Extend coverage of documentation to lib/structure.g[di]
This commit is contained in:
Glen Whitney
parent
82c69a16a9
commit
e9e38ec41c
@ -35,7 +35,8 @@ Perhaps the following ⪆ interactive session, which constructs the
|
||||
conjugation quandle of the symmetric group on three elements and then performs
|
||||
a few simple computations on that quandle, will give the flavor of &RAQ;. (It is
|
||||
presumed that the &RAQ; package has already been loaded with
|
||||
`LoadPackage("RAQ");` prior to these example commands being executed.)
|
||||
`LoadPackage("RAQ");` prior to these example commands being executed, and that
|
||||
remains true throughout the package documentation.)
|
||||
<!--@BeginExampleSession ``` -->
|
||||
```
|
||||
gap> S3 := SymmetricGroup(3);
|
||||
|
||||
@ -1,11 +1,29 @@
|
||||
@Chapter construct
|
||||
@ChapterTitle Constructing One-Sided Quasigroups, Racks, and Quandles.
|
||||
@Section from_scratch
|
||||
@SectionTitle Direct constructors
|
||||
All of the functions in this section produce magmas (of one of the
|
||||
categories with which &RAQ; is concerned) from data of other (non-domain)
|
||||
types.
|
||||
|
||||
@Chapter operate
|
||||
@ChapterTitle Operations on One-Sided Quasigroups, Racks, and Quandles.
|
||||
|
||||
@Chapter basic
|
||||
@ChapterTitle Basic Notions
|
||||
In order to build up and define one-sided quasigroups, racks, and
|
||||
quandles, &RAQ; must define several lower-level objects and properties,
|
||||
which are documented in this section. Although logically they come before
|
||||
the domain constructors and operations, they are presented afterwards
|
||||
because it's rare that one needs to use them directly when working with
|
||||
&RAQ;.
|
||||
@Section elements
|
||||
@SectionTitle Categories of elements
|
||||
@Section collections
|
||||
@SectionTitle Categories of collections
|
||||
|
||||
@Chapter technical
|
||||
This chapter covers computational/operational aspects of &RAQ;
|
||||
rather than mathematical ones.
|
||||
|
||||
@ChapterTitle Technical Details
|
||||
|
||||
@ -6,4 +6,8 @@ AutoDoc(rec(
|
||||
autodoc := rec(files := ["README.md", "doc/chapters.autodoc"]),
|
||||
maketest := rec(name := "tst/AutoDoc_tests.g")
|
||||
));
|
||||
QUIT;
|
||||
|
||||
if not IsBound(RAQ_makedoc_no_quit) or
|
||||
not RAQ_makedoc_no_quit then
|
||||
QUIT_GAP();
|
||||
fi;
|
||||
|
||||
181
lib/bytable.gd
181
lib/bytable.gd
@ -1,43 +1,192 @@
|
||||
## bytable.gd RAQ Quasigroups, racks, and quandles by multiplication tables.
|
||||
|
||||
## Self-distributivity
|
||||
# Predicates on tables:
|
||||
#! @Chapter basic
|
||||
#! @Section table_predicates
|
||||
#! @SectionTitle Predicates on multiplication tables
|
||||
#! @Arguments matrix
|
||||
#! @Description This property is true if <A>matrix</A> is the multiplication
|
||||
#! table of a magma which satisfies the left self-distributive property (see
|
||||
#! <Ref Filt="IsLSelfDistElement" Label="for IsMultiplicativeElement"/>))
|
||||
#! for all triples of elements.
|
||||
DeclareProperty( "IsLeftSelfDistributiveTable", IsMatrix );
|
||||
#! @Arguments matrix
|
||||
#! @Description This property is true if <A>matrix</A> is the multiplication
|
||||
#! table of a magma which satisfies the rightt self-distributive property (see
|
||||
#! <Ref Filt="IsLSelfDistElement" Label="for IsMultiplicativeElement"/>))
|
||||
#! for all triples of elements.
