If \(a, b\), and \(c\) are integer vectors, this function
try to find, at each coordinate, the solution of the MLE
\(a x = b\) mod \(n\). If the MLE \(a x = b mod n\) has not
solutions (see modlin), the value reported for the
coordinate will be 0 and the corresponding translation.
Arguments
- a
An integer or a vector of integers.
- b
An integer or a vector of integers.
- n
An integer or a vector of integers.
- no.sol
Values to return when the equation is not solvable or yield the value 0. Default is 0.
Value
If the solution is exact, then a numerical vector will be returned, otherwise, if there is not exact solution for some coordinate, the a list carrying the element on the diagonal matrix and a translation vector will be returned.
Details
For \(a, b\), and \(c\) integer scalars, it is just a
wrapper function to call modlin.
Examples
## Set the vector x, y, and m.
x <- c(9,32,24,56,60,27,28,5)
y <- c(8,1,0,56,60,0,28,2)
modulo <- c(64,125,64,64,64,64,64,64)
## Try to solve the modular equation a x = b mod n
m <- modlineq(a = x, b = y, n = modulo)
m
#> [1] 8 43 0 1 1 0 1 26
## Or in matrix form
diag(m)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 8 0 0 0 0 0 0 0
#> [2,] 0 43 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 1 0 0 0 0
#> [5,] 0 0 0 0 1 0 0 0
#> [6,] 0 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 1 0
#> [8,] 0 0 0 0 0 0 0 26
## The reverse mapping is an affine transformation
mt <- modlineq(a = y, b = x, n = modulo, no.sol = 1L)
mt
#> $diag
#> [1] 1 32 1 1 1 1 1 1
#>
#> $translation
#> [1] 1 0 24 0 0 27 0 3
#>
## That is, vector 'x' is revovered with the transformaiton
(y %*% diag(mt$diag) + mt$translation) %% modulo
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 9 32 24 56 60 27 28 5
# Or
cat("\n---- \n")
#>
#> ----
(y %*% diag(mt$diag) + mt$translation) %% modulo == x
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE