Library that solves discrete math operations of the group Zn, provides both as calculator program or third party library.

# Znop

Library that solves discrete math operations of the group Zn, provides both as calculator program or third party library.

The group Zn consists of the elements {0, 1, 2, . . . , n−1} with addition mod n as the operation. You can also multiply elements of Zn, but you do not obtain a group: The element 0 does not have a multiplicative inverse, for instance. However, if you confine your attention to the units in Zn — the elements which have multiplicative inverses — you do get a group under multiplication mod n. It is denoted Un, and is called the group of units in Zn.

## Program Usage

Describe how to install the calculator and its commands.

Note: This program will always create a znop_db.json file if it doesn't exist in the directory you execute the program, this file is aimed to save your last ~30 commands and the Zn group (default n=10) set on your program.

### Install from source

1. Make sure to have python > v3.6 installed.
2. $git clone https://github.com/paaksing/Znop.git 3. $ cd Znop
4. $python setup.py install 5. $ znop.

### Install using pip

1. Make sure to have python > v3.6 installed and pip installed.
2. $pip install znop. 3. $ znop.

### Install as executable

1. Find the latest executable in this repository's Releases.
3. Execute it.

### Commands

All payload passed to the commands should strictly match this regex: [a-zA-Z0-9\+\-\*\^]

Command Description
set n=<setnumber> Set the set number of Z
reduce <expression> Reduce a Zn expression or equation
solve <equation> Solve an one-dimensional Zn equation
help Usage of this program
quit Quit this program

### Example

(n=10) reduce (3x*9)+78-4x
3x+8

(n=10) set n=6
OK

(n=6) solve x^2+3x+2=0
x ∈ {1, 2, 4, 5}

(n=6) quit


## Library Usage

Describe usage and API of this library.

### Requirements and installation

• Python 3.6 (due to requirements of f-strings)
• Install using pip install znop

## API Documentation

This library consists of 3 modules: core and exceptions. All objects in this library can be "copied" or "reinstantiated" by doing eval(repr(obj)) where obj is an znop object. str() will return the string representation of the object and repr() will return the string representation of the object in python syntax.

Import the object from the respective modules e.g.: from znop.core import ZnEquation

### znop.core.ZnTerm

Represents a term in the group of ZnTerm

• __init__(n: int, raw: str): Create an instance of ZnTerm, arguments: n (set number), raw (raw string of term, e.g. '2x').

• __add__, __sub__, __mul__, __neg__, __eq__: This object supports [+, -, *] operations between ZnTerms, with the exception of multiplications that it can multiply a ZnExpression by doing distributive, it will always return a new ZnTerm. Supports - (negate) operation and returns a new ZnTerm. It also supports equality comparison == between ZnTerms.

• eval(values: Dict[str, int]): Evaluate the variables in the term, receives a mapping of variable name to value e.g. {'x': 6}, and return a new ZnTerm.

### znop.core.ZnExpression

• __init__(n: int, raw: str): Create an instance of ZnExpression, arguments: n (set number), raw (raw string of expression, e.g. '2x+x-3'). This expression is automatically reduced to its simplest form.

• __mul__, __eq__: This objects supports * between ZnExpressions and ZnTerms by doing distributive, It also supports equality comparison == between ZnExpressions.

• reduce(): Reduce the expression to the simplest form, this function is automatically called on instantiation.

• eval(values: Dict[str, int]): Evaluate the variables in the expression, receives a mapping of variable name to value e.g. {'x': 6}, and return a new ZnExpression.

### znop.core.ZnEquation

• __init__(n: int, raw: str): Create an instance of ZnEquation, arguments: n (set number), raw (raw string of equation, e.g. '2x^2+3=0'). This equation is automatically reduced to its simplest form.

• reduce(): Reduce the equation to the simplest form, this function is automatically called on instantiation.

• solve(): Solve the equation by returning a list of solutions (ints). If the equation cannot be solved, then ResolveError will be raised.

### znop.exceptions.ZSetError

Operation between ZnInt of different Z set.

### znop.exceptions.ZVarError

Operation between ZnInt of different variables outside products.

### znop.exceptions.ParseError

Indicates a parsing error, reason will be stated when ParseError is thrown.

### znop.exceptions.ResolveError

Could not resolve equation.

## Project details

Uploaded source
Uploaded py3