This is the cl-buchberger Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Tue Jul 15 03:40:05 2025 GMT+0.
cl-buchberger/cl-buchberger.asdcl-buchberger/code/package.lispcl-buchberger/code/parser.lispcl-buchberger/code/vector.lispcl-buchberger/code/ring.lispcl-buchberger/code/ring-element.lispcl-buchberger/code/term.lispcl-buchberger/code/monomial-orderings.lispcl-buchberger/code/polynomial-ring.lispcl-buchberger/code/polynomial.lispcl-buchberger/code/arithmetic.lispcl-buchberger/code/groebner.lispcl-buchberger/code/ideal.lispThe main system appears first, followed by any subsystem dependency.
cl-buchbergercl-buchberger: A Common Lisp implementation of Buchberger’s algorithm.
Juan M. Bello Rivas <jmbr@superadditive.com>
X11
asdf (system)., at least version "3.1.2"
code (module).
Modules are listed depth-first from the system components tree.
cl-buchberger/codecl-buchberger (system).
package.lisp (file).
parser.lisp (file).
vector.lisp (file).
ring.lisp (file).
ring-element.lisp (file).
term.lisp (file).
monomial-orderings.lisp (file).
polynomial-ring.lisp (file).
polynomial.lisp (file).
arithmetic.lisp (file).
groebner.lisp (file).
ideal.lisp (file).
Files are sorted by type and then listed depth-first from the systems components trees.
cl-buchberger/cl-buchberger.asdcl-buchberger/code/package.lispcl-buchberger/code/parser.lispcl-buchberger/code/vector.lispcl-buchberger/code/ring.lispcl-buchberger/code/ring-element.lispcl-buchberger/code/term.lispcl-buchberger/code/monomial-orderings.lispcl-buchberger/code/polynomial-ring.lispcl-buchberger/code/polynomial.lispcl-buchberger/code/arithmetic.lispcl-buchberger/code/groebner.lispcl-buchberger/code/ideal.lispcl-buchberger/code/parser.lisppackage.lisp (file).
code (module).
monomial-indeterminates (reader).
(setf monomial-indeterminates) (writer).
parse-polynomial (function).
polynomial-terms (reader).
(setf polynomial-terms) (writer).
term-coefficient (reader).
(setf term-coefficient) (writer).
term-monomial (reader).
(setf term-monomial) (writer).
*zero-polynomial* (special variable).
copy-monomial (function).
copy-polynomial (function).
copy-term (function).
make-monomial (function).
make-polynomial (function).
make-term (function).
monomial (structure).
monomial-p (function).
parse-coefficient (function).
parse-expt-symbol (function).
parse-monomial (function).
parse-term (function).
polynomial (structure).
polynomial-p (function).
term (structure).
term-p (function).
cl-buchberger/code/vector.lispparser.lisp (file).
code (module).
vector+ (function).
vector- (function).
vector-equal-p (function).
vector-zero-p (function).
vector> (function).
cl-buchberger/code/ring.lispvector.lisp (file).
code (module).
ring (class).
cl-buchberger/code/ring-element.lispring.lisp (file).
code (module).
ring* (generic function).
ring+ (generic function).
ring- (generic function).
ring-equal-p (generic function).
ring-identity-p (generic function).
ring-lcm (generic function).
ring-zero-p (generic function).
ring/ (generic function).
add (generic function).
div (generic function).
divides-p (generic function).
divmod (generic function).
element->string (generic function).
mul (generic function).
operands (reader method).
ring-copy (generic function).
ring-division-by-zero (condition).
ring-element (class).
ring-mod (generic function).
sub (generic function).
cl-buchberger/code/term.lispring-element.lisp (file).
code (module).
initialize-instance (method).
print-object (method).
ring-equal-p (method).
ring-zero-p (method).
coefficient (reader method).
(setf coefficient) (writer method).
element->string (method).
monomial (reader method).
(setf monomial) (writer method).
term (class).
cl-buchberger/code/monomial-orderings.lispterm.lisp (file).
code (module).
