R Under development (unstable) (2023-12-13 r85679 ucrt) -- "Unsuffered Consequences"
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> 
>  library(rcdd)
If you want correct answers, use rational arithmetic.
See the Warnings sections in help pages for
    functions that do computational geometry.
> 
>  d <- 4
>  qux <- makeH(- diag(d), rep(0, d), rep(1, d), 1)
>  print(qux)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    1   -1   -1   -1   -1
[2,]    0    0    1    0    0    0
[3,]    0    0    0    1    0    0
[4,]    0    0    0    0    1    0
[5,]    0    0    0    0    0    1
attr(,"representation")
[1] "H"
>  out <- scdd(qux)
>  print(out)
$output
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    0    1    0    0    0    1
[2,]    0    1    0    0    1    0
[3,]    0    1    0    1    0    0
[4,]    0    1    1    0    0    0
attr(,"representation")
[1] "V"

> 
>  qux1 <- addHeq(1:d, 2.2, qux)
>  print(qux1)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1  1.0   -1   -1   -1   -1
[2,]    0  0.0    1    0    0    0
[3,]    0  0.0    0    1    0    0
[4,]    0  0.0    0    0    1    0
[5,]    0  0.0    0    0    0    1
[6,]    1  2.2   -1   -2   -3   -4
attr(,"representation")
[1] "H"
>  out1 <- scdd(qux1)
>  print(out1)
$output
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    0    1  0.6  0.0  0.0  0.4
[2,]    0    1  0.4  0.0  0.6  0.0
[3,]    0    1  0.0  0.8  0.2  0.0
[4,]    0    1  0.0  0.9  0.0  0.1
attr(,"representation")
[1] "V"

> 
>  qux1q <- qux1
>  qux1q[6, 2] <- "11/5"
>  print(qux1q)
     [,1] [,2]   [,3] [,4] [,5] [,6]
[1,] "1"  "1"    "-1" "-1" "-1" "-1"
[2,] "0"  "0"    "1"  "0"  "0"  "0" 
[3,] "0"  "0"    "0"  "1"  "0"  "0" 
[4,] "0"  "0"    "0"  "0"  "1"  "0" 
[5,] "0"  "0"    "0"  "0"  "0"  "1" 
[6,] "1"  "11/5" "-1" "-2" "-3" "-4"
attr(,"representation")
[1] "H"
>  out1q <- scdd(qux1q)
>  print(out1q)
$output
     [,1] [,2] [,3]  [,4]   [,5]  [,6]  
[1,] "0"  "1"  "3/5" "0"    "0"   "2/5" 
[2,] "0"  "1"  "2/5" "0"    "3/5" "0"   
[3,] "0"  "1"  "0"   "4/5"  "1/5" "0"   
[4,] "0"  "1"  "0"   "9/10" "0"   "1/10"
attr(,"representation")
[1] "V"

> 
>  out1$output
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    0    1  0.6  0.0  0.0  0.4
[2,]    0    1  0.4  0.0  0.6  0.0
[3,]    0    1  0.0  0.8  0.2  0.0
[4,]    0    1  0.0  0.9  0.0  0.1
attr(,"representation")
[1] "V"
>  q2d(out1q$output)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    0    1  0.6  0.0  0.0  0.4
[2,]    0    1  0.4  0.0  0.6  0.0
[3,]    0    1  0.0  0.8  0.2  0.0
[4,]    0    1  0.0  0.9  0.0  0.1
attr(,"representation")
[1] "V"
>  qmq(out1$output, out1q$output)
     [,1] [,2] [,3]                    [,4]                   
[1,] "0"  "0"  "-1/45035996273704960"  "0"                    
[2,] "0"  "0"  "-13/90071992547409920" "0"                    
[3,] "0"  "0"  "0"                     "-13/45035996273704960"
[4,] "0"  "0"  "0"                     "-1/11258999068426240" 
     [,5]                  [,6]                 
[1,] "0"                   "7/90071992547409920"
[2,] "1/11258999068426240" "0"                  
[3,] "1/5629499534213120"  "0"                  
[4,] "0"                   "1/11258999068426240"
attr(,"representation")
[1] "V"
> 
> 
> proc.time()
   user  system elapsed 
   0.14    0.03    0.15