RedcrabX – MathBox Guide

How to enter formulas, fractions, roots, exponents, matrices, and variables  |  Version 1.0

Table of Contents

• 1. Overview
• 2. Basic Arithmetic
• 3. Fraction (Visual Fraction Bar)
• 4. Square Root Symbol
• 5. Exponent / Superscript
• 6. Greek Letters
• 7. Parentheses and Brackets
• 8. Matrix Input
• 9. Navigation between Elements
• 10. Variables
• 11. String Variables and Arrays
• 12. Numeric Arrays
• 13. Functions
• 14. Angle Mode (DEG / RAD)
• 15. Output Format
• 16. Definite Integral – integral()
• 17. Sets – {} Literals and Set Functions
• 18. Duration / Time – dur() and hms()
• 19. Electrical Engineering Functions
• 20. Complete Examples

1. Overview

A MathBox is a single formula line in the RedcrabX workspace. It displays expressions as a mix of text fields and visual elements (fraction bars, root symbols, matrices). Press Enter to evaluate the expression; the result appears to the right of the formula in gray.

Each MathBox evaluates independently and can store results in named variables, which are immediately available in other MathBoxes on the same workspace.

2. Basic Arithmetic

Type expressions directly into the input field using standard operators.

3. Fraction (Visual Fraction Bar)

A visual fraction with a horizontal bar — numerator on top, denominator below — is inserted by typing // anywhere in the expression.

Examples

Type:  3 //  →  fraction appears, type 4 in the denominator
Result: ¾  =  0.75

Type:  (a+b) //  →  type (a-b) in the denominator
Result: (a+b)/(a-b)

4. Square Root Symbol

A visual root symbol (√‾) is inserted with a keyboard shortcut. The radicand is entered inside the symbol's bounding box.

Examples

Ctrl+1, type:  x+1
Result:  √(x+1)

Type:  2*  then Ctrl+1, type:  a²+b²
Result:  2·√(a²+b²)

Select "a+b", press Ctrl+1
Result:  √(a+b)

5. Exponent / Superscript

Superscript characters (⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻) are entered using a toggle mode activated by a keyboard shortcut. While the mode is active, digits and signs are automatically converted to their Unicode superscript equivalents.

Examples

x, then Ctrl+^, 2, then Ctrl+^   →   x²

a, Ctrl+^, 2, Ctrl+^, +b, Ctrl+^, 2, Ctrl+^   →   a²+b²

10, Ctrl+^, -3, Ctrl+^   →   10⁻³   =   0.001

6. Greek Letters

Greek letters can be entered directly in any MathBox input field using Ctrl + Latin letter for lowercase, and Ctrl + Shift + Latin letter for uppercase. The Latin key corresponds to the first letter of the Greek name (with a few exceptions: q → θ, w → ω, c → χ, f → φ, y → ψ, h → η).

Examples

Ctrl+a, Ctrl+b                   →   αβ

Type:  r := 3
Type:  area :=   then Ctrl+p   * r, Ctrl+^, 2, Ctrl+^
Result:  area := π * r²       →   28.274

Ctrl+Shift+s, Ctrl+Shift+w       →   ΣΩ

7. Parentheses and Brackets

Parentheses are entered as plain text characters. They are not visual elements but are fully understood by the expression parser.

8. Matrix Input

Matrices can be entered as text literals or as visual grid controls inserted from the Matrix panel. The visual control renders each cell as an individual input field.

Text Literal

A := [1, 2, 3 ; 4, 5, 6 ; 7, 8, 9]   →   3×3 matrix

B := [0,1;1,0]   →   2×2 identity swap matrix

Visual Matrix (Panel Button)

Click the matrix icon in the Physics/Matrix Panel. Choose the number of rows and columns. A grid of input fields appears inline.

