# Index of values

 '1_PI [Math] The float constant 1/pi. '2_PI [Math] The float constant 2/pi. '2_SQRT_PI [Math] The float constant 2/sqrt(pi). 'B [Functional] The `B` combinator: `B(f, a) == \x.f(a(x))`. 'B_K [Functional] The `B_K` combinator: `B_K == B(K)`. 'C [Functional] The `C` combinator: `C(f, a) == \x.(f(x))(a)`. 'E [Math] The float constant e. 'I [Functional] The `I` combinator: `I == \x.x`. 'IF [Functional] The `IF` combinator: `IF(c, t, f) == \x.if c(x) then t(x) else f(x) fi`. 'K [Functional] The `K` combinator: `K(a) == \x.a`. 'LN10 [Math] The float constant loge(10) (the logarithm is taken in base e). 'LN2 [Math] The float constant loge(2) (the logarithm is taken in base e). 'LOG10E [Math] The float constant log10(e) (the logarithm is taken in base 10). 'LOG2E [Math] The float constant log2(e) (the logarithm is taken in base 2). 'PI [Math] The float constant pi. 'PI_2 [Math] The float constant pi/2. 'PI_4 [Math] The float constant pi/4. 'S [Functional] The `S` combinator: `S(f, a) == \x.(f(x))(a(x))`. 'S4 [Functional] The `S4` combinator: `S4(f, a, b) == \x.f(a(x), b(x))`. 'S4_S [Functional] The `S4_S` combinator: `S4_S == S4(S)`. 'SQRT1_2 [Math] The float constant 1/sqrt(2). 'SQRT2 [Math] The float constant sqrt(2). '!! [System] Assertion. '!= [Math] The not-equal predicate. '!=== [Math] The negation of the `===` operator: `x !=== y` is the same as ```not(x === y)```. '* [Math] Computes the multiplication of its arguments. '** [Math] Computes the exponentiation of its first argument to the second argument. '+ [Math] Numerical sum, record merging and string concatenation. '- [Math] Computes the substraction of its arguments. '/ [Math] Computes the division of the first argument by the second. ':: [Monoidal] Add an element to a monoidal collection. '< [Math] Less than predicate. '<< [System] outputs the text representation of the value `v` in the file specified by `"file"`. '<<< [System] Force the opening of a file. '<= [Math] Less or equal predicate. '== [Math] The equality predicate. '=== [Math] The physical equality predicate. '> [Math] Greather than predicate. '>= [Math] Greather or equal predicate. '? [System] print the ascii representation of the value `v` to the standard output and then return `v`. 'abort [System] Abort the evaluation. 'abs [Math] Return the absolute value of the argument. 'acell [Scalar] Returns `true` if the argument is a acell and `false` for any other value. 'acellof [Math] Conversion into an acell. 'achain [Collections] Achain type and predicate. 'achainify [Collections] Transform its argument into a achain. 'acos [Math] The `acos` trigonometric function. 'add [Math] Prefix form of operator `+` 'add_edge [Qmf] Adds a new edge. 'add_face [Qmf] Adds a new face. 'add_ncell [Qmf] Adds a new ncell. 'add_polygon [Qmf] Adds a new polygon. 'add_polyline [Qmf] Adds a new polyline. 'add_sphere [Qmf] Adds a new sphere. 'add_square [Qmf] Adds a new square. 'add_vertex [Qmf] Adds a new vertex. 'add_volume [Qmf] Adds a new volume. 'append [Monoidal] Concatenates two monoidal collections. 'area [Delaunay] returns a sequence of values specifying the area of each voronoi cell centered on a Delaunau vertex. 'asin [Math] The `asin` trigonometric function. 'atan [Math] The `atan` trigonometric function. 'atan2 [Math] The `atan2` function calculates the arc tangent of the two arguments `x` and `y`. 'bag [Collections] Bag (multiset) type and predicate. 'beep [System] Make a sound and print a beep on standard output. 'beep_cpt [System] Beep count. 'beep_cpt_reset [System] Reset the counter of calls to the function `beep` to zero. 'bint_of [Math] Conversion into a big integer. 'bintof [Math] Conversion into a big integer. 'boundary [Achain] returns the boundary of an acell as a chain of integers. 'cartesian_prod [Achain] Return the cartesian product of the two achain arguments. 'ccells [Achain] Return the sequence of ccells of a cell or the values in a chain. 'ccellspos [Achain] Return the sequence of ccells of a cell in a chain. 'ceil [Math] Round the given float to an integer value. 