next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
MatrixRepToric :: representationMatrix

representationMatrix -- computes the right-most map of the Z-complex in degree nu)

Synopsis

Description

NOTE: the first imput need to be a list or a matrix of homogenous polynomials. It is usually composed with 'teToricRationalMap'

The integer 'nu' needs to be a 'good degree' for the first parameter '{f0,f1,f2,f3}' that can be verified by doing isGoodDegree(polinomialList,nu)

representationMatrix(teToricRationalMap{f0,f1,f2,f3},nu) computes the right-most map of the Z-complex in degree nu. Its determinant vanishes on the implicit equation of the image of the map given by (f0:...:fn) in P^n. The output matrix in 'X_0,X_1,X_2,X_3' whose rank drops when X_i = fi

i1 : S = QQ[s,t]; 
i2 : f0 = s^2+s^3*t; 
i3 : f1 = s^3*t^6+1; 
i4 : f2 = s*t^2+2*s^3*t^5; 
i5 : f3 = s^2+s^3*t^6; 
i6 : l = {f0,f1,f2,f3}; 
i7 : representationMatrix (teToricRationalMap(l),2)

o7 = | X_0  0    0    0    0    0    0    0    0    0    0    0    0    0   
     | 0    X_0  0    0    0    0    0    0    0    0    0    0    0    0   
     | 0    0    X_0  0    0    0    0    0    0    0    0    0    0    0   
     | 0    0    0    X_0  0    0    0    0    0    0    0    0    0    0   
     | -X_1 0    0    0    X_0  0    0    0    0    0    0    0    0    0   
     | 0    0    0    0    0    X_0  0    0    0    0    0    0    0    0   
     | 0    0    0    0    0    0    X_0  0    0    0    0    0    0    0   
     | 0    0    0    0    0    0    0    X_0  0    0    0    0    0    0   
     | 0    0    0    0    0    0    0    0    X_0  0    0    0    0    0   
     | -X_1 0    -X_1 0    0    0    0    0    0    X_0  0    0    0    0   
     | 0    0    0    -X_1 0    0    0    0    0    0    X_0  0    0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    X_0  0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    X_0  0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    0    X_0 
     | X_0  0    0    0    0    0    0    0    0    0    0    0    0    0   
     | 0    -X_1 0    0    0    0    0    0    0    0    0    0    0    0   
     | 0    -X_1 0    0    0    -X_1 0    0    0    0    0    0    0    0   
     | 0    0    -X_1 0    0    0    -X_1 0    0    0    0    0    0    0   
     | 0    0    0    -X_1 0    0    0    -X_1 0    0    0    0    0    0   
     | 0    0    0    0    0    0    0    0    -X_1 0    0    0    0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    0    0   
     | 0    X_0  0    0    0    0    0    0    0    0    0    0    0    0   
     | 0    0    X_0  0    0    0    0    0    0    0    0    0    0    0   
     | 0    0    0    X_0  0    0    0    0    0    0    0    0    0    0   
     | 0    0    0    0    -X_1 0    0    0    0    0    0    0    0    0   
     | 0    0    0    0    -X_1 0    0    0    0    -X_1 0    0    0    0   
     | 0    0    0    0    0    -X_1 0    0    0    0    -X_1 0    0    0   
     | 0    0    0    0    0    0    -X_1 0    0    0    0    -X_1 0    0   
     | 0    0    0    0    0    0    0    -X_1 0    0    0    0    -X_1 0   
     | 0    0    0    0    0    0    0    0    -X_1 0    0    0    0    -X_1
     | 0    0    0    0    X_0  0    0    0    0    0    0    0    0    0   
     | 0    0    0    0    0    X_0  0    0    0    0    0    0    0    0   
     | 0    0    0    0    0    0    X_0  0    0    0    0    0    0    0   
     | 0    0    0    0    0    0    0    X_0  0    0    0    0    0    0   
     | 0    0    0    0    0    0    0    0    X_0  0    0    0    0    0   
     | 0    0    0    0    0    0    0    0    0    -X_1 0    0    0    0   
     | 0    0    0    0    0    0    0    0    0    0    -X_1 0    0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    -X_1 0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    -X_1 0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    0    -X_1
     | 0    0    0    0    0    0    0    0    0    X_0  0    0    0    0   
     | 0    0    0    0    0    0    0    0    0    0    X_0  0    0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    X_0  0    0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    X_0  0   
     | 0    0    0    0    0    0    0    0    0    0    0    0    0    X_0 
     | 0    0    0    0    0    0    0    0    0    0    0    0    0    0   
     ------------------------------------------------------------------------
     0    X_2   0     0     0     0     0     0     0     0     0     0    
     0    0     X_2   0     0     0     0     0     0     0     0     0    
     0    0     0     X_2   0     0     0     0     0     0     0     0    
     0    -X_1  0     0     X_2   0     0     0     0     0     0     0    
     0    0     0     0     0     X_2   0     0     0     0     0     0    
     0    0     0     0     0     0     X_2   0     0     0     0     0    
     0    0     -X_1  0     0     0     0     X_2   0     0     0     0    
     0    0     0     -X_1  0     0     0     0     X_2   0     0     0    
     0    0     0     0     -X_1  0     0     0     0     X_2   0     0    
     0    0     0     0     0     0     0     0     0     0     X_2   0    
     0    0     0     0     0     -X_1  0     0     0     0     0     X_2  
     0    0     0     0     0     0     -X_1  0     0     0     0     0    
     0    0     0     0     0     0     0     -X_1  0     0     0     0    
     0    -2X_1 0     0     0     0     0     0     -X_1  0     0     0    
     X_0  X_2   0     0     0     0     0     0     0     -X_1  0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     -X_1  0    
     0    0     0     0     0     0     0     0     0     0     0     -X_1 
     0    0     -2X_1 0     0     0     0     0     0     0     0     0    
