gmp (version 0.5-4)

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 class 'bigz':
solve(a, b, ...)
## S3 method for class '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).

See Also

solve

Examples

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)