'close [System] Close a file. 'coboundary [Achain] returns the coboundary of an acell as a chain of integers. 'cofaces [Achain] Return the sequence of cofaces of a cell or the values in a chain. 'cofaces_in_achain [Achain] Return the sequence of cofaces of a acell belonging to a given achain. 'cofacespos [Achain] Return the sequence of cofaces of a cell in a chain. 'collection [Collections] Collection type and predicate. 'collection_name [Collections] On n'ajoute pas ce predicat � la main : ** il sera ajoute automatiquement via la table des descripteurs de types * 'common_cofaces [Achain] Return the sequence of the cofaces shared by two cells. 'common_cofaces_in_achain [Achain] Return the sequence of the cofaces shared by two acells in a given achain. 'common_cofacespos [Achain] Return the sequence of the cofaces shared by two cells in a chain. 'common_faces [Achain] Return the sequence of the faces shared by two cells. 'common_facespos [Achain] Return the sequence of the faces shared by two cells in a chain. 'common_transitive_cofaces [Achain] Return the sequence of the transitive cofaces shared by two cells. 'common_transitive_cofaces_in_achain [Achain] Return the sequence of the transitive cofaces shared by two acells in a given achain. 'common_transitive_cofacespos [Achain] Return the sequence of the transitive cofaces shared by two cells in a chain. 'common_transitive_faces [Achain] Return the sequence of the transitive faces shared by two cells. 'common_transitive_facespos [Achain] Return the sequence of the transitive faces shared by two cells in a chain. 'compare [Math] The generic comparison. 'cons [Monoidal] Add an element to a monoidal collection. 'copy_gmap [Qmf] Returns a copy of a gmap. 'cos [Math] The `cos` trigonometric function. 'cosh [Math] The `cosh` hyperbolic function. 'count [Collections] Counts the number of occurences of an element in a collection. 'create_edge [Qmf] Links 2 vertices by a new edge when it's possible. 'create_face [Qmf] Creates a new face from given indepdendant edges. 'create_volume [Qmf] ??? 'delaunayfy [Collections] Build a delaunay. 'delete_ncell [Qmf] Deletes a ncell. 'diff [Monoidal] Set or bag difference. 'dimension [Achain] Return the dimension of a acell or a achain. 'div [Math] Prefix form of operator `/` 'dot [Record] Computed record access. 'empty [Collections] Returns `true` if the argument is an empty collection and `false` if the argument is a non-empty collection. 'empty_from_coll [Collections] Return an empty collection of the same type has its argument. 'epsilon_float [Math] The smallest positive float `x` such that `1.0 +. x <> 1.0`. 'equal [Math] Prefix form of operator `==` 'exists [Collections] Existential predicate. 'existsD [Achain] Existential predicate. 'exit [System] Exit the evaluation. 'exp [Math] Exponential. 'extension [Collections] Build a collection of a specified type from the listing of its elements and positions. 'faces [Achain] Return the sequence of faces of a cell or the values in a chain. 'facespos [Achain] Return the sequence of faces of a cell in a chain. 'filter [Monoidal] returns all the elements of the monoidal collection `c` that satisfy the predicate `p`. 'filtration [Achain] Computes the filtration of an abstract chain. 'fixpoint [Functional] The `'fixpoint` keyword specifies fixed-point iteration in function application. 'fixrule [Functional] is equivalent to `'fixpoint`. 'flatten [Monoidal] flattens a sequence of sequences, or a set of sets, or a bag of bags. 'float_of [Math] Conversion into a float. 'floatof [Math] Conversion into a float. 'floor [Math] Round the given float to an integer value. 'fold [Collections] Fold a function over the elements of a collection. 'foldD [Achain] Fold a function over the elements of a particular dimension of a collection. 'foldD_indexed [Achain] Fold a function over the elements of a particular dimension of a collection with their position. 'fold_indexed [Collections] Fold a function over the elements of a collection with their position. 