     0    0     X_2   -2X_1 0     0     0     0     0     0     0     0    
     0    0     0     X_2   -2X_1 0     0     0     0     0     0     0    
     0    0     0     0     X_2   0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     -2X_1 0     0     0     0     0     0    
     -X_1 0     0     0     0     X_2   -2X_1 0     0     0     0     0    
     0    0     0     0     0     0     X_2   -2X_1 0     0     0     0    
     0    0     0     0     0     0     0     X_2   -2X_1 0     0     0    
     0    0     0     0     0     0     0     0     X_2   -2X_1 0     0    
     0    0     0     0     0     0     0     0     0     X_2   0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     -2X_1 0    
     -X_1 0     0     0     0     0     0     0     0     0     X_2   -2X_1
     0    0     0     0     0     0     0     0     0     0     0     X_2  
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     0    0     0     0     0     0     0     0     0     0     0     0    
     X_0  0     0     0     0     0     0     0     0     0     0     0    
     ------------------------------------------------------------------------
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     X_2   0     0     0     0              0        0        0       
     0     X_2   0     0     0              0        0        0       
     0     0     X_2   0     0              0        0        0       
     0     0     0     X_2   0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              2X_0     0        0       
     0     0     0     0     0              0        2X_0     0       
     0     0     0     0     0              0        0        2X_0    
     -X_1  0     0     0     0              0        0        0       
     0     -X_1  0     0     0              0        0        0       
     0     0     -X_1  0     0              0        0        0       
     0     0     0     -X_1  X_2            0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              0        0        0       
     0     0     0     0     0              -2X_3    0        0       
     0     0     0     0     0              X_2      -2X_3    0       
     0     0     0     0     0              -X_0     X_2      -2X_3   
     0     0     0     0     0              0        -X_0     X_2     
     0     0     0     0     0              0        0        -X_0    
     0     0     0     0     0              0        0        0       
     0     0     0     0     -4X_0+4X_3     0        0        0       
     0     0     0     0     -X_1-2X_2+X_3  0        0        0       
     0     0     0     0     0              -2X_1    0        0       
     0     0     0     0     0              X_2      -2X_1    0       
     0     0     0     0     0              0        X_2      -2X_1   
     0     0     0     0     0              0        0        X_2     
     0     0     0     0     0              -X_1+X_3 0        0       
     0     0     0     0     0              0        -X_1+X_3 0       
     -2X_1 0     0     0     -X_2           0        0        -X_1+X_3
     X_2   -2X_1 0     0     0              0        0        0       
     0     X_2   -2X_1 0     4X_3           0        0        0       
     0     0     X_2   -2X_1 -2X_2          0        0        0       
     0     0     0     X_2   2X_0+2X_1-2X_3 0        0        0       
     ------------------------------------------------------------------------
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        X_2            0              0             
     0        0        0        0              X_2            0             
     0        0        0        0              0              X_2           
     2X_0     0        0        0              0              0             
     0        2X_0     0        0              0              0             
     0        0        2X_0     0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        0              0              0             
     0        0        0        -4X_0+4X_3     0              0             
     0        0        0        -X_1-2X_2+X_3  -4X_0+4X_3     0             
     0        0        0        0              -X_1-2X_2+X_3  -4X_0+4X_3    
     -2X_3    0        0        0              0              -X_1-2X_2+X_3 
     X_2      -2X_3    0        0              0              0             
     -X_0     X_2      -2X_3    0              0              0             
     0        -X_0     X_2      0              0              0             
     0        0        -X_0     0              0              0             
     0        0        0        -X_2           0              0             
     0        0        0        0              -X_2           0             
     0        0        0        4X_3           0              -X_2          
     -2X_1    0        0        -2X_2          4X_3           0             
     X_2      -2X_1    0        2X_0+2X_1-2X_3 -2X_2          4X_3          
     0        X_2      -2X_1    0              2X_0+2X_1-2X_3 -2X_2         
     0        0        X_2      0              0              2X_0+2X_1-2X_3
     -X_1+X_3 0        0        0              0              0             
     0        -X_1+X_3 0        0              0              0             
     0        0        -X_1+X_3 0              0              0             
     0        0        0        0              0              0             
     ------------------------------------------------------------------------
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     X_2            0              0              0               
     0              X_2            0              0               
