Modulus of a Big Integer
The modulus of a bigz
number a is
“unset” when a is a regular integer, a \in Z).
Or the modulus can be set to m which means
a in Z/mZ), i.e., all arithmetic with
a is performed ‘modulo m’.
modulus(a) modulus(a) <- value
x <- as.bigz(24) modulus(x) # NULL, i.e. none # x element of Z/31Z : modulus(x) <- 31 x+x # 48 |-> (17 %% 31) 10*x # 240 |-> (23 %% 31) x31 <- x # reset modulus to "none": modulus(x) <- NA; x; x. <- x x <- x31 modulus(x) <- NULL; x stopifnot(identical(x, as.bigz(24)), identical(x, x.), identical(modulus(x31), as.bigz(31)))
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