'fold_io [System] fold_io(f, zero, str) applys the binary function f to the lines of the file str and replaces EOF by the zero argument. 'following [GBF] Build a GBF from a sequence of values and a sequence of directions. 'forall [Collections] Universal predicate. 'forallD [Achain] Universal predicate. 'gbf [Collections] Set type and predicate. 'gensym [Scalar] `gensym(s)` generates a symbol from the string or the symbol `s`. 'geq [Math] Prefix form of operator `>=`. 'get_coord_from_vertex [Qmf] Returns the embedding of a vertex in libgmapkernel. 'get_gmap_from [Qmf] Returns the gmap of a ncell or a qmf. 'glue2FacesBy4Verteces [Qmf] ??? 'gmap [Scalar] Returns `true` if the argument is a gamap and `false` for any other value. 'graphify [Collections] Transform a delaunay-type graph into a graph. 'gt [Math] Prefix form of operator `>`. 'hd [Collections] Pick one element in a collection. 'icells [Achain] Return the sequence of icells of a cell or the values in a chain. 'icellspos [Achain] Return the sequence of icells of a cell in a chain. 'infinity [Math] ieee positive infinite value. 'insert_edge [Qmf] Splits a face into two faces separated by a new edge. 'insert_face [Qmf] Splits a volume into two volumes separated by a new face. 'insert_vertex [Qmf] Splits an edge into two edges separated by a new vertex. 'int_of [Math] Conversion into an integer. 'inter [Monoidal] Set or bag intersection. 'interlude [Functional] Optionnal wrapper function for iterated application. 'intof [Math] Conversion into an integer. 'iota [Monoidal] Enumerate the `n` first integers. 'isomorphism [Collections] Test the isomorphism of two graphs. 'iter [Functional] The `'iter` keyword specifies bounded iteration in function application. 'iter [Collections] Iter a function over the elements of a collection. 'iterD [Achain] Iter a function over the elements of a particular dimension of a collection. 'iterD_indexed [Achain] Iter a function over the elements of a particular dimension of a collection with their position. 'iter_indexed [Collections] Iter a function over the elements of a collection with their position. 'join [Monoidal] Join two values. 'last [Collections] Return the last element in a sequence. 'left [Monoidal] Returns the value at the left of an element in a sequence. 'leibniz [Collections] Leibniz type and predicate. 'leq [Math] Prefix form of operator `<=`. 'listvar [System] Return a sequence of strings. 'load_moka [Qmf] Loads in a gmap an ASCII Moka file 'log [Math] The natural logarithm. 'log10 [Math] The base-10 logarithm. 'lt [Math] Prefix form of operator `<`. 'map [Collections] Map a function over the elements of a collection. 'map_indexed [Collections] Map a function over the elements of a collection with their position. 'matrix_check [Monoidal] checks if `s` is a matrix of dimension 2. 'matrix_dim [Monoidal] returns the maximal nesting of sequences in `s`. 'matrix_matrix_product [Monoidal] computes the product of two matrices. 'matrix_vector_product [Monoidal] computes the product of matrix `m` with vector `v`. 'matrixify [Monoidal] returns a proper matrix build on `s`. 'max [Math] `max(a,b)` returns `a` if `compare(a, b) > 0`. 'max_float [Math] The largest positive finite value of type `float`. 'max_int [Math] The greatest representable integer. 'member [Collections] Membership predicate. 'min [Math] `min(a,b)` returns `a` if `compare(a, b) < 0`. 'min_float [Math] The smallest positive, non-zero, non-denormalized value of type `float`. 'min_int [Math] The smallest representable integer. 'mod [Math] Integer and float remainder. 'monoidal [Collections] Monoidal type and predicate. 'mult [Math] Prefix form of operator `*` 'nAp [Math] Number of different permutations. 'nCp [Math] Binomial coefficient and number of different combinations. 'nan [Math] ieee not a number value. 'ncell [Scalar] Returns `true` if the argument is a ncell and `false` for any other value. 'neg_infinity [Math] ieee negative infinite value 'neighbor [Collections] Specific neighbors in a GBF or a chain. 