Matrix Operations

A := [1,2;3,4]
B := [5,6;7,8]
A * B =            →   matrix multiplication

det(A) =           →   determinant
inv(A) =           →   inverse
tr(A) =            →   trace
flat(A) =          →   flatten to 1-D array: [1,2,3,4]
getAt(A,0,1) =     →   element at row 0, col 1: 2

9. Navigation between Elements

A MathBox can contain multiple elements (text fields, fractions, roots, matrices) in a horizontal row. Use the arrow keys to move between them.

10. Variables

Variables are assigned using =. Once defined, they are available immediately in all other MathBoxes on the same workspace.

a := 5
b := a * 2       →   10

r := 3
area := pi * r²  →   28.27

Clearing a Variable

Clear the expression (select all, delete) and press Enter. The variable is removed from the store and no longer available in other boxes.

11. String Variables and Arrays

Text values are entered in double quotes. They can be assigned to variables and used as axis labels in Plot and Chart boxes.

String Scalar

greeting := "Hello World"

String Array

months := ["Jan", "Feb", "Mar", "Apr", "May", "Jun",
           "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]

Using String Arrays as Axis Labels

In a Plot or Chart Box, enter the variable name in the X-Variable field (optionally with a label using Label = variable):

X-variable field:   Month = months

This displays Month as the axis title and uses the string array as tick labels.

12. Numeric Arrays

Numeric arrays are enclosed in square brackets with comma-separated values. They support element-wise operations and aggregation functions.

Defining Arrays

data := [10, 20, 30, 40, 50]
x    := [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Range Literals

A compact range notation generates arrays automatically without listing every value. The syntax is [start..end] for integer steps or [start..end:step] for a custom step size.

x := [1..6]          →   [1, 2, 3, 4, 5, 6]
sum(x)               =   21

t := [0..2*pi:0.1]   →   63-element array
plot(t, sin(t))      →   sine wave

v := [1..12:0.1]
len(v)               =   111

Element-wise Operations

data * 2         →   [20, 40, 60, 80, 100]
data + [1,2,3,4,5]   →   [11, 22, 33, 42, 55]
sin(x)           →   element-wise sine of each value

Array Construction Functions

Array Transformation Functions

Aggregate Functions (Array → Scalar)

13. Functions

Functions are entered using the standard notation name(argument). They can be typed directly or inserted by clicking the corresponding button in one of the function panels.

Commonly Used Functions

Constants

Inserting Functions via Panel

Click a button in any open function panel (General, Business, Special, Geometry, …). The function text is inserted at the cursor position in the active MathBox. If the function has parameters (e.g. clip(x,min,max)), the first parameter is automatically selected so you can type the replacement immediately.

14. Angle Mode (DEG / RAD)

Trigonometric functions interpret their argument either in degrees or radians, depending on the active mode in the MathBox toolbar.

Click DEG or RAD in the MathBox toolbar to switch. The expression is recalculated immediately.

15. Output Format

Use the dropdown and decimal places selector in the MathBox toolbar to control how results are displayed.

The decimal places field limits how many digits are shown after the decimal point. Leave it blank or set it to 0 for automatic precision.

16. Complete Examples

Example 1 – Pythagorean Theorem

a := 3
b := 4
c := sqrt(a^2 + b^2)     →   5

Example 2 – Visual Fraction

Type:  sin(alpha) //  then in denominator:  cos(alpha)
Result:  tan(alpha)   (fraction bar with sin on top, cos below)

Example 3 – Quadratic Formula with Root Symbol

p := -5
q := 6
Press Ctrl+1 to insert root, type:  p^2 - 4*q  inside the root
Result:  √(25 - 24)  =  1

x1 := (-p + √(p^2 - 4*q)) / 2   →   3
x2 := (-p - √(p^2 - 4*q)) / 2   →   2

Example 4 – Superscript Exponents

E := m * c²          (type: m*c, Ctrl+^, 2, Ctrl+^)
m := 1               →   E = 8.99e16  (c = speed of light)

