Solve a system of equation
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.
## S3 method for class 'bigz' solve(a, b, ...) ## S3 method for class 'bigq' solve(a, b, ...)
a,b |
A element of class bigz or bigq |
... |
Unused |
It uses the Gauss and trucmuch algo ... (to be detailled).
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.
Antoine Lucas
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))))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.