*monomial-ordering* (special variable).
degree (function).
grevlex> (function).
grlex> (function).
lex> (function).
with-monomial-ordering (macro).
cl-buchberger/code/polynomial-ring.lispmonomial-orderings.lisp (file).
code (module).
*ring* (special variable).
initialize-instance (method).
polynomial-ring (class).
print-object (method).
with-polynomial-ring (macro).
base-field (reader method).
variables (reader method).
cl-buchberger/code/polynomial.lisppolynomial-ring.lisp (file).
code (module).
doterms (macro).
lc (generic function).
lm (generic function).
lt (generic function).
make-polynomial (function).
mapterm (function).
multideg (generic function).
polynomial (class).
print-object (method).
ring-zero-p (method).
base-ring (reader method).
(setf base-ring) (writer method).
element->string (method).
make-polynomial-from-term-list (function).
ring-copy (method).
terms (reader method).
(setf terms) (writer method).
terms->list (function).
cl-buchberger/code/arithmetic.lisppolynomial.lisp (file).
code (module).
cl-buchberger/code/groebner.lisparithmetic.lisp (file).
code (module).
groebner (function).
reduce-gb (function).
reduced-groebner (function).
s-poly (function).
criterion (function).
make-index-set (function).
normal-form (function).
pair-member (function).
cl-buchberger/code/ideal.lispgroebner.lisp (file).
code (module).
basis (function).
ideal (class).
make-ideal (function).
member-p (function).
print-object (method).
generators (reader method).
(setf generators) (writer method).
ring (reader method).
(setf ring) (writer method).
Packages are listed by definition order.
cl-buchberger-parsercommon-lisp.
monomial-indeterminates (reader).
(setf monomial-indeterminates) (writer).
parse-polynomial (function).
polynomial-terms (reader).
(setf polynomial-terms) (writer).
term-coefficient (reader).
(setf term-coefficient) (writer).
term-monomial (reader).
(setf term-monomial) (writer).
*zero-polynomial* (special variable).
copy-monomial (function).
copy-polynomial (function).
copy-term (function).
make-monomial (function).
make-polynomial (function).
make-term (function).
monomial (structure).
monomial-p (function).
parse-coefficient (function).
parse-expt-symbol (function).
parse-monomial (function).
parse-term (function).
polynomial (structure).
polynomial-p (function).
term (structure).
term-p (function).
cl-buchbergercommon-lisp.
*monomial-ordering* (special variable).
*ring* (special variable).
basis (function).
degree (function).
doterms (macro).
grevlex> (function).
grlex> (function).
groebner (function).
ideal (class).
lc (generic function).
lex> (function).
lm (generic function).
lt (generic function).
make-ideal (function).
make-polynomial (function).
mapterm (function).
member-p (function).
multideg (generic function).
polynomial (class).
polynomial-ring (class).
reduce-gb (function).
reduced-groebner (function).
ring* (generic function).
ring+ (generic function).
ring- (generic function).
ring-equal-p (generic function).
ring-identity-p (generic function).
ring-lcm (generic function).
ring-zero-p (generic function).
ring/ (generic function).
s-poly (function).
with-monomial-ordering (macro).
with-polynomial-ring (macro).
add (generic function).
base-field (generic reader).
base-ring (generic reader).
(setf base-ring) (generic writer).
coefficient (generic reader).
(setf coefficient) (generic writer).
criterion (function).
div (generic function).
divides-p (generic function).
divmod (generic function).
element->string (generic function).
generators (generic reader).
(setf generators) (generic writer).
make-index-set (function).
make-polynomial-from-term-list (function).
monomial (generic reader).
(setf monomial) (generic writer).
mul (generic function).
normal-form (function).
operands (generic reader).
pair-member (function).
ring (generic reader).
(setf ring) (generic writer).
ring (class).
ring-copy (generic function).
ring-division-by-zero (condition).
ring-element (class).
ring-mod (generic function).
sub (generic function).
term (class).
terms (generic reader).
(setf terms) (generic writer).
terms->list (function).
variables (generic reader).
vector+ (function).
vector- (function).
vector-equal-p (function).
vector-zero-p (function).
vector> (function).