Example 5 – Statistics on an Array

data := [12, 45, 23, 67, 34, 89, 11, 56]
mean(data) =          →   42.125
stdev(data) =         →   27.38
median(data) =        →   39.5
quantile(data,0.75) = →   61.75

Example 6 – Matrix Calculation

A := [1,2;3,4]
B := inv(A)
A * B =             →   identity matrix [1,0;0,1]
det(A) =            →   -2

Example 7 – String Labels for Chart

months  := ["Jan","Feb","Mar","Apr","May","Jun"]
revenue := [12000, 15400, 11800, 17200, 19500, 21000]

In the Chart Box, set:

• Y-series: Revenue = revenue
• X-variable: Month = months

The chart will display month names on the X axis and bar heights for each month.

16. Definite Integral – integral()

RedcrabX can compute a definite integral numerically using adaptive Gauss–Kronrod quadrature (provided by MathNet.Numerics). The result is a real number approximation of ∫_a^b f(x) dx.

Syntax

integral(expr, var, a, b)

Basic Examples

Using Other Variables as Bounds or Parameters

Bounds and the integrand may reference any variable that is already defined in the worksheet:

n   := 3
a   := 0
b   := 2
r   := integral(x^n, x, a, b)   →   4  (= 2⁴/4)

k   := 2
f   := integral(k * sin(x), x, 0, pi)   →   4  (= k * 2)

Nested and Complex Integrands

expr may be any expression the MathBox can evaluate, including nested function calls:

integral(sin(x)^2, x, 0, pi)        →   1.5708…   (= π/2)
integral(x * exp(-x), x, 0, 10)     →   0.9999…   (≈ 1)
integral(log(x), x, 1, exp(1))      →   1         (∫₁ᵉ ln x dx = 1)
integral(tan(x), x, 0, pi/4)        →   0.3466…   (= ½ ln 2)

Double Integral (nested calls)

A double integral ∫∫ f(x,y) dx dy can be approximated by nesting two integral() calls. The outer integral treats the inner result as a function of the outer variable:

// ∫₀¹ ∫₀¹ (x + y) dy dx = 1
dbl := integral( integral(x + y, y, 0, 1) , x, 0, 1)   →   1

Common Errors

Quick-Reference Card

integral(x^2,      x, 0, 1)          ∫₀¹ x² dx           = 1/3
integral(sin(x),   x, 0, pi)         ∫₀^π sin x dx        = 2
integral(cos(x),   x, 0, pi/2)       ∫₀^(π/2) cos x dx   = 1
integral(exp(x),   x, 0, 1)          ∫₀¹ eˣ dx            = e−1
integral(1/x,      x, 1, exp(1))     ∫₁ᵉ 1/x dx           = 1
integral(x^n,      x, a, b)          bounds / powers from variables
integral(k*f(x),   x, a, b)          constant factor k from worksheet
integral(integral(x+y,y,0,1),x,0,1)  double integral ≈ ∫∫ f dA

RedcrabX  |  MathBox Guide  |  generated from source

17. Sets – {} Literals and Set Functions

RedcrabX supports mathematical sets directly inside the MathBox. A set is written with curly braces { }, just as in standard mathematics. Sets are always sorted and contain no duplicate elements.

Set Literals

Write a set literal by listing numeric expressions separated by commas inside { }:

{ 3, 1, 2, 1 }       →   {1, 2, 3}    (sorted, duplicates removed)
{ 5 }                →   {5}           (singleton)
{ }                  →   {}            (empty set)

Expressions and variables are fully supported inside the braces:

n := 4
{ n, n+1, n+2 }      →   {4, 5, 6}
{ sqrt(2), pi, 1 }   →   {1, 1.41421, 3.14159}

Assigning a Set to a Variable

Use the standard assignment operator :=:

A := {1, 2, 3}
B := {2, 3, 4}

The variable name is shown in the title bar, and the value is displayed as {1, 2, 3}. The set variable can be used in all set functions listed below.

Set Functions

All set functions are also available as ribbon buttons in the Functions panel under the Sets expander.

