[General Topics] Skyica:
Advanced General-Purpose Calculators

Hiper Calc​

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This app stands out with quite comprehensive, reliable, and powerful functionality, and an exceptional user interface.

It seems to be very good at equation solving and minima / maxima finding (however there also is a bug).

On the other hand, there are significant problems with simplification, more complicated integrals cannot be solved symbolically, and statistics is very limited.

Graphing is very limited but still useful.

The functionality is very well organized and efficient and easy to use, but it still has some inconveniences, see the feature list.

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Numeric and symbolic calculation​

Symbolic computation essentials:

Bad Already some easy simplifications are not done, e.g., ln(2)+ln(3) is not simplified to ln(6), and 2x/(x^2-1)-1/(x-1) is not simplified to 1/(x+1)

Bad In results, polynomials are always given in expanded form, which not always is the simplest one

Feature Factorization, but works only with one variable.

Equation solving:

BUG In some cases it incorrectly returns “No solution exists”, e.g., for sin(1/x) = 0, and for ln(x*y) = ln( y)

Feature Equation systems, entered one equation per line

Feature Inequalities

Good Apart from some special cases (see above), equation solving seems to work very well, and quite complicated equations and equation systems can be solved symbolically, and even more complicated ones numerically. Periodic solutions are handled well.

Differentiation and integration:

Bad Some more complicated integrals cannot be solved symbolically even if they are elementary, e.g. (e^x-1)/(e^x+1). Nonelementary integrals cannot be solved symbolically.

Other calculus and analysis:

Feature Symbolic minima and maxima, also for periodic functions.

Good It correctly found all minima of sin(1/x), what WolframAlpha did not

Statistics and probability:

Missing Only one-variable statistics

Bad Input of data is inconvenient, especially with frequencies.

Missing No regression

Feature High precision calculation with up to 100 digits significand and 9 digits exponent

2D and 3D graphing​

Missing Graphs are only shown in the “calculation details”, and only one graph can be drawn at a time (or two for equations)

Graph types:

Missing No parametric plots

Feature Implicit plots in 2D, but for equations involving periodic functions only one “branch” is shown, e.g. for sin(x+y) = 0

Display:

Good Both 2D and 3D graphs are high quality

Navigation:

Missing 3D: No complete navigation: Rotation only around z axis, inclination cannot be changed

Bad 3D: One must change between rotate and translate/zoom “modes” (one finger for rotate and 2 for translate/zoom would be more convenient)

Bad Equal / independent scale of axes in 3D does not to work well

Analysis:

Missing Tracing

Environment and user interface​

Variables and functions:

Feature Custom-named variables

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

However, note that variable names other than x and y and function names cannot be typed but must be inserted from a menu. Also, variables other than x and y must be defined in this menu before they can be used in symbolic computation. While this is an inconvenience, one may get used to it.

Input and output:

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

Missing No undo & Redo

Good Keyboard is well designed.

Bad Since recently, the equal sign must be selected from a menu.

Feature Automatic calculation without tapping enter key

Feature Good “Quick Info”

Adaption and customization:

Feature Tablet layout that makes good use of the space available (but only in landscape layout)

Feature Different predefined keyboard layouts and custom keyboard layouts

Feature Many high-quality themes

Bad For larger calculations (e.g. equation systems) the small display area is inconvenient. When the display text size is reduced, the display becomes also smaller (and the keys larger) so that no vertical space is won.

(When multi-line display is enabled the keys are much too small on phones. A solution is to define a custom keyboard with more columns which makes the keys smaller and thus the keyboard lower.)

Documentation and source​

Good There is a well-organized complete in-app help.