|
||||
DeclareProperty( "IsRightSelfDistributiveTable", IsMatrix );
|
||||
#! @Arguments matrix
|
||||
#! @Description This property is true if for all $i$ less than or equal to the
|
||||
#! number of rows of <A>matrix</A>, the $(i,i)$ entry of <A>matrix</A> is
|
||||
#! $i$.
|
||||
DeclareProperty( "IsElementwiseIdempotentTable", IsMatrix );
|
||||
|
||||
## Attributes (typically used on the families of elements created from a
|
||||
## multiplication table) to store sections and division tables
|
||||
#! @Chapter operate
|
||||
#! @Section table
|
||||
#! @Section Information related to the multiplication table.
|
||||
#! Note that typically the functions in this section will fail unless the
|
||||
#! argument was either created with a multiplication table, or at least has
|
||||
#! had its multiplication table explicitly computed.
|
||||
#! @Arguments obj
|
||||
#! @Returns a list of permutations of length equal to `Size(obj)`, or fail
|
||||
#! @Description The $i$th element of the list returned is the permutation
|
||||
#! determined by the $i$th row of the multiplication table of
|
||||
#! <A>obj</A> (in the sense of the core &GAP;
|
||||
#! function `PermList`). Returns fail if any row of the multiplication table
|
||||
#! does not determine a permuation.
|
||||
DeclareAttribute("LeftPerms", HasMultiplicationTable);
|
||||
DeclareAttribute("RightPerms", HasMultiplicationTable);
|
||||
DeclareAttribute("LeftDivisionTable", HasMultiplicationTable);
|
||||
DeclareAttribute("RightDivisionTable", HasMultiplicationTable);
|
||||
#! @BeginExampleSession
|
||||
#! gap> D3 := LeftQuandleByMultiplicationTable([[1,3,2],[3,2,1],[2,1,3]]);
|
||||
#! <left quandle with 3 generators>
|
||||
#! gap> LeftPerms(D3);
|
||||
#! [ (2,3), (1,3), (1,2) ]
|
||||
#! @EndExampleSession
|
||||
|
||||
## Create Quasigroups and racks from multiplication tables
|
||||
#! @Arguments obj
|
||||
#! @Returns a list of permutations of length equal to `Size(obj)`, or fail
|
||||
#! @Description The $i$th element of the list returned is the permutation
|
||||
#! determined by the $i$th column of the multiplication table of
|
||||
#! <A>obj</A> (in the sense of the core &GAP;
|
||||
#! function `PermList`). Returns fail if any column of the multiplication table
|
||||
#! does not determine a permuation.
|
||||
DeclareAttribute("RightPerms", HasMultiplicationTable);
|
||||
#! @Arguments obj
|
||||
#! @Returns an operation table matrix, or fail
|
||||
#! @Description Presuming it is well-defined, this produces the operation
|
||||
#! table (following similar conventions for multiplication tables, e.g.,
|
||||
#! every entry is a natural number less than `Size(obj)`) for `LeftQuotient`
|
||||
#! on the given <A>obj</A>. Returns fail if `LeftQuotient` is not
|
||||
#! well-defined for <A>obj</A>.
|
||||
DeclareAttribute("LeftDivisionTable", HasMultiplicationTable);
|
||||
#! @Arguments obj
|
||||
#! @Returns an operation table matrix, or fail
|
||||
#! @Description Presuming it is well-defined, this produces the operation
|
||||
#! table for `\/` (the typical elementwise (right) quotient) on the given
|
||||
#! <A>obj</A>. Returns fail if `\/` is not
|
||||
#! well-defined for <A>obj</A>.
