In [6]:

    

import numpy as np
from numpy.linalg import *
rg = matrix_rank
from IPython.display import display, Math, Latex, Markdown

from sympy import *
from sympy import Matrix, solve_linear_system


    

In [22]:

    

pr = lambda s: display(Markdown('$'+str(latex(s))+'$'))
def psym_matrix(a, intro='',ending='',row=False):
    try:
        if row:
                return(intro+str(latex(a))+ending)
        else:
                display(Latex("$$"+intro+str(latex(a))+ending+"$$"))
    except TypeError:
        display(latex(a)) #TODO MAY BY...
pr = lambda s: display(Markdown('$'+str(latex(s))+'$'))

def pmatrix(a, intro='',ending='',row=False):
    if len(a.shape) > 2:
        raise ValueError('pmatrix can at most display two dimensions')
    lines = str(a).replace('[', '').replace(']', '').splitlines()
    rv = [r'\begin{pmatrix}']
    rv += ['  ' + ' & '.join(l.split()) + r'\\' for l in lines]
    rv +=  [r'\end{pmatrix}']
    if row:
        return(intro+'\n'.join(rv)+ending)
    else:
        display(Latex('$$'+intro+'\n'.join(rv)+ending+'$$'))
def crearMatrix(name,shape=(2,2)):
    X = []
    for i in range(shape[0]):
        row = []
        for j in range(shape[1]):
            row.append(Symbol(name+'_{'+str(i*10+j+11)+'}'))
        X.append(row)
    return Matrix(X)
from re import sub
def matrix_to_word(A):
    replaced = sub(r"begin{matrix}", r"(■( ", psym_matrix(A,row=1))
    replaced = sub(r"{", r"", replaced)
    replaced = sub(r"}", r"", replaced)
    replaced = sub(r"\\\\\\\\", r" @ ", replaced)
    replaced = sub(r"\\\\", r" @ ", replaced)
    replaced = sub(r"[\[\]]", r"", replaced)
    replaced = sub(r"left", r"", replaced)
    replaced = sub(r".endmatrix.right", r" ))", replaced)
    replaced = sub(r"\\", r"", replaced)
    print(replaced )
def isNilpotent(A):
    i = 0
    for n in range(25):
        if A**n == zeros(4,4):
            return i;
        else:
            i+=1
    return 0


    

In [11]:

    

D1= crearMatrix("d^1")
C1= crearMatrix("c^1")
D2= crearMatrix("d^2")
C2= crearMatrix("c^2")


psym_matrix(D1, intro="D^1=")
psym_matrix(C1, intro="C^1=")
psym_matrix(D2, intro="D^2=")
psym_matrix(C2, intro="C^2=")


    

    






$$D^1=\left[\begin{matrix}d^1_{11} & d^1_{12}\\d^1_{21} & d^1_{22}\end{matrix}\right]$$






    






$$C^1=\left[\begin{matrix}c^1_{11} & c^1_{12}\\c^1_{21} & c^1_{22}\end{matrix}\right]$$






    






$$D^2=\left[\begin{matrix}d^2_{11} & d^2_{12}\\d^2_{21} & d^2_{22}\end{matrix}\right]$$






    






$$C^2=\left[\begin{matrix}c^2_{11} & c^2_{12}\\c^2_{21} & c^2_{22}\end{matrix}\right]$$

In [25]:

    

D1 = Matrix([[1,1],
             [1,2]])
C1 = Matrix([[2,1],
             [1,0]])
D2 = Matrix([[1,-1],
             [0,1]])
C2 = Matrix([[1,1],
             [0,1]])


    

In [26]:

    

R1 =( Matrix([ # How???
    [ C1[0,0], 0     , C1[0,1], 0     ,],
    [ 0     , C1[0,0], 0     , C1[0,1],],
    [ C1[1,0], 0     , C1[1,1], 0     ,],
    [ 0     , C1[1,0], 0     , C1[1,1],]
])).T
T1 = Matrix([ # How???
    [D1[0,0],D1[0,1],   0  , 0    ],
    [D1[1,0],D1[1,1],   0  , 0    ],
    [ 0    , 0    ,D1[0,0],D1[0,1]],
    [ 0    , 0    ,D1[1,0],D1[1,1]]
])
R2 = (Matrix([ # How???
    [ C2[0,0], 0     , C2[0,1], 0     ,],
    [ 0     , C2[0,0], 0     , C2[0,1],],
    [ C2[1,0], 0     , C2[1,1], 0     ,],
    [ 0     , C2[1,0], 0     , C2[1,1],]
])).T
T2 = (Matrix([ # How???
    [D2[0,0],D2[0,1],   0  , 0    ],
    [D2[1,0],D2[1,1],   0  , 0    ],
    [ 0    , 0    ,D2[0,0],D2[0,1]],
    [ 0    , 0    ,D2[1,0],D2[1,1]]
]))


    

In [27]:

    

psym_matrix(R1, ending=psym_matrix(T1,row=1))
psym_matrix(R2, ending=psym_matrix(T2,row=1))


    

    






$$\left[\begin{matrix}2 & 0 & 1 & 0\\0 & 2 & 0 & 1\\1 & 0 & 0 & 0\\0 & 1 & 0 & 0\end{matrix}\right]\left[\begin{matrix}1 & 1 & 0 & 0\\1 & 2 & 0 & 0\\0 & 0 & 1 & 1\\0 & 0 & 1 & 2\end{matrix}\right]$$






    






$$\left[\begin{matrix}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\1 & 0 & 1 & 0\\0 & 1 & 0 & 1\end{matrix}\right]\left[\begin{matrix}1 & -1 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & -1\\0 & 0 & 0 & 1\end{matrix}\right]$$

In [28]:

    

psym_matrix(R1*T1+R2*T2)


    

    






$$\left[\begin{matrix}3 & 1 & 1 & 1\\2 & 5 & 1 & 2\\2 & 0 & 1 & -1\\1 & 3 & 0 & 1\end{matrix}\right]$$

In [24]:

    

psym_matrix(crearMatrix('g').T)


    

    






$$\left[\begin{matrix}g_{11} & g_{21}\\g_{12} & g_{22}\end{matrix}\right]$$

In [ ]: