custom-math-module

The my_math module is a custom module with mathematical functions and classes designed to facilitate work on my other projects.

Contains functions pertaining to primes: primes less than N, primality tests, factorization.

Contains a vector class to implement vector algebra and operations:

angle(v2):
    Angle between two Vectors.
antiparallel(v2):
    Returns True if the instance Vector and v2 Vector are anti-parallel. False otherwise.
cross_prod(v2):
    Cross product of instance Vector and v2; only defined in 3D.
cylindrical():
    Prints a 3D Vector's cylindrical coordinates.
dot(v2):
    Dot product of two Vectors.
magnitude():
    Finds the magnitude of the Vector.
opposite(v2):
    Returns True if the instance Vector and v2 Vector are opposite. False otherwise.
parallel(v2):
    Returns True if the instance Vector and v2 Vector are parallel. False otherwise.
perpendicular(v2):
    Returns True if the instance Vector and v2 Vector are perpendicular. False otherwise.
scalar_proj(v2):
    Scalar projection of the instance Vector onto the v2 Vector.
spherical():
    Prints a 3D Vector's spherical coordinates.
to_matrix():
    Converts the instance Vector to a one row Matrix.
transpose():
    Transposes the instance Vector from a row Vector to a column Vector. This is represented in Matrix form.
unit():
    Returns the unit Vector in the direction of the instance Vector.
vector_proj(v2):
    Vector projection of the instance Vector onto the v2 Vector.

Contains a matrix class to implement matrix algebra and operations:

adjugate():
    Returns the adjugate of a square Matrix.
count_cols():
    Counts the number of columns in the Matrix.
count_rows():
    Counts the number of rows in the Matrix.
determinant():
    Returns the determinant of a square Matrix.
getcols():
    Returns the columns of a Matrix.
getrows():
    Returns the rows of a Matrix.
identity(n):
    Returns the nxn identity Matrix.
inverse():
    Returns the inverse of a square Matrix.
isdiagonal():
    Checks if a Matrix is diagonal.
isidentity():
    Checks if a Matrix is the identity.
isinvertible():
    Checks if a Matrix is invertible.
issquare():
    Checks if a Matrix is square.
minor(i, j):
    Returns the i,j minor of the instance Matrix.
plus_minus_ones(n,m=None):
    Returns an nxm Matrix of alternating +-1.
remove_col(j):
    Returns a copy of the instance Matrix without the jth column.
remove_row(i):
    Returns a copy of the instance Matrix without the ith row.
solve_linear(b,vec=False):
    Solves the linear system A*x=b for x where A is the instance Matrix. b can be a Vector, list, tuple, row Matrix, or a column Matrix.
to_vector():
    Converts a row or a column Matrix to a row Vector.
trace():
    Returns the trace of a square Matrix.
transpose():
    Returns the transpose of a Matrix.
zero(n,m=None):
    Returns an nxm Matrix of 0.

Contains functions to perform numerical integration and derivation.

Contains an implementation of euler's method of solving ODEs of the form x'(t)=f(t,x(t)).

Contains a vector function class to implement vector function algebra and operations:

angle(x,vec):
    Finds the angle between the instance VectorFunction at x and the given Vector.
antiparallel(x,vec):
    Returns True if the instance VectorFunction evaluated at x is anti-parallel to the vec Vector. False otherwise.
arc_length(start,stop,steps=100):
    Approximates the arc length of the instance VectorFunction between start and stop.
binormal(x,error=10**-5):
    Approximates the binormal Vector of the instance VectorFunction at x. Only defined in 3D.
eval_derivative(x,error=10**-5):
    Approximates the derivative of the instance VectorFunction at x.
magnitude():
    Returns a function that finds the magnitude of the instance VectorFunction when called.
normal(x,error=10**-5):
    Approximates the unit normal Vector of the instance VectorFunction at x.
opposite(x,vec):
    Returns True if the instance VectorFunction evaluated at x is opposite to the vec Vector. False otherwise.
parallel(x,vec):
    Returns True if the instance VectorFunction evaluated at x is parallel to the vec Vector. False otherwise.
perpendicular(x,vec):
    Returns True if the instance VectorFunction evaluated at x is perpendicular to the vec Vector. False otherwise.
scalar_proj(x,vec):
    Finds the scalar projection of the instance VectorFunction at x onto the given Vector.
unit(x):
    Returns the unit Vector in the direction of the instance VectorFunction evaluated at x.
vector_proj(x,vec):
    Finds the vector projection of the instance VectorFunction at x onto the given Vector.
tangent(x,error=10**-5):
    Approximates the unit tangent Vector of the instance VectorFunction at x.

Contains functions to perform statistical operations: mean, standard deviation, variance, standard error, weighted mean, percent error, fitting linear model to data, calculating residuals of a fit, chi square test, root mean square, Durbin-Watson test.

Contains implementations of basic Stack, Queue, and Deque data structures.

Contains a function to perform binary search.

Contains a factorial function.

Contains a function to approximate a series.