     0              0              X_2            0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     -4X_0+4X_3     0              0              0               
     -X_1-2X_2+X_3  -4X_0+4X_3     0              6X_2            
     0              -X_1-2X_2+X_3  -4X_0+4X_3     -6X_0+6X_3      
     0              0              -X_1-2X_2+X_3  -3X_2+4X_3      
     0              0              0              -5X_0-2X_2      
     0              0              0              0               
     0              0              0              0               
     0              0              0              0               
     -X_2           0              0              0               
     0              -X_2           0              0               
     4X_3           0              -X_2           -4X_2           
     -2X_2          4X_3           0              5X_2            
     2X_0+2X_1-2X_3 -2X_2          4X_3           -6X_1+6X_3      
     0              2X_0+2X_1-2X_3 -2X_2          0               
     0              0              2X_0+2X_1-2X_3 8X_0+3X_1-3X_3  
     0              0              0              -10X_0+2X_1-2X_3
     ------------------------------------------------------------------------
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               -6X_0+6X_3      0               0              
     0               -3X_2           0               0              
     0               3X_0-8X_3       0               0              
     0               -2X_0+4X_2      0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     6X_0            0               0               0              
     0               6X_2            0               0              
     0               5X_2            6X_2            0              
     0               -6X_1+2X_2+6X_3 -6X_0+6X_3      6X_2           
     0               0               -3X_2           -6X_0+6X_3     
     0               3X_1-3X_3       3X_0-8X_3       -3X_2          
     0               -10X_0          -2X_0+4X_2      3X_0-8X_3      
     0               -4X_0-4X_1+4X_3 0               -2X_0+4X_2     
     -6X_0+6X_3      0               0               0              
     -3X_2           0               0               0              
     3X_0-8X_3       0               0               0              
     -2X_0+4X_2      0               0               0              
     0               0               5X_2            0              
     0               0               -6X_1+2X_2+6X_3 5X_2           
     0               0               0               -6X_1+2X_2+6X_3
     0               0               3X_1-3X_3       0              
     0               0               -10X_0          3X_1-3X_3      
     -X_2            0               -4X_0-4X_1+4X_3 -10X_0         
     -6X_1+2X_2+6X_3 0               0               -4X_0-4X_1+4X_3
     0               0               0               0              
     3X_1-3X_3       0               0               0              
     2X_0            0               0               0              
     -4X_0-4X_1+4X_3 0               0               0              
     ------------------------------------------------------------------------
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     6X_2            0               0               0              
     -6X_0+6X_3      6X_2            0               0              
     -3X_2           -6X_0+6X_3      6X_2            0              
     3X_0-8X_3       -3X_2           -6X_0+6X_3      6X_2           
     -2X_0+4X_2      3X_0-8X_3       -3X_2           -6X_0+6X_3     
     0               -2X_0+4X_2      3X_0-8X_3       -3X_2          
     0               0               -2X_0+4X_2      3X_0-8X_3      
     0               0               0               -2X_0+4X_2     
     0               0               0               0              
     0               0               0               0              
     5X_2            0               0               0              
     -6X_1+2X_2+6X_3 5X_2            0               0              
     0               -6X_1+2X_2+6X_3 5X_2            0              
     3X_1-3X_3       0               -6X_1+2X_2+6X_3 5X_2           
     -10X_0          3X_1-3X_3       0               -6X_1+2X_2+6X_3
     -4X_0-4X_1+4X_3 -10X_0          3X_1-3X_3       0              
     0               -4X_0-4X_1+4X_3 -10X_0          3X_1-3X_3      
     0               0               -4X_0-4X_1+4X_3 -10X_0         
     0               0               0               -4X_0-4X_1+4X_3
     ------------------------------------------------------------------------
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     2X_2            0               0               0              
     -8X_0+8X_3      2X_2            0               0              
     -2X_1-4X_2      0               2X_2            0              
     4X_0+X_2-4X_3   0               0               2X_2           
     -X_0+2X_2       0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     X_2+8X_3        -8X_0+8X_3      0               0              
     -4X_2           -2X_1-4X_2      -8X_0+8X_3      0              
     4X_1-4X_3       4X_0+X_2-4X_3   -2X_1-4X_2      -8X_0+8X_3     
     -X_1+X_3        -X_0+2X_2       4X_0+X_2-4X_3   -2X_1-4X_2     
     -2X_0-2X_1+2X_3 0               -X_0+2X_2       4X_0+X_2-4X_3  
     0               0               0               -X_0+2X_2      
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     0               X_2+8X_3        0               0              
     0               -4X_2           X_2+8X_3        0              
     0               4X_1-4X_3       -4X_2           X_2+8X_3       
     0               -X_1+X_3        4X_1-4X_3       -4X_2          
