Computing Tools

SigmaCalculator  SigmaCalculator Advanced scientific expression-based calculator Available in Google Play Features:
Standard functions (exp, log, ln, sin, cos, tan, factorial, random, ...) Built-in constants, Integrated keypad (Numeric and Alphabetic) Angle unit in radian or degree, Calculation history, User-defined variables, Function graphing, Equation solving, Complex numbers, etc.
SigmaCalculator is available in english and french.

SigmaCalculator supports the most common and useful mathematical functions. It’s easy to use: to evaluate a mathematical expression, simply type it in the input box, using operators (+ - * / ^), parenthesis and mathematical functions and press Calculate or the EXE button. You can use the SigmaCalculator keypad to enter numbers, operators, functions and define variables. You can set variables (with any non-reserved name); use fundamental constants; solve equations; plot functions; statistics; etc.

Examples:
Define variable: a=-3
Define variable: b=3
Calculate: a*b/(1+a^2)
Calculate: Sin(2*π/3)

Operators:

-   subtract
*   multiply
/   divide
//   modulo (example 5//2 gives 1)
%   percentage (example 50%4 gives 2)     a long press on the ^ button insert %
!   factorial (example 4! gives 24)
^   power (example 7^2 gives 49)
**   power (example 7**2 gives 49)

Functions:

Exp(x) exponential
Ln(x) natural logarithm
Log(x) decimal logarithm
Log2(x) base-2 logarithm
Sin(x) sine
Cos(x) cosine
Tan(x) tangent
Asin(x) arc sine
Acos(x) arc cosine
Atan(x) arc tangent
Sinh(x) hyperbolic sine
Cosh(x) hyperbolic cosine
Tanh(x) hyperbolic tangent
Abs(x) absolute value
Sqrt(x) square root
Ceil(x) ceiling, the smallest integer not less than x
Floor(x) integer part of x
Rand() random number between 0 and 1
Sign(x) sign of x (-1 if x < 0, +1 if x > 0 and 0 if x = 0)
Erf(x) error function
Fact(x) factorial of x

Constants:

Pi π
e Natural logarithm base (2.71828...)

Universal constants in international units (SI)
q Electron charge (C)
me Electron mass (kg)
mp Proton mass (kg)
kB Boltzmann constant (J/K)
h Planck constant (Js)
c Speed of Light in vacuum (m/s)
ε0 Electric constant (F/m)
μ0 Magnetic constant (N/A²)
G Constant of gravitation (m³/kg/s²)
Ri Rydberg constant (1/m)
R Molar gas constant(J/mol/K)

Commands:

help show help
tol=fval set the tolerance (precision) to fval (tol is used in the equation solving algorithm)
iter=ival set the number of iterations to ival (iter is also used in the equation solving algorithm)

Guide:

Buttons: a long click on the DEL button clears the input; With the left and right arrows, you can move the cursor in the input, and a long click on the left arrow has the same effect than clicking the DEL button, and a long click on the right arrow inserts space. In landscape mode (when rotating your phone), additional buttons will be available giving you the possibility to navigate in the calculation history (curved arrows), clear the input, etc.

If you perform a long-press on a the input area, a floating list of menu items appears with the most common functions and constants.
With this menu, you can also (i) display the calculation history, recall and edit a previous expression by clicking on the correspond item ; (ii) display the variables list dialog and insert a variable in your expression. Note that the calculation history and the user-defined variables are permanently saved and can be re-used after restarting SigmaCalculator.

To switch the angle unit between Radian and Degree, click the Deg/Rad button.

To navigate in the history calculation, long click the right or left parenthesis button.

By pressing the ABC button (or f(x) button), you can switch between the SigmaCalculator Alphabetic Keypad and Functions Keypad;
A press on an alphabetic button inserts the first letter and a long press inserts the second letter.

To define a variable, type the name, click the = button (available if the SigmaCalculator Keypad is set to Alphabetic), type the variable value and then press Calculate or EXE. Note that the variable names are not case sensitive.
You can insert or delete variable by selecting menu/Variables.

