The Coefficient Ring package

ring

$\parbox{\pboxargslen}{\em + $-$\space * / gcd lcm zerop unit length signum numerator denominator \/}$ [STRUCTURE]

The structure whose slots are bound to functions performing usual ring operations. In addition to usual arithmetical operations, bindings for other common operations which increase efficiency of Grobner basis calculations are also included. They are as follows: GCD $-$ greatest common divisor; LCM $-$ least common multiple; ZEROP $-$ test whether an element is zero; SIGNUM $-$ the sign of a ring element (+1, $-$1 or zero); UNIT $-$ the unit of the ring; NUMERATOR $-$ the numerator, if a ring of fractions DENOMINATOR $-$ the denominator, if a ring of fractions LENGTH $-$ an integer giving the approximate length of the representation; for example, for integers its default binding is #'integer$-$length;

*ring$-$of$-$integers*

$\parbox{\pboxargslen}{\em (make$-$ring :+ \char93 '+ :$-$\space \char... ...$-$length :numerator \char93 'numerator :denominator \char93 'denominator) \/}$ [VARIABLE]

Operations in the ring of integers.

*field$-$of$-$rationals*

$\parbox{\pboxargslen}{\em (make$-$ring :+ \char93 '+ :$-$\space \char... ...or x)))) :numerator \char93 'numerator :denominator \char93 'denominator) \/}$ [VARIABLE]

Operations on the field of rational numbers.

field$-$modulo$-$prime

$\parbox{\pboxargslen}{\em modulus \/}$ [FUNCTION]

Return a RING structure with operations bound to the arithmetical operations modulo MODULUS, which should be a prime.

*coefficient$-$ring*

$\parbox{\pboxargslen}{\em *ring$-$of$-$integers* \/}$ [VARIABLE]

The default RING structure, used in most operations on the coefficients of polynomials. It should be carefully set if rings other than the default ring is used.