Definitions are sorted by export status, category, package, and then by lexicographic order.
Specifies the ordering of monomials in a polynomial
Default polynomial ring
Returns an array of generators for IDEAL.
Returns the total degree of a monomial
Graded Reverse Lex Order
Graded Lex Order
Returns a Groebner basis for the ideal generated by POLYNOMIALS.
Lexicographic Order
Create a new ideal generated by the elements contained in the GENERATORS list.
Return an instance of POLYNOMIAL in RING constructed from SEXP.
Apply FUNCTION to successive terms of POLYNOMIAL. Return list of FUNCTION return values.
Return T if ELEMENT is a member of IDEAL, NIL otherwise.
Parse polynomial in SEXP.
Returns a reduced Groebner basis.
Computes and reduces a Groebner basis of the ideal generated by F.
Returns the S-polynomial of f and g
Returns the leading coefficient of a polynomial
polynomial)) ¶Returns the leading monomial of a polynomial. That is, the leading term with 1 as coefficient
polynomial)) ¶Returns the leading term of a polynomial.
polynomial)) ¶Returns the multidegree of a polynomial
polynomial)) ¶polynomial) &rest more-polynomials) ¶polynomial) &rest more-polynomials) ¶polynomial) &rest more-polynomials) ¶Returns t if e1 equals e2, nil otherwise
Returns t if element is the multiplicative identity, nil otherwise
Returns the LCM of e1 and e2
Returns t if element is zero, nil otherwise
polynomial)) ¶polynomial) &rest more-polynomials) ¶polynomial-ring) &key) ¶polynomial) stream) ¶polynomial-ring) stream) ¶(error "you must specify a ring for the polynomial ideal.")
:ring
ring.
(error "you must provide a set of generators for the ideal.")
:generators
ring.
(error "you must specify at least one variable")
:variables
This slot is read-only.
(quote rational)
:base-field
This slot is read-only.
Representation of the zero polynomial.
Returns T if S_{ij} ought to be considered, NIL otherise.
Construct a set of index pairs represented as a hash table.
The returned set contains all the pairs whose indices are below SIZE.
Return a polynomial on RING defined by TERM-LIST.
The terms are of the form (COEFFICIENT POWER-1 POWER-2 ...) where POWER-I is the power to which the I-th indeterminate of RING is raised.
Return T if I J belong to INDEX-SET, NIL otherwise.
Parse coefficient in SEXP.
Parse (possibly exponentiated) symbol in SEXP.
Parse monomial in SEXP.
Parse term in SEXP.
Returns the sum of the two vectors V1 and V2.
Returns the difference of the two vectors V1 and V2.
Returns T if both vectors V1 and V2 have the same components, NIL otherwise.
Returns T if every compoment in V is zero.
Returns T if every component in V1 is greater than the corresponding component in V2, NIL otherwise.
Adds ring elements
polynomial) (p2 polynomial)) ¶polynomial) (tm term)) ¶polynomial-ring)) ¶automatically generated reader method
polynomial)) ¶automatically generated reader method
polynomial)) ¶automatically generated writer method
Divides ring elements
Returns t if e1 divides e2 in the base ring
Returns quotient(s) and remainder if we are working in an Euclidean ring.
polynomial) fs) ¶Returns a human-readable string representation of an element
polynomial) &key) ¶Multiplies ring elements
polynomial) (p2 polynomial)) ¶polynomial) (tm term)) ¶polynomial) (num number)) ¶ring-division-by-zero)) ¶Returns a deep copy of an element
polynomial)) ¶polynomial) &rest fs) ¶Subtracts ring elements
polynomial) (p2 polynomial)) ¶polynomial) (tm term)) ¶polynomial)) ¶automatically generated reader method
polynomial)) ¶automatically generated writer method
polynomial-ring)) ¶automatically generated reader method
error.
Association list whose keys are indeterminates (symbols) and the corresponding values are the powers.
structure-object.
structure-object.
Base class for rings.
Base class for ring elements.
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