     0               -2X_0-2X_1+2X_3 -X_1+X_3        4X_1-4X_3      
     0               0               -2X_0-2X_1+2X_3 -X_1+X_3       
     0               0               0               -2X_0-2X_1+2X_3
     0               0               0               0              
     0               0               0               0              
     0               0               0               0              
     ------------------------------------------------------------------------
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     2X_2            0               0               0        0       
     0               2X_2            0               0        0       
     0               0               2X_2            0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               -X_0+X_3 0       
     0               0               0               X_3      -X_0+X_3
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     -8X_0+8X_3      0               0               0        0       
     -2X_1-4X_2      -8X_0+8X_3      0               -X_0     0       
     4X_0+X_2-4X_3   -2X_1-4X_2      -8X_0+8X_3      0        0       
     -X_0+2X_2       4X_0+X_2-4X_3   -2X_1-4X_2      0        0       
     0               -X_0+2X_2       4X_0+X_2-4X_3   0        0       
     0               0               -X_0+2X_2       0        0       
     0               0               0               0        X_3     
     0               0               0               0        0       
     0               0               0               0        0       
     0               0               0               0        0       
     X_2+8X_3        0               0               0        0       
     -4X_2           X_2+8X_3        0               0        -X_0    
     4X_1-4X_3       -4X_2           X_2+8X_3        0        0       
     -X_1+X_3        4X_1-4X_3       -4X_2           0        0       
     -2X_0-2X_1+2X_3 -X_1+X_3        4X_1-4X_3       0        0       
     0               -2X_0-2X_1+2X_3 -X_1+X_3        0        0       
     0               0               -2X_0-2X_1+2X_3 0        0       
     ------------------------------------------------------------------------
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     0        0        0        0        0        6X_3                
     0        0        0        0        0        0                   
     0        0        0        0        0        0                   
     -X_0+X_3 0        0        0        0        0                   
     0        -X_0+X_3 0        0        0        0                   
     0        0        -X_0+X_3 0        0        0                   
     0        0        0        -X_0+X_3 0        0                   
     0        0        0        0        -X_0+X_3 0                   
     0        0        0        0        0        -6X_0+6X_3          
     0        0        0        0        0        -3X_2               
     0        0        0        0        0        3X_0-8X_3           
     0        0        0        0        0        -2X_0+4X_2          
     0        0        0        0        0        0                   
     X_3      0        0        0        0        0                   
     0        X_3      0        0        0        0                   
     0        0        X_3      0        0        0                   
     0        0        0        X_3      0        0                   
     0        0        0        0        X_3      5X_2                
     -X_0     0        0        0        0        -6X_1+2X_2+6X_3     
     0        -X_0     0        0        0        0                   
     0        0        -X_0     0        0        3X_1-3X_3           
     0        0        0        -X_0     0        -10X_0+12X_3        
     0        0        0        0        -X_0     -4X_0-4X_1-6X_2+4X_3
     ------------------------------------------------------------------------
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           -2X_0+2X_3     0              0              0             
     0           2X_3           -2X_0+2X_3     0              0             
     0           -4X_0-X_2+4X_3 0              -2X_0+2X_3     0             
     0           X_0-2X_2       0              0              -2X_0+2X_3    
     0           0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     X_3         0              0              0              0             
     0           0              0              0              0             
     0           0              0              0              0             
     0           -X_2           0              0              0             
     0           0              2X_3           0              0             
     0           4X_3           -4X_0-X_2+4X_3 2X_3           0             
     0           X_1-2X_2-X_3   X_0-2X_2       -4X_0-X_2+4X_3 2X_3          
     0           2X_0+2X_1-2X_3 0              X_0-2X_2       -4X_0-X_2+4X_3
     0           0              0              0              X_0-2X_2      
     0           0              0              0              0             
     0           0              0              0              0             
     -2X_0+2X_3  0              0              0              0             
     -X_2        0              0              0              0             
     0           0              -X_2           0              0             
     0           0              0              -X_2           0             
     0           0              4X_3           0              -X_2          
     0           0              X_1-2X_2-X_3   4X_3           0             
     0           0              2X_0+2X_1-2X_3 X_1-2X_2-X_3   4X_3          
