RatCalc

Exact rational arithmetic calculator with interval support

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Commands

BASIC ARITHMETIC:

+, -, *, / - Basic operations
^ - Exponentiation (standard)
** - Multiplicative exponentiation (interval)
! - Factorial
!! - Double factorial
( ) - Parentheses for grouping

NUMBERS:

123 - Integers
3/4 - Fractions
1.25 - Decimals
1..2/3 - Mixed numbers (1 and 2/3)
0.#3 - Repeating decimals (0.333...)
3.~7~15~1 - Continued fractions
1.23[+-0.01] - Decimals with uncertainty
1.2[3,6] - Decimal concatenation (1.23:1.26)
12[34,42] - Integer concatenation (1234:1242)
2:5 - Intervals (from 2 to 5)
1E3, 2.5E-2 - Scientific notation

EXAMPLES:

1/2 + 3/4 → 5/4 (1.25)
2^3 → 8
5! → 120
1:2 * 3:4 → 3:8 (interval arithmetic)
0.#3 → 1/3
3.~7~15~1 → 355/113
1.5[+-1] → 1.49:1.51
1.5[+10,-0.1] → 1.499:1.6
1.2[3,6] → 1.23:1.26 (decimal concatenation)
12[15,18] → 1215:1218 (integer concatenation)

CONCATENATION RULES:

Valid: 12[34,42] → 1234:1242 (integer parts: 34,42 both 2 digits)
Valid: 1[19.2,20] → 119.2:120 (integer parts: 19,20 both 2 digits)
Valid: 1.2[3,6] → 1.23:1.26 (decimal base allows any)
Invalid: 1[9,20] (integer parts: 9=1 digit, 20=2 digits)
Invalid: 1[9.2,20] (integer parts: 9=1 digit, 20=2 digits)
Invalid: 1.2[3.4,5.6] (double decimal points)

VARIABLES & FUNCTIONS:

x = 5 - Assign value to single-letter variable
P[x,y] = x^2 - y - Define function with parameters
P(3,4) - Call function with arguments
SUM[i](i^2,1,10) - Sum expression from i=1 to 10
PROD[j](j,1,5) - Product expression from j=1 to 5
SEQ[k](k^3,0,5,2) - Sequence expression from k=0 to 5 step 2
VARS - Show defined variables and functions

COMMANDS:

DECI - Show results as decimals only
RAT - Show results as fractions only
BOTH - Show both decimal and fraction (default)
SCI - Show results in scientific notation
CF - Show results as continued fractions
MIX - Toggle mixed number display (default: on)
LIMIT <n> - Set decimal display limit to n digits (default: 20)
LIMIT - Show current decimal display limit
SCIPREC <n> - Set scientific notation precision to n digits (default: 10)
SCIPERIOD - Toggle period info display in scientific notation
CLEAR - Clear calculation history

BASE COMMANDS:

BASE - Show current base system
BASE <n> - Set base to n (2-62, e.g. BASE 16 for hex)
BASE <sequence> - Set custom base (e.g. BASE 0-9a-f)
BIN, HEX, OCT - Quick shortcuts for binary, hex, octal
DEC - Return to decimal (base 10)
BASES - Show available base systems

FORMAT AFTER EXPRESSIONS:

<expr> BASE <n> - Show result in specified base
<expr> BIN - Show result in binary
<expr> HEX - Show result in hexadecimal
<expr> OCT - Show result in octal
<expr> DECI - Show result in decimal format
<expr> RAT - Show result in rational format
<expr> CF - Show result as continued fraction
<expr> MIX - Show result with mixed numbers toggled

VISUALIZATION:

📊 - Click visualization icon next to interval results to open interactive viewer
Tab - Navigate between interval endpoints and whole intervals
Click - Select interval endpoints or drag whole intervals
←/→ - Move selected elements by current step size
↑/↓ - Adjust drag step size (1/2, 1/3, 1/4, 1/5, 1/8, 1/10, etc.)
Drag - Move endpoints individually or whole intervals together

KEYBOARD SHORTCUTS:

↑/↓ - Navigate command history
Escape - Close help modal
Enter - Execute calculation