Step-by-Step Example

// Define two sets
A := {1, 2, 3}          →  {1, 2, 3}
B := {2, 3, 4}          →  {2, 3, 4}

// Set operations
union(A, B)              →  {1, 2, 3, 4}
intersect(A, B)          →  {2, 3}
setdiff(A, B)            →  {1}
setdiff(B, A)            →  {4}
symdiff(A, B)            →  {1, 4}

// Cardinality and membership
card(A)                  →  3
in(2, A)                 →  1
in(9, A)                 →  0

// Subset test
subset({1,2}, A)         →  1    // {1,2} ⊆ {1,2,3}  ✓
subset({1,5}, A)         →  0    // 5 ∉ A             ✗

// Converting between arrays and sets
data := [5, 3, 1, 3, 2]
S    := toset(data)      →  {1, 2, 3, 5}
back := toarray(S)       →  [1, 2, 3, 5]

Combining Set Operations

// Chaining: union of three sets
C := {4, 5, 6}
ABC := union(union(A, B), C)    →  {1, 2, 3, 4, 5, 6}

// Cardinality of union (inclusion-exclusion)
card(union(A, B)) = card(A) + card(B) - card(intersect(A, B))
                 = 3 + 3 - 2  =  4

Important Notes

Quick-Reference Card

A := {1,2,3}    B := {2,3,4}
union(A,B)          →  {1, 2, 3, 4}   // A ∪ B
intersect(A,B)      →  {2, 3}         // A ∩ B
setdiff(A,B)        →  {1}            // A \ B
setdiff(B,A)        →  {4}            // B \ A
symdiff(A,B)        →  {1, 4}         // A △ B
card(A)             →  3              // |A|
in(2,A)             →  1              // 2 ∈ A
subset({1,2},A)     →  1              // {1,2} ⊆ A
toset([3,1,2,1])    →  {1, 2, 3}      // array → set
toarray(A)          →  [1, 2, 3]      // set → array

18. Duration / Time – dur() and hms()

MathBox stores time durations as total seconds (double), so all ordinary arithmetic operators work on them. The result is automatically displayed in a human-readable format.

Output Format

Nd HH:MM:SS           days present, no milliseconds
Nd HH:MM:SS.mmm       days present, milliseconds present
HH:MM:SS              less than one day, no milliseconds
HH:MM:SS.mmm          less than one day, milliseconds present

Syntax – dur()

Parameters are always in order: days → hours → minutes → seconds → milliseconds.
All parameters after the first are optional and default to 0.

Syntax – hms()

Shorthand starting from hours (no days parameter).

Arithmetic with Durations

Because the internal value is seconds, normal operators apply:

dur(1) + dur(0,12)       →  1d 12:00:00   // 1 day + 12 hours
hms(2,30) * 2            →  05:00:00      // double 2.5 h
dur(0,8) - hms(1,30)     →  06:30:00      // difference
dur(0,6) / 2             →  03:00:00      // half of 6 hours

Storing Durations in Variables

shift := dur(0,8)        // stores 28800 s
break := hms(0,30)       // stores 1800 s
work  := shift - break   // stores 27000 s  (7.5 h)
dur(0) + work            →  07:30:00      // display using dur()

Quick-Reference Card

dur(d)            days only
dur(d,h)          days + hours
dur(d,h,m)        days + hours + minutes
dur(d,h,m,s)      days + hours + minutes + seconds
dur(d,h,m,s,ms)   all components incl. milliseconds
hms(h,m)          hours + minutes
hms(h,m,s)        hours + minutes + seconds

19. Electrical Engineering Functions

The Electrics & Electronics panel provides a growing collection of physics and engineering formulas covering Coulomb’s law, Ohm’s law, capacitors, inductors, power factor, and three-phase networks.

The full reference with all function tables, formulas, units, and examples has been moved to its own dedicated document:

📄 ElectricsGuide – Electrical Engineering Functions Reference