solve.bigz: Solve a system of equation

Description

This generic function solves the equation \(a \%*\% x = b\) for \(x\), where \(b\) can be either a vector or a matrix.

If a and b are rational, return is a rational matrix.

If a and b are big integers (of class bigz) solution is in Z/nZ if there is a common modulus, or a rational matrix if not.

Usage

# S3 method for bigz
solve(a, b, ...)
# S3 method for bigq
solve(a, b, ...)

Arguments

a,b

A element of class bigz or bigq

…

Unused

Value

If a and b are rational, return is a rational matrix.

If a and b are big integers (of class bigz) solution is in Z/nZ if there is a common modulus, of a rational matrix if not.

Details

It uses the Gauss and trucmuch algo … (to be detailled).

Examples

Run this code

# NOT RUN {
x <- matrix(1:4,2,2)  ## standard solve :
solve(x)

q <- as.bigq(x) ## solve with rational
solve(q)

z <- as.bigz(x)
modulus(z) <- 7  ## solve in Z/7Z :
solve(z)

b <- c(1,3)
solve(q,b)
solve(z,b)

## Inversion of ("non-trivial") rational matrices :

A <- rbind(c(10, 1,  3),
           c( 4, 2, 10),
           c( 1, 8,  2))
(IA.q <- solve(as.bigq(A))) # fractions..
stopifnot(diag(3) == A %*% IA.q)# perfect

set.seed(5); B <- matrix(round(9*runif(5^2, -1,1)), 5)
B
(IB.q <- solve(as.bigq(B)))
stopifnot(diag(5) == B %*% IB.q, diag(5) == IB.q %*% B,
          identical(B, asNumeric(solve(IB.q))))
# }