source: CGBLisp/doc/coefficient-ring.txt@ 1

;;; RING (+ - * / gcd lcm zerop unit length signum numerator        [STRUCTURE]
;;;       denominator)
;;;    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* ((make-ring :+ #'+ :- #'- :* #'* :/ #'floor   [VARIABLE]
;;;                     :gcd #'gcd :lcm #'lcm :zerop #'zerop :signum
;;;                     #'signum :unit 1 :length #'integer-length
;;;                     :numerator #'numerator :denominator
;;;                     #'denominator))
;;;    Operations in the ring of integers.
;;;
;;; *FIELD-OF-RATIONALS* ((make-ring :+ #'+ :- #'- :* #'* :/ #'/     [VARIABLE]
;;;                       :gcd #'
;;;                       (lambda (&rest r) (declare (ignore r)) 1)
;;;                       :lcm #'(lambda (&rest r) (apply #'* r))
;;;                       :zerop #'zerop :signum #'signum :unit 1
;;;                       :length #'
;;;                       (lambda (x)
;;;                       (+ (integer-length (numerator x))
;;;                       (integer-length (denominator x))))
;;;                       :numerator #'numerator :denominator
;;;                       #'denominator))
;;;    Operations on the field of rational numbers.
;;;
;;; FIELD-MODULO-PRIME (modulus)                                     [FUNCTION]
;;;    Return a RING structure with operations bound
;;;    to the arithmetical operations modulo MODULUS, which
;;;    should be a prime.
;;;
;;; *COEFFICIENT-RING* (*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.
;;;