If you press the Android menu, you can view the function graph; view the defined variables or the calculation history; switch between the Android soft keyboard and SigmaCalculator keypad; and show this help.

You can solve nonlinear equation f(x)=0: type your f(x) expression and click the Solve button. If necessary, you will be prompted to define the solution interval. You can also define this interval [a b] by manually setting a and b variables, or within the interval dialog shown after a long press on the Solve button. The solution accuracy depends on this interval.
Example:
Type      x^2 - x - 1
Click      Solve

You can graph a function y = f(x). To do so, type your f(x) expression, and click Plot. The graph window will then appear.
Example:
Type      x^2 - x - 1
Click      Plot
Note that the f(x) function can contain user-defined variables or built-in constants.
Example:
v*x^2 - w*x - 1
Where v and w are already defined and are taken as parameters.
With the menu, you can add or remove curve, set the graph scale, etc.
In the Scale dialog, you can set the x and y-range or automatically scale the graph (by clicking the AutoScale button). If you check the X-Range button in the Scale dialog, the curves data will be recalculated in the new X-Range.
In the Settings dialog, you can:
(i) Set the number of points or the X-Step (if the step button is checked, the number of points will be calculated based on the step).
(ii) Plot curves with symbols if the Symbol button is checked.
If you click the graph, the corresponding (x,y) coordinates will be displayed on the top of the graph. On the graph top-right corner, the legend is displayed. If you long press one item in this legend, you can activate the corresponding curve. If you activate a curve, you can display the (x,y) coordinates for this curve, by clicking the graph.

Descriptive Statistics:
The statistics module calculates the descriptive parameters of a list of values:
Number of values (N), Minimum (Min), Maximum (Max), Sum (Σx), Mean (μ), Median (Med), Variance (σ²), Standard Deviation (σ), Coefficient of Variation (CV), Root Mean Square (RMS), Skewness (Skw) and Kurtosis excess (Kur).

Formulas:
Mean: Variance: Skewness: Kurtosis: To evaluate the statistics parameters, firstly enter your list of values: type each value and store it by pressing the Add button.
When ready, click one of the statistics button (N, Min, Max, Σx, μ, ...) to calculate and view the corresponding parameter.
To view the list, select menu/List button. With the appeared dialog you can modify the values in the list.
You can graphically view you data, by clicking the Scatter button. In this scatter plot, two lines indicate respectively the mean and the median.

Complex numbers:
Select menu/Complex to activate the Complex numbers module. With this module, you can do basic operations with complex numbers such as add, subtract, multiply, divide, calculate the square root, the absolute value (modulus), phase, sine, cosine, tangent, etc.
You can enter two complex numbers (real and imaginary part) and click the button corresponding to the operation you want to perform.
The calculation result is then displayed. You can copy the result to the first complex number by clicking Res.→z button (useful if you perform some repetitive calculations).
To calculate the absolute value (modulus) of z, click Abs(z) button.
To calculate the conjugate of z, click Conj(z) button.
To swap the two complex numbers values, simply click Swap button.
You can switch between the cartesian (z = x + iy) and the the polar form (z = r exp(iφ)), by clicking the Cart./Pol. button.
To convert z from polar to cartesian (if in polar form) or from cartesian to polar (if in cartesian form), click z→xy or z→rφ button.
To enter the complex number, you can use the numeric (phone) keyboard or the alphanuneric keyboad: select menu/Keyboard to switch between.
You can enter any formula supported by SigmaCalculator in the input: for example : pi/2 or 3*7/9 ... You can evaluate immediately the expression: long press the input and select the Evaluate menu.
You can view the the complex numbers in the complex plane (Argand diagram) by selecting menu/Diagram. The Argand diagram, including the two complex numbers and the operation result, is then shown.
Rem: In the Argand diagram, a complex number x + iy is the vector from the origin to the point (x,y).
NB: the first complex number is labelled z.
the second complex number is labelled z₂.
the operation result is labelled z₃.
NB: φ is always in radian in the Complex numbers module.