[General Topics] Skyica:
Scientific Calculator (by Philip Stephens)​

View attachment 5930521

View attachment 5930523

This app stands out with very powerful 3D graphing and some important user interface features that are missing from most or all other calculator apps (see the feature list).

Numeric computation seems to be good, and the statistics and probability functionality is extensive.

Symbolic computation is very limited however.

There are great graphing features (e.g. implicit surfaces), but also problems with graphing.

While the user interface has some great features, it also has significant inconveniences. Documentation is missing, and many things are not obvious.

View attachment 5930677 View attachment 5930679 View attachment 5941165

Numeric and symbolic calculation​

Symbolic computation essentials:

Bad Calculation with exact values mostly does not work:

E.g, pi²/pi gives pi, but (pi²+pi)/pi already gives a decimal or is not simplified at all. Using the sym() function from sym-menu helps sometimes but not for more complicated expressions

Bad Similarly, expressions with variables are only simplified in very simple cases

Equation solving:

Bad The expected problems with simplification

Bad Equations with parameter variables cannot be solved

Feature Equation systems (up to 3 equations), but maximal one solution is shown

Feature Specification of variable range, but only for equations in one variable

Differentiation and integration

Bad Only very simple integrals can be solved symbolically. Integrating e.g. Ln(x)², or 1/(1+x)^2 returns “undefined”

Specific multiple / nested operations, but special templates must be selected

Other calculus and analysis

Missing No min / max finding,

Bad Sums and products of sequences only numeric

Bad Limits only numeric

Feature Taylor series

Matrices and vectors

Feature Vector calculus

Statistics and probability

(I did not test this much)

Missing No plots

Feature Confidence interval calculations

Feature Many statistical tests

Feature Many probability distribution calculations

Feature Random number generators for normal, Poisson, binomial distributions

2D and 3D graphing​

Graph types:

Missing No parametric surfaces

Feature Implicit plots with high quality

Feature Spherical, and cylindrical graphs

Feature “Inverse” and implicit plots also for polar, spherical, and cylindrical coordinates

Feature Inequality plots

Feature Complex plots where real and imaginary parts are shown in two separate 3d graphs.

In these plots it is however difficult to relate real and imaginary part, especially since rotation is not linked.

Feature Many special functions like Error and Gamma function can be used for graphing

Display:

Good Both 2D and 3D graphs are high quality

Good 2D: Grid with major and minor lines that adapts to zoom by fading lines in and out

Missing No landscape orientation

Navigation:

Feature Independent scale of axes

Good Individual translation in coordinate directions

Good Individual scale of coordinate axes by using two-finger-pinch on the axis-controls, this is not documented!

Bad No translation perpendicular to view-direction

Missing 3D: No equal scale of axes. Two-finger zoom does not work to change the drawing area.

Analysis:

Bad Tracing works very poorly

Environment and user interface​

Variables and functions

Only x, y, z can be used as variables. Additionally, there are 5 memories, and 5 constants can be defined.

Feature User-defined functions

Input and output:

This is the only app where parts of expressions can be selected and copied in textbook notation. This generally works as expected but could be improved. Pasting at a specific location is inconvenient or impossible because long-tap triggers selection.

Missing No undo/redo

Feature Automatic calculation without tapping enter key

Good Keyboard is well designed for numeric calculations

Bad History limited to 10 calculations

Missing No import / export

Adaption and customization:

Good Multi-touch display zoom

Feature Scalable keyboard

Feature Custom colors for all UI elements

Documentation and source​

Missing No help document, only a few hints when using some features for the first time.