|
||||
DeclareAttribute("RightDivisionTable", HasMultiplicationTable);
|
||||
#! @BeginExampleSession
|
||||
#! gap> A4 := RightQuandleByMultiplicationTable([[1,4,2,3],
|
||||
#! > [3,2,4,1],
|
||||
#! > [4,1,3,2],
|
||||
#! > [2,3,1,4]]);
|
||||
#! <right quandle with 4 generators>
|
||||
#! gap> RightDivisionTable(A4);
|
||||
#! [ [ 1, 3, 4, 2 ], [ 4, 2, 1, 3 ], [ 2, 4, 3, 1 ], [ 3, 1, 2, 4 ] ]
|
||||
#! @EndExampleSession
|
||||
#! @Chapter construct
|
||||
#! @Section from_scratch
|
||||
#! @BeginGroup table_constructors
|
||||
#! @GroupTitle Constructors from tables
|
||||
#! @Returns a magma of the designated category
|
||||
#! @Description These functions produce magmas from their multiplication
|
||||
#! tables, exactly analogously with the core &GAP; function
|
||||
#! `MagmaByMultiplicationTable` (q.v.); all of the same conventions are
|
||||
#! followed, such as the table should be an $n\times n$ matrix in which
|
||||
#! every entry is a natural number less than or equal to $n$. These
|
||||
#! functions verify that the tables supplied in fact define an example of
|
||||
#! the designated category.
|
||||
#! @GroupInitialArguments table
|
||||
DeclareGlobalFunction("LeftQuasigroupByMultiplicationTable");
|
||||
DeclareGlobalFunction("LeftQuasigroupByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("LeftRackByMultiplicationTable");
|
||||
DeclareGlobalFunction("LeftRackByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("LeftQuandleByMultiplicationTable");
|
||||
DeclareGlobalFunction("LeftQuandleByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("RightQuasigroupByMultiplicationTable");
|
||||
DeclareGlobalFunction("RightQuasigroupByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("RightRackByMultiplicationTable");
|
||||
DeclareGlobalFunction("RightRackByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("RightQuandleByMultiplicationTable");
|
||||
#! @EndGroup
|
||||
|
||||
#! @BeginExampleSession
|
||||
#! gap> D3 := LeftQuandleByMultiplicationTable([[1,3,2],[3,2,1],[2,1,3]]);
|
||||
#! <left quandle with 3 generators>
|
||||
#! gap> SpecifyElmNamePrefix(D3, "d");
|
||||
#! gap> Elements(D3);
|
||||
#! [ d1, d2, d3 ]
|
||||
#! gap> IsBound(d1);
|
||||
#! false
|
||||
#! gap> BindElmNames(D3);
|
||||
#! gap> d1 * d2;
|
||||
#! d3
|
||||
#! @EndExampleSession
|
||||
|
||||
#! @BeginGroup unchecked_table_constructors
|
||||
#! @GroupTitle Unchecked constructors from tables
|
||||
#! @Returns a magma of the designated category
|
||||
#! @Description Each of these functions is exactly like its counterpart
|
||||
#! without the `NC` suffix, except that it does not perform any verification
|
||||
#! that the supplied table in fact satisfies the necessary axioms for the
|
||||
#! designated category. (The verification is skipped to save computation
|
||||
#! time, for use in cases when the properties are known to hold.) Hence, use
|
||||
#! with caution: the behavior of this
|
||||
#! package if you supply a table which does not satisfy the appropiate
|
||||
#! axioms is undefined.
|
||||
#! @GroupInitialArguments table
|
||||
DeclareGlobalFunction("LeftQuasigroupByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("LeftRackByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("LeftQuandleByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("RightQuasigroupByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("RightRackByMultiplicationTableNC");
|
||||
DeclareGlobalFunction("RightQuandleByMultiplicationTableNC");
|
||||
#! @EndGroup
|
||||
|
||||
## Property of a collection that its elements know their multiplication table
|
||||
#! @Chapter technical
|
||||
#! @Section reps
|
||||
#! @SectionTitle Representational issues
|
||||
#! @Arguments collection
|
||||
#! @Description True if the family of the elements in the collection possesses
|
||||
#! a global multiplication table. This value is used to control whether more
|
||||
#! efficient algorithms are used in particular cases.
