Semigroupe Version
*** Jean-Eric Pin,
September 1999 ***
Give the type of computation : 

/* Menu principal */
Give your choice : 
Semigroup
Monoid
Ordered syntactic semigroup
Ordered syntactic monoid
Standard example
Read a file
Modify preferences

/* Menu Semigroupe */
Number of letters of the alphabet ?
Give the type of semigroup : 
Transitions
Partial transitions
Boolean matrices
Max-Plus matrices
Min-Plus matrices
Tropical Max-Plus matrices
Tropical Min-Plus matrices
Projective Max-Plus matrices
Matrices with integer coefficients
Finite presentation
Would you like to specify the initial and final states (y/n) ?
Would you like to specify the final states (y/n) ?
The size of the
should be at most
Would you like to compute the reverse semigroup (y/n) ?
Would-you like to save these generators (y/n) ?
semigroup
monoid

/* Menu Exemples */
Symetric group Sn
Transformation monoid Tn
Monoid of partial functions Fn
Monoid of injective partial functions In
Monoid RBn generated by the regular relations on {1, ..., n}
Monoid of order preserving functions on {1, ..., n}
Monoid POPIn
Group Z/nZ
Brandt semigroup BAn
Brandt monoid BAn
Monoid of triangular Boolean matrices of size n x n
Monoid of unitriangular Boolean matrices of size n x n
Syntactic monoid of (a(a(a...a(ab)*)b)* ... b)*)b)*)b)*  (n times)
Monoid generated by the matrices [1 0 / 1 1] and [1 1 / 0 1]
A semigroup in LJ but not in B1
An example of transitions semigroup
An example of monoid of Boolean matrices
An example of semigroup of matrices with integer entries
An example of semigroup of matrices with Max-Plus entries

/* Utilitaires */
Give the value of n
at most
The size of
this semigroup
This semigroup
this monoid
This monoid
is

/* Menu varietes */
On which variety would you like to make the test ?
DA (Regular D-classes are idempotent)
LI (locally trivial)
LG (locally group)
B1 (dot-depth one)
B1+ (dot-depth 1/2)
Ecom (commuting idempotents)
BG (block-groups)

/* Options */
Options : 
List of elements
List of relations
List of idempotents
Syntactic quasi-order
Minimal ideal
Green's relations
Computation of the inverses 
Computation of a local submonoid
Computation of an element
Computation of the kernel
Variety tests
Do another computation 
Quit Semigroupe

Give the idempotent
Give the word
This element is not idempotent !
Generators : 
Relations : 
Here are the R-classes :
Here are the L-classes :
Here are the D-classes :

/* Sortie varietes, reponses positives */
is commutative
is idempotent
is in J1
is nilpotent
is aperiodic
is a group
is J-trivial
is R-trivial
is L-trivial
is in DA
is in LI
is in LG
is in B1
is in B1+
is in Ecom
is in BG

/* Sortie varietes, reponses negatives */
is not commutative, because
is not idempotent,
is not dans J1,
is not nilpotent
is not aperiodic,
is not a group
is not R-trivial, nor L-trivial
is not R-trivial
is not L-trivial
is not in DA,
is not in LI,
is not in LG,
is not in B1,
is not in B1+,
is not in Ecom,
is not in BG,

/* Sortie varietes, justificatifs */
is different from
because the identity uu = u is not satisfied when
because the identity u^u = u^ is not satisfied when
because the identity (xy)^(yx)^(xy)^ = (xy)^ is not satisfied when
because the identity ese = e is not satisfied when
because the identity (ese)^ = e is not satisfied when
because the identity (epfqe)^pfs(erfse)^ = (epfqe)^(erfse)^ is not satisfied when
because the identity ese <= e is not satisfied when
because the identity ef = fe is not satisfied when
because the identity (ef)^ = (fe)^ is not satisfied when

/* Calculs en cours */
Computing the idempotents...
Computation of idempotents terminated.
No zero
Number of elements :
Number of idempotents :
Number of relations :
Computation terminated. Maximal length of words :
Computation of the R-classes
Computation of the R-classes terminated :
R-class
R-classes
Computation of the L-classes
Computation of the L-classes terminated :
L-class
L-classes
Computation of the D-classes
Computation of the D-classes terminated :
D-class
D-classes
List of inverses :
List of weak inverses (non inverses) :
Fin

/* Differents types de semigroupes */
The semiring is Z_{
Threshold of the semiring ?
Period of the semiring ?
Semiring Z_{st} where s is the threshold and t is the period 
Semiring {-infinity, 0, 1, ..., s} where s is the threshold
Semiring {0, 1, ..., s, +infinity} where s is the threshold
Type % for "- infinity"
Type % for "+ infinity"
Number of letters
Number of states of the automaton ?
Size of the matrices
Size of the matrices ?
Size of the Boolean matrices ?

/* Problemes de memoire */
Problem during memory allocation of
a matrix
of the products
of the generators
of the transition table
of a pile
of the hash table
of the table of elements
of a word
of the transitions
of a graph
of a list
of the initial states
of the final states
of the messages

/* Fichiers */
Give the name of the file :
Problem during creation of
Problem during closure of a file !
Problem during opening of
Give an upper bound on the size of the semigroup
Give the path to the examples folder
(for instance  :My Folder:Examples:) --> 
(for instance   $HOME/Examples/) :  

/* Preordre syntactique */
Give the initial states and end with }
Give the final states and end with }
Give the element numbers of P and end with }

/* Derniere ligne */