Martin Becker
and 1 contributors

# NAME

Math::ModInt::Trivial - integer arithmetic modulo one

# VERSION

This documentation refers to version 0.012 of Math::ModInt::Trivial.

# SYNOPSIS

``````  use Math::ModInt qw(mod);

\$a = mod(0, 1);                                 # 0 [mod 1]
\$b = \$a->new(0);                                # 0 [mod 1]
\$c = \$a + \$b;                                   # 0 [mod 1]
\$d = \$a**2 - \$b/\$a;                             # 0 [mod 1]

print \$d->residue, " [mod ", \$b->modulus, "]";  # prints 0 [mod 1]
print "\$d\n";                                   # prints mod(0, 1)

\$bool = \$c == \$d;                               # true``````

# DESCRIPTION

Math::ModInt::Trivial is an implementation of Math::ModInt for modulus one. Like all Math::ModInt implementations, it is loaded behind the scenes when there is demand for it, without applications needing to worry about it.

The residue class modulo one is the only ring where division by zero is defined, because the single element is its own multiplicative inverse. While operating on a one-element space may seem rather pointless, modular arithmetic would be incomplete without it, as it is a valid quotient ring of the ring of integers.

# AUTHOR

Martin Becker, <becker-cpan-mp@cozap.com>