Index of values

A
add [Ring.T]
add [Ring.Float]
add [Ring.Int]
add [Ring.Bool]
add [Monoid.Abelian]
add [Globular.Presentation]

Add an n-cell.

add [Field.Fractions]
add [Ring.Polynomial]
add [Series.Make]

Addition.

add [Alphabet.Map]
add [Alphabet.Pow]
add [Module.FreeLeft.E]
add [Module.FreeLeft]
add0 [Globular.Presentation]

Add a 0-cell.

add_edge [Graph.Presentation]
add_monomial [Module.FreeLeft]
add_relation [Algebra.Presentation]

Add a relation to a presentation.

add_rule [Monoid.Presentation]
add_rule [Algebra.Presentation]

Add a rule to a presentation.

add_transition [Automaton.Make]
add_vertex [Graph.Presentation]
app [Alphabet.Map]
app [Module.FreeLeft.Presentation.Map]

Apply a morphism to an element.

app [Module.FreeLeft.Map]
B
bind [Module.FreeLeft.Map]
bind [Algebra.Presentation.Anick.AMod.Map]
boundary [Precategory.Make.Presentation]
braid [Algebra.Generate]
buchberger [Algebra.Presentation]

Buchberger's completion algorithm.

C
canonize [Field.Fractions]
chains [Algebra.Presentation.Anick]

Array of Anick chains up to degree n.

cinj [Module.FreeLeft]
cinj [Algebra.Presentation.Anick.AKMod]
cinj [Module.FreeRight]
cmul [Module.Right]

Right action of the ring.

cmul [Module.Left]

Left action of the ring.

cmul [Ring.Polynomial]
cmul [Series.Make]

Multiplication by a constant.

cmul [Algebra.T]
cmul [Module.FreeLeft]
cmul [Algebra.Presentation.Anick.AKMod]
cmul [Module.FreeRight]
coeff [Ring.Polynomial]
coeff [Series.Make]
coeff [Module.FreeLeft]

Coefficient of an element.

cols [Matrix.Make]
comp [Category.T]

Composition of morphisms.

comp [Category.Monoid]
comp [Category.Free]
compact [Ring.Polynomial]
compare [Monoid.T]

Comparison.

compare [Monoid.Presentation.Make]
compare [Alphabet.T]
compare [Alphabet.Pow]
compare [Alphabet.Prod3]
compare [Alphabet.Prod]
compare [Alphabet.Unit]
compare [Alphabet.Int]
compare [Alphabet.Char]
compare [Monoid.Free.Anick]
compare [Monoid.Free]
complete [Monoid.Presentation]

Knuth-Bendix completion wrt a total order.

complex [Algebra.Presentation.Anick]

Tor complex, whose homology is the one of the algebra (in right A-modules).

compose [Precategory.Make]

Composition of two cells on the boundary of maximal dimension.

concat [Automaton.Regexp]
create [Automaton.Make]
D
deglex [Monoid.Free.Order]
degree [Ring.Polynomial]

Degree of a polynomial.

dim [Precategory.Make.Presentation.Cell]

Dimension of a cell.

dim [Precategory.Make]

Dimension of a cell.

dim [Globular.T]

Dimension.

dim [Globular.Presentation.Make]
dim [Globular.Presentation]

Dimension of a generator.

dim [Globular.Terminal]
dim [Module.FreeLeft.Presentation]

Dimension of a presentation.

div [Ring.Euclidean]
div [Field.RationalFractions.Polynomial]

Euclidean division.

E
empty [Precategory.Make.Presentation]

Empty signature.

empty [Graph.Presentation]
empty [Globular.Presentation]

The empty globular set.

empty [Automaton.Regexp]
empty [Alphabet.Map]
empty [Alphabet.Pow]
empty [Monoid.Free.Anick]

The empty chain.

eq [Ring.T]
eq [Ring.Float]
eq [Ring.Int]
eq [Ring.Bool]
eq [Monoid.Abelian]
eq [Monoid.T]

Equality.

eq [Monoid.Presentation.Make]
eq [Field.Fractions]
eq [Ring.Polynomial]
eq [Series.Make]

Equality.

eq [Alphabet.T]
eq [Alphabet.Pow]
eq [Alphabet.Prod3]
eq [Alphabet.Prod]
eq [Alphabet.Unit]
eq [Alphabet.Int]
eq [Alphabet.Char]
eq [Module.FreeLeft]
eq [Monoid.Free.Anick]
eq [Monoid.Free]
eval [Monoid.Free.Anick]

Concatenation of the elements of the chain.

exchange [Matrix.Make.Row]

Exchange two rows.

expn [Series.Make]

Integer exponential.

extend [Monoid.Free.Anick]

Compute (n+1)-chains from n-chains.

exterior [Algebra.Generate]
F
find [Matrix.Make.Labeled.L]
free [Algebra.Presentation]
fresh [Globular.Theory.Cons]
fresh [Globular.Theory.Var]
G
gcd [Field.Fractions]

Greatest common divisor.

geq [Alphabet.Int]
geq [Alphabet.Char]
get [Series.Make]

Get a coefficient.

get [Matrix.Make.Labeled]
get [Matrix.Make]
graded [Algebra.Presentation.Augmentation]

Traditional augmentation for graded algebras.

