@mainpage Manuel Linear Algebra Solver
Members : Valentin Koeltgen
License : GNU General Public License

This project goal is to create a program with a simple command-line interface to do calculations on polynomial, matrices and variables.
Right now the project is limited to handling real values but imaginary values handling can be added in the future.

The program should be able to handle advanced maths in the form of simple user commands or script files containing commands.
It should be able to handle all kind of objects, like polynomials, matrices, vectors (matrices with 1 column) or simple values.

Command List

This is a list of commands that are available to the user

Simple commands

The following commands don't need any arguments, they are used to do action related to the user

help This command display this page in the terminal
displayAll This command display the whole content of the main register
clear This command empty the main register
readScript(<link>) This command apply the content of a script located at <link>, it reads it line by line and apply every command

Simple operations

The following commands are final but accept composite operations as argument

display(<operation>) This command display the result of <operation> in the terminal
eig(<operation>) This command display the eigen values of <operation>, <operation> must be a matrix
solve(<operation>) This command display the result of solving <operation>,

• if <operation> is an augmented matrix, the result will be the matrix in echelon form
• if <operation> is a polynomial, the result will be the roots of the polynomial

Composite operations

The following commands are not final, they can be used recursively

<objectName> = <operation> This command create a new object in the register which contain the result of operation and has for name <objectName>
<operation1> + <operation2> This command return the sum of <operation1> and <operation2> if they are of the same type (or a polynomial with a variable)
<operation1> - <operation2> This command return the difference of <operation1> and <operation2> if they are of the same type (or a polynomial with a variable)
<operation1> * <operation2> This command return the product of <operation1> and <operation2> if they are of the same type (or a polynomial/matrix with a variable)
<operation1> / <operation2> This command return the quotient of <operation1> and <operation2> if they are of the same type (or a polynomial with a variable)
trans(<operation>) This command return the transposed of <operation>, <operation> must be a matrix
adj(<operation>) This command return the adjugate of <operation>, <operation> must be a matrix
inv(<operation>) This command return the inverse of <operation>, <operation> must be a matrix
eigVectors(<operation>) This command return the eigen vectors of <operation> in matrix form completed with orthonormal vectors if needed, <operation> must be a matrix
triangularise(<operation>) This command return the triangularised form of <operation>, <operation> must be a matrix
PLambda(<operation>) This command return the polynomial P(lambda) = det(<operation> - lambda * I) of <operation>, <operation> must be a matrix
derive(<operation>) This command return the derivative of <operation>, <operation> must be a polynomial
trace(<operation>) This command return the trace of <operation>, <operation> must be a matrix
det(<operation>) This command return the determinant of <operation>, <operation> must be a matrix

Basic object

The following arguments can be used as fundamentals to create or call objects

<objectName> This will refer to the object with the same name, it must have been created beforehand. An object name can take any ASCII character but cannot be X, contain [ or ] and can only be the size of one word, no space accepted
[<matrixFormat>] This will create a matrix object. The format used to create a matrix is the following :

• all values in a row are separated by a ,
• all rows are separated by a ;, the last one doesn't need it

Example : [1,2,3;4,5,6;7,8,9] is a correct 3x3 matrix, [1,2;3,4,5] is not correct since the 2nd row has more values than the first

<polynomialFormat> This will create a polynomial object. The format used to create a polynomial is the following :

• to write coefficient, one must use the format <coefficient>X^<power> with <coefficient> any real value and <power> a positive integer
  • if <power> is 1, the coefficient can be written as <coefficient>X
  • if <power> is 0, the coefficient can be written as <coefficient>
  • if <coefficient> is 1, it can be omitted

Example : 2X + X^2 * (2X + 2) is correct an will create the polynomial 2X^3 + 2X^2 + 2X + 0, X + 2X^-1.5 is not correct because the power of the second is not a positive integer