vectors

Installation

You can just use pip by typing:

pip install git+https://github.com/hearot/vectors.git

Initialization

Constructor

You can initialize a Vector object by invoking its constructor and passing the three coordinates x, y and z in order. Example:

>>> from vectors import Vector
>>> Vector(1, 2, 3)
Vector(1, 2, 3)

From the unit vector notation

You can also initialize a Vector object with the unit vector notation by invoking the Vector.from_symbols static method. Example:

>>> from vectors import Vector, i, j, k
>>> Vector.from_symbols(i+2*j+3*k)
Vector(1, 2, 3)

Using spherical coordinates

In the end, you can even use spherical coordinates in order to create a Vector object by invoking the Vector.from_polar and passing the module, the azimuthal angle and the polar angle in order. Example:

>>> from sympy import pi
>>> from vectors import Vector
>>> Vector.from_polar(1, pi/2, pi/2) 
Vector(0, 1, 0)

Notations

• a*b - equivalent to a.dot(b), the dot product between a and b.
• a**b - equivalent to a.cross(b), the cross product between a and b.
• a|b - the angle between a and b (computer using the dot product).
• a^b - the angle between a and b (computed using the cross product).
• a.azimuthal - the azimuthal angle (see Spherical Coordinates on Wikipedia and Wolfram MathWorld).
• abs(a) - equivalent to a.module, the module of the vector.
• a.polar - the polar angle (see Spherical Coordinates on Wikipedia and Wolfram MathWorld).

Proofs

• proofs/linear.py - proof of a**b being always orthogonal to a linear combination of a and b.