'neighbors [Collections] The neighbors of an element in a collection. 'neighborspos [Collections] The neighbors position of an element in a collection. 'new_acell [Achain] Creates a new acell of a given dimension. 'new_edge [Achain] Creates a new acell of dimension 1. 'new_face [Achain] Creates a new acell of dimension 2. 'new_gmap [Qmf] Creates a new empty gmap. 'new_vertex [Achain] Creates a new acell of dimension 0. 'newton [Collections] Newton type and predicate. 'norm [Qmf] No comment 'normal_form [Qmf] No comment 'normalise [Achain] Build a new achain where the acell that have the same faces are quotiented. 'not [Scalar] any_bool 'notequal [Math] Prefix form of operator `!=`. 'notpequal [Math] Prefix form of operator `!===`. 'open [System] open(str, io) opens file str for input (io = 0) or output (io = 1) and returns the file descriptor associated to it. 'outerproduct [Monoidal] computes the outer product of matrix or vector `s1` and `s2`. 'pad_left [Monoidal] makes a sequence of length `n` by truncating or padding `s` with `v0` on the left. 'pad_right [Monoidal] makes a sequence of length `n` by truncating or padding `s` with `v0` on the right. 'parse [System] Parse and evaluate a string. 'partition [Monoidal] `partition(n, s)`, with `n` an integer, partitions a monoid `s` (i.e. 'partition_eq [Monoidal] partitions a sequence `s` into subsequences of elements of the same equivalence class. 'pequal [Math] Prefix form of operator `===`. 'posgbf [Scalar] Returns `true` if the argument is a posgbf and `false` for any other value. 'pospredicate_from_coll [Collections] Return the type predicate of the positions of a collection. 'postlude [Functional] Optionnal wrapper function for iterated application. 'pow [Math] Computes the exponentiation of its first argument to the second argument. 'power [Math] Exponentiation. 'predicate_from_coll [Collections] Return the type predicate of the type of its argument. 'prelude [Functional] Optionnal wrapper function for iterated application. 'print_coll [System] Print a collection with prefix, infix and suffix strings. 'print_coll2 [System] Print a nested collection with prefix, infix and suffix strings. 'qmf [Collections] Qmf type and predicate. 'qrngdimension [Math] returns the dimension of the space that is filled by the quasi-random generator. 'qrngget [Math] returns a sequence of quasi-random floating values using always the same storage array. 'qrnginit [Math] initializes the generator of quasi-random values. 'qrngmake [Math] returns a handle (of type `int`) for producing quasi-random values. 'qrngname [Math] returns the name of the generator used. 'qrngsample [Math] returns a sequence of quasi-random floating values using each time a new storage array. 'quotient [Achain] Build a new achain where the acell have been quotiented. 'random [Math] returns a random value. 'rank [Monoidal] returns the rank of the argument. 'read_line [System] read_line(str) returns a line from the file str. 'record [Collections] Record type and predicate. 'remove_field [Record] Remove the field of a record. 'remove_ncell [Qmf] Remove a ncell. 'reset_default_error_handler [System] This function with no argument changes the current error handler for the default one. 'reverse [Monoidal] Sequence reversal. 'right [Monoidal] Returns the value at the right of an element in a sequence. 'rotate_left [Monoidal] cycles the elements in the sequence argument one position to the left. 'rotate_right [Monoidal] cycles the elements in the sequence argument one position to the right. 'save_moka [Qmf] Saves a gmap in an ASCII Moka file 'scalarproduct [Monoidal] computes the scalar product of two vectors `s1` and `s2`. 'seq [Collections] Seq type and predicate. 'sequify [Collections] Transform its argument into a sequence. 'set [Collections] Set type and predicate. 'set_color [Collections] Return its first argument with its color changed for the second one or raise an error if it is not possible. 'set_coord_of_vertex [Qmf] Modifys the embedding of a vertex in libgmapkernel. 