H
hadamard [Series.Make]

Hadamard product.

hd [Monoid.Free.Anick]

Head of the chain.

heads [Algebra.Presentation]

Minimal reducible words.

homology [Module.FreeLeft.Presentation.Complex]

Compute the homology of the complex.

homology [Algebra.Presentation.Anick]
I
id [Category.T]

Identity morphism.

id [Category.Monoid]
id [Category.Free]
included [Module.FreeLeft]
included [Monoid.Free]
init [Ring.Polynomial]
init [Matrix.Make]
inj [Module.FreeLeft]
inj [Algebra.Presentation.Anick.AKMod]
inj [Monoid.Free]
intset [Monoid.Generate]
intset [Algebra.Generate]
inv [Group.T]
inv [Field.T]

Inverse.

inv [Field.Fractions]
inv [Field.Int]
inv [Field.Float]
inv [Field.Bool]
inv [Series.Make]

Inverse.

is_zero [Matrix.Make.Row]

A a row null?

iter [Alphabet.Map]
iter [Alphabet.Pow]
iter [Matrix.Make.Labeled.L]
iter [Matrix.Make.Labeled]

Iterate over source and target basis.

iter [Module.FreeLeft.Presentation]

Iterate a function on the generators of a module.

iter [Module.FreeLeft]
iter [Algebra.Presentation.Anick.AKMod]
iter_src [Matrix.Make.Labeled]

Iterate over source basis.

iter_tgt [Matrix.Make.Labeled]

Iterate over target basis.

K
kleene [Automaton.Make]
L
leading [Algebra.Free]
length [Ring.Polynomial]
length [Module.FreeLeft.Presentation.Complex]

Length of a chain complex.

length [Monoid.Free.Anick]

Dimension of the chain.

length [Monoid.Free]
leq [Alphabet.Int]
leq [Alphabet.Char]
letter [Automaton.Regexp]
lexicographic [Monoid.Free.Order]
M
madd [Matrix.Make.Row]

Add to a row q times another row.

make [Monoid.Presentation]
make [Series.Make]
make [Module.FreeLeft.Presentation.Complex]

Create a chain complex.

make [Module.FreeLeft.Presentation]

Create a presentation.

make [Algebra.Presentation.Augmentation]

Construct an augmentation by defining it on generators.

make [Algebra.Presentation]

Create a presentation from an alphabet and a list of monomials.

map [Matrix.Functor.Labeled]
map [Matrix.Functor]
map [Module.FreeLeft]

Map a linear function.

map [Algebra.Presentation.Anick.AKMod]

Map a K-linear function.

maps [Module.FreeLeft.Presentation.Complex]
matrix [Matrix.Make.Labeled]

Underlying (non-labeled) matrix.

mem [Precategory.Make.Presentation.Cell]

Ensure that a cell uses only generators defined in the signature.

mem [Precategory.Make.Presentation]

Does a generator belong the signature?

mem [Globular.Presentation]
mem [Alphabet.Pow]
modules [Module.FreeLeft.Presentation.Complex]
monoid [Algebra.Presentation.Augmentation]

Traditional augmentation for monoids / groups.

monomial [Ring.Polynomial]
mul [Ring.T]
mul [Ring.Op]
mul [Ring.Float]
mul [Ring.Int]
mul [Ring.Bool]
mul [Monoid.T]

Multiplication.

mul [Monoid.Presentation.Make]
mul [Field.Fractions]
mul [Ring.Polynomial]
mul [Series.Make]

Multiplication.

mul [Algebra.Presentation.Algebra]
mul [Monoid.Free]
mul [Algebra.Free]
mul_monomial [Algebra.Free]
mult [Matrix.Make.Row]

Multiply a row by a coefficent.

N
neg [Ring.T]
neg [Ring.Float]
neg [Ring.Int]
neg [Ring.Bool]
neg [Group.Abelian]
neg [Field.Fractions]
neg [Ring.Polynomial]
neg [Series.Make]

Negation.

neg [Module.FreeLeft]
nf [Monoid.Presentation.Make]
normalize [Monoid.Presentation]

Normalize a word.

normalize [Algebra.Presentation.Anick.AMod]

Normalize a polynomial.

normalize [Algebra.Presentation]

Normalize words.

nullity [Matrix.Make.Labeled]
nullity [Matrix.Make]

Dimension of the kernel.

nullity [Module.FreeLeft.Presentation.Map]

Nullity of a map.

