This is the cl-buchberger Reference Manual, version 0.0.4, generated automatically by Declt version 4.0 beta 2 "William Riker" on Sun Sep 15 03:46:23 2024 GMT+0.
cl-buchberger/cl-buchberger.asdcl-buchberger/package.lispcl-buchberger/vector.lispcl-buchberger/ring.lispcl-buchberger/ring-element.lispcl-buchberger/term.lispcl-buchberger/monomial-orderings.lispcl-buchberger/polynomial-ring.lispcl-buchberger/polynomial.lispcl-buchberger/arithmetic.lispcl-buchberger/groebner.lispcl-buchberger/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>
GNU GPLv2
0.0.4
package.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/package.lispcl-buchberger/vector.lispcl-buchberger/ring.lispcl-buchberger/ring-element.lispcl-buchberger/term.lispcl-buchberger/monomial-orderings.lispcl-buchberger/polynomial-ring.lispcl-buchberger/polynomial.lispcl-buchberger/arithmetic.lispcl-buchberger/groebner.lispcl-buchberger/ideal.lispcl-buchberger/cl-buchberger.asdcl-buchberger (system).
cl-buchberger/vector.lisppackage.lisp (file).
cl-buchberger (system).
vector+ (function).
vector- (function).
vector-zero-p (function).
vector= (function).
vector> (function).
cl-buchberger/ring.lispvector.lisp (file).
cl-buchberger (system).
ring (class).
cl-buchberger/ring-element.lispring.lisp (file).
cl-buchberger (system).
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/term.lispring-element.lisp (file).
cl-buchberger (system).
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/monomial-orderings.lispterm.lisp (file).
cl-buchberger (system).
*monomial-ordering* (special variable).
degree (function).
grevlex> (function).
grlex> (function).
lex> (function).
with-monomial-ordering (macro).
cl-buchberger/polynomial-ring.lispmonomial-orderings.lisp (file).
cl-buchberger (system).
*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/polynomial.lisppolynomial-ring.lisp (file).
cl-buchberger (system).
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).
ring-copy (method).
terms (reader method).
(setf terms) (writer method).
terms->list (function).
cl-buchberger/arithmetic.lisppolynomial.lisp (file).
cl-buchberger (system).
cl-buchberger/groebner.lisparithmetic.lisp (file).
cl-buchberger (system).
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/ideal.lispgroebner.lisp (file).
cl-buchberger (system).
basis (generic function).
make-ideal (function).
member-p (generic function).
print-object (method).
generators (reader method).
(setf generators) (writer method).
ideal (class).
ring (reader method).
(setf ring) (writer method).
Packages are listed by definition order.
com.superadditive.cl-buchbergercl-buchberger
asdf/interface.
common-lisp.
*monomial-ordering* (special variable).
*ring* (special variable).
basis (generic function).
degree (function).
doterms (macro).
grevlex> (function).
grlex> (function).
groebner (function).
lc (generic function).
lex> (function).
lm (generic function).
lt (generic function).
make-ideal (function).
make-polynomial (function).
mapterm (function).
member-p (generic 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).
ideal (class).
make-index-set (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-zero-p (function).
vector= (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 the total degree of a monomial
Graded Reverse Lex Order
Graded Lex Order
Returns a Groebner basis for the ideal generated by the specified array of polynomials.
Lexicographic Order
Create a new ideal generated by the elements contained in the ‘generators’ list.
Apply FUNCTION to successive terms of POLYNOMIAL. Return list of FUNCTION return values.
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 an array of generators for ‘ideal’.
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)) ¶ring-element) (ideal ideal)) ¶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-ring) stream) ¶polynomial) stream) ¶add.
add.
(setf base-ring).
base-ring.
divides-p.
divmod.
element->string.
lc.
lm.
lt.
mul.
mul.
mul.
multideg.
print-object.
ring*.
ring+.
ring-.
ring-copy.
ring-zero-p.
ring/.
sub.
sub.
(setf terms).
terms.
(error "you must specify a base ring")
:ring
hash-table
(make-hash-table :test (function equalp))
:terms
ring.
(error "you must specify at least one variable")
:variables
This slot is read-only.
(quote rational)
:base-field
This slot is read-only.
Returns t if S_{ij} has to be considered
Returns the sum of the two vectors V1 and V2.
Returns the difference of the two vectors V1 and V2.
Returns T if every compoment in V is zero.
Returns T if both vectors V1 and V2 have the same components, NIL otherwise.
Returns T if every component in V1 is greater than the corresponding component in V2, NIL otherwise.
Adds ring elements
polynomial) (p2 polynomial)) ¶Returns the sum of two polynomials
polynomial) (tm term)) ¶Returns the polynomial with the added 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) ¶Divides F by the polynomials in the sequence FS and returns the quotients (as an array) and a remainder.
Returns a human-readable string representation of an element
polynomial) &key) ¶Multiplies ring elements
polynomial) (p2 polynomial)) ¶Returns the product of two polynomials
polynomial) (tm term)) ¶Returns the product of a polynomial by a term
term) (t2 term)) ¶Multiplies two terms storing the result in the first term.
polynomial) (num number)) ¶ring-division-by-zero)) ¶Returns a deep copy of an element
polynomial)) ¶Returns a (deep) copy of the given polynomial
Subtracts ring elements
polynomial) (p2 polynomial)) ¶Returns the result of subtracting two polynomials.
polynomial) (tm term)) ¶Returns the result of subtracting the term from the polynomial
polynomial)) ¶automatically generated reader method
polynomial)) ¶automatically generated writer method
polynomial-ring)) ¶automatically generated reader method
error.
Base class for rings.
Base class for ring elements.
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