys are quite small for phones

Good Quite optimal for tablets

Documentation and source​

Missing No complete user guide. This is a real problem since some things are not obvious.

Feature Function / command reference with search (but not full-text) and examples

Bad Help is fetched from the internet on demand and takes sometimes long to load (several seconds)

Open Source GeoGebra is essentially open source and uses the open-source CAS Giac/Xcas.