O
of_array [Matrix.Make.Labeled.L]
of_list [Alphabet.Pow]
of_map [Module.FreeLeft.Presentation.Map]

Create from a map with given source and target.

one [Ring.T]
one [Ring.Float]
one [Ring.Int]
one [Ring.Bool]
one [Monoid.T]

Unit.

one [Monoid.Presentation.Make]
one [Field.Fractions]
one [Ring.Polynomial]
one [Series.Make]

One.

one [Monoid.Free]
one [Algebra.Free]
ordered_unifiers [Monoid.Free]

All unifiers with first on the left.

ordered_unifiers_bicontext [Monoid.Free]
orient [Monoid.Presentation]

Orient rules according to a partial order.

orient [Algebra.Presentation]

Orient a polynomial as a rule.

P
p [Monoid.Presentation.Make]
peq [Monoid.Free]

Partial equality (equality on subwords).

polynomial [Series.Make]

Canonical injection of polynomials.

presentation_to_string [Module.FreeLeft.Presentation]
R
rank [Matrix.Make.Labeled]
rank [Matrix.Make]

Dimension of the image.

rank [Module.FreeLeft.Presentation.Map]

Rank of a map.

rational [Series.Make]

Canonical injection of rational fractions.

reduce [Monoid.Presentation]

Reduce a presentation.

reduce [Algebra.Presentation]

Reduce a presentation.

replace [Matrix.Make.Row]

Replace a row by another one.

resolution [Algebra.Presentation.Anick]

Compute the Anick resolution.

row_echelon [Matrix.Make]

Put a matrix in row echelon form.

rows [Matrix.Make]
S
series [Automaton.Regexp]

Generating series of a regular expression.

set [Matrix.Make.Labeled]
set [Module.FreeLeft.Map]
simpl [Automaton.Regexp]
singleton [Monoid.Free.Anick]

The singleton chain.

singletons [Monoid.Free.Anick]

Singleton chains.

source [Precategory.Make.Presentation]

Source of a generator.

src [Graph.T]

Source.

src [Graph.Terminal]
src [Globular.T]

Source.

src [Globular.Presentation.Make]
src [Globular.Presentation]

Source of a cell.

src [Globular.Terminal]
src [Category.Monoid]
src [Category.Free]
star [Series.Make]
star [Automaton.Regexp]
states [Automaton.Make]
sub [Ring.Polynomial]
sub [Series.Make]

Subtraction.

sub [Module.FreeLeft]
sub [Monoid.Free]
symmetric [Algebra.Generate]

The symmetric algebra.

T
target [Precategory.Make.Presentation]

Target of a generator.

tgt [Graph.T]

Target.

tgt [Graph.Terminal]
tgt [Globular.T]

Target.

tgt [Globular.Presentation.Make]
tgt [Globular.Presentation]

Target of a cell.

tgt [Globular.Terminal]
tgt [Category.Monoid]
tgt [Category.Free]
tl [Monoid.Free.Anick]

Tail of the chain.

to_map [Module.FreeLeft.Presentation.Map]

Convert to a map.

to_string [Ring.T]
to_string [Ring.Float]
to_string [Ring.Int]
to_string [Ring.Bool]
to_string [Precategory.Make]

String representation of a cell.

to_string [Monoid.Abelian]
to_string [Monoid.T]

String representation.

to_string [Monoid.Presentation.Make]
to_string [Globular.T]
to_string [Globular.Theory.Cons]
to_string [Globular.Theory.Var]
to_string [Globular.Presentation.Make]
to_string [Globular.Terminal]
to_string [Field.Fractions]
to_string [Ring.Polynomial]
to_string [Series.Make]
to_string [Automaton.Regexp]
to_string [Alphabet.T]
to_string [Alphabet.Pow]
to_string [Alphabet.Prod3]
to_string [Alphabet.Prod]
to_string [Alphabet.Unit]
to_string [Alphabet.Int]
to_string [Alphabet.Char]
to_string [Module.FreeLeft.Presentation.Complex]

String representation.

to_string [Matrix.Make]
to_string [Module.FreeLeft.Presentation.Map]
to_string [Module.FreeLeft.Presentation]

String representation.

to_string [Module.FreeLeft.Map]
to_string [Module.FreeLeft]
to_string [Module.FreeRight]
to_string [Monoid.Free.Anick]

String representation.

to_string [Monoid.Free]
to_string [Algebra.Presentation]
trans [Automaton.Make]
U
unifier [Monoid.Free]

The leftmost unifier where u is on the left and v on the right

unifiers_bicontext [Monoid.Free]

All unifiers, with contexts on the left and on the right.

union [Automaton.Regexp]
unions [Automaton.Regexp]
V
valid [Module.FreeLeft.Presentation.Complex]

Ensure that a chain complex satsifies d^2=0.

var [Series.Make]
W
weq [Monoid.Free.Anick]
Z
zero [Ring.T]
zero [Ring.Float]
zero [Ring.Int]
zero [Ring.Bool]
zero [Monoid.Abelian]
zero [Field.Fractions]
zero [Ring.Polynomial]
zero [Series.Make]

Zero.

zero [Matrix.Make.Labeled]
zero [Matrix.Make]
zero [Module.FreeLeft.Presentation.Map]

The zero morphism.

zero [Module.FreeLeft.Map]
zero [Module.FreeLeft]