AxiomX 0.1.4

A dynamic Python math library containing numerous mathematical functions implemented from scratch.

AxiomX

AxiomX is a lightweight, pure-Python mathematical library built from first principles - designed for accuracy, learning, and mathematical exploration.

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📦 Contents

𝛑 AxiomX.constants - Constants module

AxiomX.constants is the constants module of AxiomX. It has a wide variety of constants. Here are the constants we provide:

• 𝛑 (pi)
• e (Euler's number)
• ϖ (lemniscate constant)
• Square roots of 2, 3 and 5
• Metallic ratio
• Bernoulli Numbers - NEW
• Stieltjes Numbers - NEW
• Harmonic Numbers - NEW

∫ AxiomX.calculus - Calculus module

AxiomX.calculus is the calculus module of AxiomX. It provides three functions:

• integrate(function, lowlim, uplim)
• summation(lowlim, uplim, function)
• converges(function)

Usage

from AxiomX.calculus import *
import math  # just for demo. We will show you our function later. 

print(integrate(lambda x: 1 / math.cosh(x), -100, 100)) # prints 3.141592...
print(summation(1, float("inf"), lambda x: 1 / x**2)) # prints 1.64493...

⚙️ AxiomX.functions - Arithmetic functions module

AxiomX.functions is the module of AxiomX which contains all kinds of arithmetic functions. These are the functions the module provides:

• absolute(x)
• gamma(x)
• sqrt(n)
• cbrt(n)
• factorial(n)
• zeta(n)
• beta(n)
• bc(n, k)
• pascal(row)

Usage

from AxiomX.functions import *

print(gamma(0.5)) # prints 1.7724...
print(zeta(3)) # prints 1.20205...
print(beta(2)) # prints 0.91596...

📈 AxiomX.exp - Exponential and Logarithmic functions

The AxiomX.exp module contains exponential and logarithmic functions. These are the functions we provide:

• exp(n)
• ln(x)
• log10(x)
• log2(x)
• log(x,b)

Usage

from AxiomX.exp import *

print(exp(2)) # prints 7.389...
print(ln(2)) # prints 0.693...
print(log10(2)) # prints 0.301...

🔥 AxiomX.hyperbolic - Hyperbolic functions

The AxiomX.hyperbolic module deals with hyperbolic functions and their inverses. These are the functions provided:

• sinh(x), cosh(x), tanh(x), coth(x), sech(x), cosech(x)
• their inverses.

Usage

from AxiomX.hyperbolic import *

print(sinh(1)) # returns 1.17520...
print(sech(1)) # returns 0.64805...

📐 AxiomX.trig - Trigonometric functions

The AxiomX.trig module deals with trigonometric functions, their inverses and also angle conversion from degrees to radians and vice-versa. Here are the functions provided:

• sin(x), cos(x), tan(x), cot(x), sec(x), cosec(x)
• their inverses
• radians(deg) - degrees to radians
• degrees(rad) - radians to degrees

Usage

from AxiomX.trig import *
from AxiomX.constants import *

print(radians(180)) # prints 3.141592...
print(sin(pi / 2)) # prints 1.0
print(arctan(1)) # prints 0.785398...

🔢 AxiomX.matrix - Matrix operations

The AxiomX.matrix module has been introduced since version 0.1.2. It has a class Matrix which has all sorts of operations.

Features supported

• Matrix creation and indexing
• Addition, subtraction, multiplication
• Scalar multiplication
• Determinant (recursive expansion)
• Matrix inverse (adjoint method)
• Rank (Gaussian elimination)
• Transpose
• Identity and zero matrix generation

Example

from AxiomX.matrix import Matrix

A = Matrix.from_list([[1,2],[3,4]])
B = Matrix.from_list([[5,6],[7,8]])

print(A + B)
print(A**2)

📊 AxiomX.graph - plotting graphs for functions

AxiomX.graph is one of the latest additions of AxiomX, added on from version 0.1.3. This graph has now enhanced a lot. Look at our features.

Features

• Plot one or multiple functions
• Smooth zoom (PageUp / PageDown)
• Pan using arrow keys
• Infinite-style grid rendering
• Dynamic tick spacing (auto-adjusts with zoom)
• Real-time mouse coordinate tracking

Example Usage

Single Function

from AxiomX.trig import *
from AxiomX.graph import plot

plot(sin,-10,10) # plots the sine curve

Multiple Functions

from AxiomX.trig import *
from AxiomX.graph import plot

plot([lambda x: sin(x)**2, lambda y: cos(y)**2, lambda z: 1]) # explanation for sin²x + cos²x = 1

🎮 Graph Controls

⌨️ Keyboard

• PgUp - zooming out
• PgDn - zooming in
• Arrow keys - for panning around the graph

🖱️ Mouse

• shows realtime graph coordinates.

🖥️ GUI Buttons

• There are GUI buttons at the bottom with commands.

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🚀 Installation

You can directly install via pip. Go to your terminal and type: pip install AxiomX. Or rather install with the wheel file or the gzipped package.

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🛣️ Roadway

• PNG exporter for graph
• Mouse panning
• Function accepting GUI

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🤝 Contributions

If you have any suggestions or if you see bugs, just email at [e-mail]. Thanks for acknowledging AxiomX.

🪪 License

MIT