vectogebra v 0.0.10 - 29 May 2022

Python module for vector algebra

easy to use vector algebra library for python, that lets you work with vectors in an efficient way. apart from core vector object, many other vector operations are supported. these can be imported from vectogebra.utilities.

this library was made by keeping its applications in Physics in mind (Mechanics, Optics, etc.)

• does not depend on any external libraries except math library.
• fully functional
• easy to use
• supports nearly all vector operations
• beginner friendly
• physics friendly
• Open for modifications

🌠 Install

pip install --upgrade vectogebra

⭐ Start by importing the vector class

import vectogebra.vector as vect

OR

from vectogebra import vector as vect

⭐ Also import useful utility functions

import vectogebra.utitlies as vut

OR

from vectogebra import utilities as vut

⭐ import functions for geometry applications :

from vectogebra import geometry as geo

OR

import vectogebra.geometry as geo

🧾 Description of the module

this module currently have two components : one is vectogebra.vector, which is the vector class (boject) defination. it contains the basic functionality. the second component, vectogebra.utilities contains useful functions that are defined for the above mentioned vector class like, function to find angle between two vectors, etc.

Create a vector object :

import vectogebra.vector as vect

v1 = vect(1,2,3)

🔢 Algebric operations :

1. Addition

consider two(or more) vectors : a,b,... their sum will be given by : s = a + b + ... sum s will also be a vector object.

2. Subtraction

Vectors can be subtracted using the minus (-) operator.

example :

s = a - b + c - d + ...

resultant s will also be a vector object.

3. Dot product / scalar product and scalar multiplication

the * operator will be used for dot product, or multiplication by a scalar.

example :

p = a * b * c * d * ... is same as "a dot b dot c dot ...".

p = 5*v OR v*5 is same as "scalar 5 multiplied to vector v".

4. Cross product / vector multiplication

the ^ operator (XOR operator) will be used for cross product, or vector product.

example :

p = a^b is same as "p equals a cross b".

5. division by a scalar

simply divide a vector by a scalar. NOTE : division by zero or division vector is not supported.

example :

p = v / 5 is same as "p equals v divided by 5".

❌✔️ Logical operations :

1. Equality

a == b returnes True when a and b are equal in magnitude and direction. else, it returns False

2. Inequality

a != b have its usual meaning

3. grater / lesser

the magnitude of the vectors can be compared using common logical operators.

# a and b are vectors
a > b
a < b
a >= b
a <= b

Attributes of the vector object

Components

for a vector v1,

1. v1.x OR v1.i
2. v1.y OR v1.j
3. v1.z OR v1.k

Magnitude

4. v1.magnitude OR v1.mod

Magnitude squared (useful when precesion is required)

5. v1.magnitude_squared OR v1.mod_squared

Type

6. v1.type different from type(v1)

🚀 Vectogebra's Utitlies (vut)

important utility functions for the vector object. import :

import vectogebra.utilities as vut

S. no.	function	Return value
1.	vut.angle(v1,v2)	angle between v1 and v
2.	vut.dot(v1,v2)	dot product (or scalar product) of vectors v1 and v2
3.	vut.cross(v1,v2)	cross product (or vector product) of v1 and v2
4.	vut.magnitude(v1)	magnitude of v1 and v2
5.	vut.is_perpendicular(v1,v2)	True when v1 is perpendicular to v2 else it returns False
6.	vut.is_parallel(v1,v2)	True whe v1 is parallel to ve else False
7.	vut.scalar_component_parallel(v1,v2)	Magnitude of component of v1 parallel to v2
8.	vut.scalar_component_perpendicular(v1,v2)	Magnitude of component of v1 perpendicular to v2
9.	vut.vector_component_parallel(v1,v2)	Vector component of v1 parallel to v2
10.	vut.vector_component_perpendicular(v1,v2)	Vector compoment of v1 perpendicular to v2
11.	vut.unit_vector(v) OR vut.direction(v)	Returns the unit vector parallel to v
12.	vut.dot(v1,v2)	dot product
13.	vut.cross(v1,v2)	cross product
14.	vut.parallelogram_area(v1,v2)	parallelogram's area formed by joining v1 and v2 tail to tail
15.	vut.box(a,b,c)	Box product or scalar triple product
16.	vut.collinear(a,b,c)	returns True if a,b,c are collinear
⭐	Conversions
17.	vut.vector_to_list(v)	a list of the components of v
18.	vut.vector_to_dict(v)	a dictionary of the components of v
19.	vut.vector_to_tuple(v)	a tuple of the components of v
20.	vut.list_to_vector(l)	a vector object from a list of components
21.	vut.dict_to_vector(d)	a vector object from a dictionary of components
22.	vut.tuple_to_vector(t)	a vector object from a tuple of components
23.	vut.proportional(v1, v2)	True if two vectors are proportional, otherwise : False

(more to come)

📈 Geometry related functions :

consider vectors a, b and c :

S. no.	function	Return value	⚠ Warning	📃 Special instructions
1.	divider(a,b,m,n)	a position vector of a point that divides the line segment joining a and b by in the ratio m:n.	atleast one of m or n must be non-zero
2.	distance(a,b)	distance between a and b
3.	area_line(a,b)	signed area under the line segment joining a and b.	x-y plane only (or area under projection of line on x-y plane)
4.	area_polygon(*args)	Signed area of polygon whose vertices are given as input	x-y plane only (or projection on x-y plane)	if vertices listed in cyclic manner the area will be +ve else -ve.
5.	area_triangle(a, b, c)	Area of triangle with vertices a , b, and c
6.	coplanar(*args)	True : If all the points are coplanar else False	Arguments must be position vectors.	Keep in mind the difference between a vector and a position vector

Useful classes for 3-Dimentional Geometry

line :

represents a line in a 3D space

construction of a line :

1. Two - point form

• two points (positions vectors) or list/tuple/dict/string-representation of coordinates must be given to the constructor

• examples :

  import vectogebra.vector as vect
  import vectogebra.geometry as geo
  
  line1 = geo.line(vect(5,8,9),vect(1,6,3))
  line2 = geo.line((5,8,9),(1,6,3)) # can replace tuples whit lists.
  line3 = geo.line('5 8 9', '1 6 3')
  # dict of components can also be used.

2. Point-direction form :

• one point on the line, and the direction vector can be used to define a line :

  line1 =  geo.line(p = (1,5,3), d= (5,2,8))
  # instead of thuples, list, or string 'x y z' or vectogebra's vector can also be used.

Attributes :

1. for direction : d or dir or direction
2. for point : p or pt or point

class line have many useful functions defined. check them in the source code. they will be listed here later.

plane :

Methods of defining a plane

1. by a point and a normal vector :

plane(point=(x,y,z),normal=(a,b,c))

• vector object or list of componens can also be used instead of tuples.
• instead of point, p or pt can also be used.
• instead of normal, n or norm can also be used.

2. by three points :

plane((x1,y1,z1),(x2,y2,z2),(x3,y3,z3))

vector vectogebra.vector(x,y,z) object or lists of components [x,y,z] can also be used instead of tuples.

Attributes :

• position vector of the point on the plane : p or pt or point
• normal vector of the plane : n or normal

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Author: Mohammad Maasir

License: MIT

date-created: 8th of May, 2022

PyPi :https://pypi.org/project/vectogebra/

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Copyright © 2022 Mohammad Maasir