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.asd
cl-buchberger/package.lisp
cl-buchberger/vector.lisp
cl-buchberger/ring.lisp
cl-buchberger/ring-element.lisp
cl-buchberger/term.lisp
cl-buchberger/monomial-orderings.lisp
cl-buchberger/polynomial-ring.lisp
cl-buchberger/polynomial.lisp
cl-buchberger/arithmetic.lisp
cl-buchberger/groebner.lisp
cl-buchberger/ideal.lisp
The main system appears first, followed by any subsystem dependency.
cl-buchberger
cl-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.asd
cl-buchberger/package.lisp
cl-buchberger/vector.lisp
cl-buchberger/ring.lisp
cl-buchberger/ring-element.lisp
cl-buchberger/term.lisp
cl-buchberger/monomial-orderings.lisp
cl-buchberger/polynomial-ring.lisp
cl-buchberger/polynomial.lisp
cl-buchberger/arithmetic.lisp
cl-buchberger/groebner.lisp
cl-buchberger/ideal.lisp
cl-buchberger/cl-buchberger.asd
cl-buchberger
(system).
cl-buchberger/vector.lisp
package.lisp
(file).
cl-buchberger
(system).
vector+
(function).
vector-
(function).
vector-zero-p
(function).
vector=
(function).
vector>
(function).
cl-buchberger/ring.lisp
vector.lisp
(file).
cl-buchberger
(system).
ring
(class).
cl-buchberger/ring-element.lisp
ring.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.lisp
ring-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.lisp
term.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.lisp
monomial-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.lisp
polynomial-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.lisp
polynomial.lisp
(file).
cl-buchberger
(system).
cl-buchberger/groebner.lisp
arithmetic.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.lisp
groebner.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-buchberger
cl-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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