'set_error_handler [System] Change the current error handler. 'set_field [Record] Set the field of a record. 'shape [Collections] Rebuild a collection from a sequence. 'sin [Math] The `sin` trigonometric function. 'sinh [Math] The `sinh` hyperbolic function. 'size [Collections] Returns the number of elements in a collection (i.e. 'sleep [System] Halts the computation for a given number of seconds 'smith [GBF] Returns the sequence of integer coefficients of the smith normal form of the GBF type of the argument. 'smith_backpos [GBF] Inverse of the `'smith` function. 'sort [Collections] Sort a collection in increasing order according to a comparison function. 'sqrt [Math] The non-negative square root. 'strategy [Functional] The `'strategy` keyword allows to choose a rule application strategy different to the default MGS maximal parallel strategy. 'string2undef [Scalar] Returns an undef value with its string argument as a comment 'string_contains [Scalar] tests if the first character of `c` appears in the string `s`. 'string_contains_from [Scalar] tests if the first character of `c` appears in the substring of `s` starting from `start` to the end of `s`. 'string_get [Scalar] returns character number `n` in string `s`. 'string_index [Scalar] returns the position of the leftmost occurrence in string `s` of the first character of string `c`. 'string_index_from [Scalar] Same as `string_index`, but start searching at the character position given as second argument. 'string_length [Scalar] Returns the length of it's string argument 'string_make [Scalar] returns a fresh string of length `n`, filled with the first character of string `c`. 'string_rcontains_from [Scalar] tests if the first character of `c` appears in the substring of `s` starting from the beginning of `s` to index `stop`. 'string_rindex [Scalar] returns the position of the rightmost occurrence in string `s` of the first character of string `c`. 'string_rindex_from [Scalar] Same as `string_rindex`, but start searching at the character position given as second argument. 'string_sub [Scalar] returns a fresh string of length `len`, containing the characters number `start` to `start + len - 1` of string `s`. 'sub [Math] Prefix form of operator `-` 'subset [Monoidal] returns true if `A` is included in `B` 'succ [Math] The (numeric) successor function. 'system [System] Execute a shell command. 'take [Collections] `take(c, p)` returns the element at position `p` in `c`. 'tan [Math] The `tan` trigonometric function. 'tanh [Math] The `tanh` hyperbolic function. 'tl [Collections] Return the collection minus one element. 'top_level [System] Change the top-level for a user function. 'trace [System] Trace the function calls. 'transitive_cofaces [Achain] Return the sequence of cofaces of a cell and the cofaces of the cofaces, recursively. 'transitive_cofaces_in_achain [Achain] Return the sequence of recursive cofaces of a acell belonging to a given achain. 'transitive_cofacespos [Achain] Return the sequence of cofaces of a cell and the cofaces of the cofaces in a chain, recursively. 'transitive_faces [Achain] Return the sequence of faces of a cell and the faces of the faces, recursively. 'transitive_facespos [Achain] Return the sequence of faces of a cell and the faces of the faces in a chain, recursively. 'transpose [Monoidal] returns the transposition of the 2-dimensionnal matrix `m`. 'undef2string [Scalar] Returns the comment of an undef value as a string 'unit_bint [Math] The big integer 1. 'untrace [System] Untrace the function calls. 'uprint_coll [System] Has the same behavior as print_coll, without any automatical indentation. 'val2bool [Scalar] Convert a value to a boolean. 'voronoi [Delaunay] returns a sequence of voronoi vertices together with the Delaunay's vertices it is adjacent to. 'what_float [Math] Classify IEEE-754 float numbers. 'while [System] The `while` operator. 'zero_bint [Math] The big integer 0. || [Scalar] returns the logical disjunction of the two arguments. and_and [Scalar] returns the logical conjunction of the two arguments.  