R Under development (unstable) (2023-04-23 r84305 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.
> 
>  A <- matrix(c("1", "2", "3", "4"), 2, 2)
>  B <- matrix(c("1/1", "1/2", "1/3", "1/4"), 2, 2)
>  C <- qmatmult(A, B)
>  print(A)
     [,1] [,2]
[1,] "1"  "3" 
[2,] "2"  "4" 
>  print(B)
     [,1]  [,2] 
[1,] "1/1" "1/3"
[2,] "1/2" "1/4"
>  print(C)
     [,1]  [,2]   
[1,] "5/2" "13/12"
[2,] "4"   "5/3"  
>  all.equal(q2d(C), q2d(A) %*% q2d(B))
[1] TRUE
> 
>  A <- matrix(paste(1:6), 2, 3)
>  B <- matrix(paste("1/", 1:12, sep = ""), 3, 4)
>  C <- qmatmult(A, B)
>  print(A)
     [,1] [,2] [,3]
[1,] "1"  "3"  "5" 
[2,] "2"  "4"  "6" 
>  print(B)
     [,1]  [,2]  [,3]  [,4]  
[1,] "1/1" "1/4" "1/7" "1/10"
[2,] "1/2" "1/5" "1/8" "1/11"
[3,] "1/3" "1/6" "1/9" "1/12"
>  print(C)
     [,1]   [,2]     [,3]      [,4]     
[1,] "25/6" "101/60" "541/504" "521/660"
[2,] "6"    "23/10"  "61/42"   "117/110"
>  all.equal(q2d(C), q2d(A) %*% q2d(B))
[1] TRUE
> 
>  A <- matrix(paste(1:6), 3, 2)
>  B <- matrix(paste("1/", 1:8, sep = ""), 2, 4)
>  C <- qmatmult(A, B)
>  print(A)
     [,1] [,2]
[1,] "1"  "4" 
[2,] "2"  "5" 
[3,] "3"  "6" 
>  print(B)
     [,1]  [,2]  [,3]  [,4] 
[1,] "1/1" "1/3" "1/5" "1/7"
[2,] "1/2" "1/4" "1/6" "1/8"
>  print(C)
     [,1]  [,2]    [,3]    [,4]   
[1,] "3"   "4/3"   "13/15" "9/14" 
[2,] "9/2" "23/12" "37/30" "51/56"
[3,] "6"   "5/2"   "8/5"   "33/28"
>  all.equal(q2d(C), q2d(A) %*% q2d(B))
[1] TRUE
> 
>  A <- matrix(paste(1:12), 3, 4)
>  B <- matrix(paste("1/", 1:8, sep = ""), 4, 2)
>  C <- qmatmult(A, B)
>  print(A)
     [,1] [,2] [,3] [,4]
[1,] "1"  "4"  "7"  "10"
[2,] "2"  "5"  "8"  "11"
[3,] "3"  "6"  "9"  "12"
>  print(B)
     [,1]  [,2] 
[1,] "1/1" "1/5"
[2,] "1/2" "1/6"
[3,] "1/3" "1/7"
[4,] "1/4" "1/8"
>  print(C)
     [,1]     [,2]      
[1,] "47/6"   "187/60"  
[2,] "119/12" "3151/840"
[3,] "12"     "307/70"  
>  all.equal(q2d(C), q2d(A) %*% q2d(B))
[1] TRUE
> 
> 
> proc.time()
   user  system elapsed 
   0.25    0.07    0.28