     -X_1        0              0              2X_0+2X_1-2X_3 X_1-2X_2-X_3  
     0           0              0              0              2X_0+2X_1-2X_3
     0           0              0              0              0             
     2X_3        0              0              0              0             
     -X_2        0              0              0              0             
     X_0+X_1-X_3 0              0              0              0             
     ------------------------------------------------------------------------
     0              0              0              X_3      0        0       
     0              0              0              0        X_3      0       
     0              0              0              0        0        X_3     
     0              0              0              0        0        0       
     0              0              0              -X_1     0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        -X_1    
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              -X_1+X_3 0        0       
     0              0              0              0        -X_1     0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     -2X_0+2X_3     0              0              0        0        0       
     0              -2X_0+2X_3     0              0        0        0       
     0              0              -2X_0+2X_3     0        -X_1+X_3 0       
     0              0              0              0        0        -X_1+X_3
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     2X_3           0              0              0        0        0       
     -4X_0-X_2+4X_3 2X_3           0              0        0        0       
     X_0-2X_2       -4X_0-X_2+4X_3 2X_3           0        0        0       
     0              X_0-2X_2       -4X_0-X_2+4X_3 0        0        0       
     0              0              X_0-2X_2       0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     0              0              0              0        0        0       
     -X_2           0              0              0        0        0       
     0              -X_2           0              0        0        0       
     4X_3           0              -X_2           0        0        0       
     X_1-2X_2-X_3   4X_3           0              0        0        0       
     2X_0+2X_1-2X_3 X_1-2X_2-X_3   4X_3           0        0        0       
     0              2X_0+2X_1-2X_3 X_1-2X_2-X_3   0        0        0       
     0              0              2X_0+2X_1-2X_3 0        0        0       
     0              0              0              0        0        0       
     ------------------------------------------------------------------------
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     X_3      0        0        0        0        0        0        0       
     0        X_3      0        0        0        0        0        0       
     0        0        X_3      0        0        0        0        0       
     0        0        0        X_3      0        0        0        0       
     0        0        0        0        X_3      0        0        0       
     0        0        0        0        0        X_3      0        0       
     0        0        0        0        0        0        X_3      0       
     -X_1     0        0        0        0        0        0        X_3     
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        -X_1     0        0        0        0        0       
     0        0        0        -X_1     0        0        0        0       
     0        0        0        0        -X_1     0        0        0       
     0        0        0        0        0        -X_1     0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     -X_1+X_3 0        0        0        0        0        0        0       
     0        -X_1     0        0        0        0        0        0       
     0        0        0        0        0        0        -X_1     0       
     0        0        0        0        0        0        0        -X_1    
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        -X_1+X_3 0        0        0        0        0        0       
     0        0        -X_1+X_3 0        0        0        0        0       
     0        0        0        -X_1+X_3 0        0        0        0       
     0        0        0        0        -X_1+X_3 0        0        0       
     0        0        0        0        0        -X_1+X_3 0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        -X_1+X_3 0       
     0        0        0        0        0        0        0        -X_1+X_3
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     0        0        0        0        0        0        0        0       
     ------------------------------------------------------------------------
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     X_3      0        0        0        |
     0        X_3      0        0        |
     0        0        X_3      0        |
     0        0        0        X_3      |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     -X_1     0        0        0        |
     0        -X_1     0        0        |
     0        0        -X_1     0        |
     0        0        0        -X_1     |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     0        0        0        0        |
     -X_1+X_3 0        0        0        |
     0        -X_1+X_3 0        0        |
     0        0        -X_1+X_3 0        |
     0        0        0        -X_1+X_3 |

                                46                          90
o7 : Matrix (QQ[X , X , X , X ])   <--- (QQ[X , X , X , X ])
                 0   1   2   3               0   1   2   3

See also

Ways to use representationMatrix :