Linear-Algebra-and-Polynomials

The project is a collection of operations related to linear algebra and polynomials.

There are two main file lin_al.py and poly.py for linear algebra and polynomials respectively.

The there is one class Matrix in the lin_al.py and two classes in poly.py -- Poly and polyTree. Some of the methods in Poly rely on the Matrix class hence, it's being imported.

Matrix class

Is a class of matrices that is initialized by inputting a list of rows (all rows are also lists)

Matrix Class Method	Description	Arguments	Default	Output Type
matrix	Checks if the input is a matrix	self	N/A	bool
_square	Checks if the matrix is a square matrix	self	N/A	bool
_constructor	Constructs the minor of the matrix with the first row and removed_col removed from the original matrix	self, removed_col	N/A	Matrix
det	Matrix determinant calculator	self	N/A	int/float
__str__	Prints the matrix	self	N/A	str
transpose	Returns the transpose of the matrix and [] is not a vaid matrix	self	N/A	Matrix
mult	Multiplie two matrices	self, other	N/A	Matrix
_vector_to_poly	Turns the vector form of the polynomial to a_n*x^n + .... + a_1*x^1 + a_0 form	self	N/A	str

Poly class

Is a class of polynomials that is initialized by inputting a string of the form a_n*x^n + .... + a_1*x^1 + a_0.

Note: the degrees cannot be floats or negative.

Poly Class Method	Description	Arguments	Default	Output Type
_separator	Splits the polynomial string into terms with + as the delimiter	self	N/A	list
degree	Returns the degree of the polynmial	self	N/A	int
coeffs	Returns the coefficients of the polynimial from the highest degree to the lowerst	self	N/A	list[int]
_poly_into_vect	Turns the polynomial into vector form	self	N/A	Matrix
poly_der	Computes the n-th derivative of the polinomial using linear algebra	self, nth	nth=1	str

polyTree class

A polynomials presented as a binary tree. Input tree is of the form p(x) = a_n*x^n + .... + a_1*x^1 + a_0.

polyTree Class Method	Description	Arguments	Default	Output Type
der	Returns the derivative as a tree	self	N/A	polyTree

Example of a class input:

p(x) = -3*x^3 + (-1)*x^2 +1*x + 1

expo1 = polyTree("^", [polyTree("x", []), polyTree(3, [])])
mult1 = polyTree("*", [polyTree(-3, []), expo1])

expo2 = polyTree("^", [polyTree("x", []), polyTree(2, [])])
mult2 = polyTree("*", [polyTree(-1, []), expo2])

mult3 = polyTree("*", [polyTree(1, []), polyTree("x", [])])

num1 = polyTree(1, [])

func = polyTree("+", [mult1, mult2, mult3, num1])

Note: There is no method that gives a str version of the trees (polynomial). I might write it some time in the future, if I have time.