Creating a table from a matrix and two vectors
 
  
 
  
 
 
 
 
 
 
    
        
        asked 4 years ago  
 
 Cyrille gravatar image  
 
 
 
 
    
        
        updated 4 years ago  
 
 slelievre gravatar image  
 
 
 
 
 
Suppose I have the following matrix (8x4) matrix
 
[1234100201454010102234101301−12−10000]
 
I want to create a table in adding the following vector above
 
[x1x2x3x4ϵ1ϵ2ϵ3b]
 
which will be invariant
 
and the following column vector on its right
 
[ϵ1ϵ2ϵ3b]
 
Two answers to my previous question
"Concatenation of symbolic vectors"
help me construct the line vector which is a concatenation of two vectors.
But I cannot use the answer in the table() mechanism
simply because it doesn't work as expected that is
 
table(name_of_the_matrix, header_row=name_of_the_line_vector)
 
Is there a way to obtain what I expect? I observed that html.table() doesn't work.
 
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Comments
I edited the question to fix the formatting and removed your technical post-scriptum:
PS. I do not understand why the formatting doesn't work for the matrix.
To answer that: it is a technical issue with escape sequences and backslash characters.
Workaround: in LaTeX code between $ ... $,  type \\ for \ and so \\\\ for\`.
This probably has to do with the MathJax configuration of the Askbot engine powering Ask Sage.
slelievre gravatar imageslelievre (
    
        4 years ago
    )
Starting input to get anyone started on an answer:
x = [SR.var(f'x_{i}', latex_name=f'x_{i}') for i in range(5)]
y = [SR.var(f'y_{i}', latex_name=f'\\epsilon_{i}') for i in range(4)]
b = SR.var('b')

a = matrix([[1,  2, 3,  4, 1, 0, 0, 20],
            [1,  4, 5,  4, 0, 1, 0, 10],
            [2,  2, 3,  4, 1, 0, 1, 30],
            [1, -1, 2, -1, 0, 0, 0,  0]])

u = vector(SR, x[1:] + y[1:] + [b])
v = vector(SR, y[1:] + [b])
Now all there is to do is to arrange a, u, v as in the question.
slelievre gravatar imageslelievre (
    
        4 years ago
    )
For reference it seems such tables are often used when applying the
"simplex algorithm" (or "simplex method")
and in that context they are sometimes called simplex tables.
slelievre gravatar imageslelievre (
    
        4 years ago
    )
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