|
||||
DeclareProperty("IsBuiltFromMultiplicationTable", IsCollection);
|
||||
|
||||
## Create quasigroups etc by permutations
|
||||
#! @Chapter construct
|
||||
#! @Section from_scratch
|
||||
#! @BeginGroup perms_constructors
|
||||
#! @GroupTitle Constructors from permutations
|
||||
#! @Returns a magma of the designated category
|
||||
#! @Description These functions produce magmas from a sequence of
|
||||
#! permutations. That is to say, because all of the categories supported in
|
||||
#! &RAQ; are quasigroups on at least one side, either the left
|
||||
#! multiplicative action of an element on the magma is always a permutation
|
||||
#! (in the case of left quasigroups) or the right multiplicative action of
|
||||
#! an element on the magma is always a permutation. Hence, a magma in these
|
||||
#! categories can always be specified by a list of $n$ permutations on
|
||||
#! the natural numbers less than or equal to $n$ (i.e., ordinary &GAP;
|
||||
#! permutations) and that's what these
|
||||
#! functions do. In effect, the argument to the `Left` functions gives the
|
||||
#! rows of the multiplication table (as permutation objects), and the to the
|
||||
#! `Right` functions gives the columns.
|
||||
#! @GroupInitialArguments permutation-list
|
||||
DeclareGlobalFunction("LeftQuasigroupByPerms");
|
||||
DeclareGlobalFunction("LeftRackByPerms");
|
||||
DeclareGlobalFunction("LeftRackByPermsNC");
|
||||
DeclareGlobalFunction("LeftQuandleByPerms");
|
||||
DeclareGlobalFunction("LeftQuandleByPermsNC");
|
||||
DeclareGlobalFunction("RightQuasigroupByPerms");
|
||||
DeclareGlobalFunction("RightRackByPerms");
|
||||
DeclareGlobalFunction("RightRackByPermsNC");
|
||||
DeclareGlobalFunction("RightQuandleByPerms");
|
||||
#! @EndGroup
|
||||
|
||||
#! @BeginExampleSession
|
||||
#! gap> D3 := LeftQuandleByPerms( [ (2,3), (1,3), (1,2) ] );
|
||||
#! <left quandle with 3 generators>
|
||||
#! gap> SpecifyElmNamePrefix(D3, "p");
|
||||
#! gap> BindElmNames(D3);
|
||||
#! gap> p2*p3;
|
||||
#! p1
|
||||
#! @EndExampleSession
|
||||
|
||||
#! @BeginGroup unchecked_perms_constructors
|
||||
#! @GroupTitle Unchecked constructors from permutations
|
||||
#! @Returns a magma of the designated category
|
||||
#! @Description These functions are exactly the same as their counterparts
|
||||
#! without `NC` except that to save time they do not verify that the given
|
||||
#! permutations satisfy the appropriate axioms. Hence use caution, as
|
||||
#! supplying a list of permutations which does not form the proper structure
|
||||
#! can lead to undefined behavior. Note that there are no unchecked versions
|
||||
#! for the bare quasigroup constructors because the only properties required
|
||||
#! are that all of the rows (or columns, in the `Right` case) are permutations.
|
||||
#! @GroupInitialArguments permutation-list
|
||||
DeclareGlobalFunction("LeftRackByPermsNC");
|
||||
DeclareGlobalFunction("LeftQuandleByPermsNC");
|
||||
DeclareGlobalFunction("RightRackByPermsNC");
|
||||
DeclareGlobalFunction("RightQuandleByPermsNC");
|
||||
#! @EndGroup
|
||||
|
||||
@ -3,8 +3,6 @@
|
||||
## GAP Categories and representations
|
||||
|
||||
#! @Chapter technical
|
||||
#! This chapter covers computational/operational aspects of &RAQ;
|
||||
#! rather than mathematical ones.
|
||||
#! @Section Messages
|
||||
#! @Description Controls the level of verbosity of &RAQ;'s informative
|
||||
#! messages. Use `SetInfoLevel` to set it to 0 to quiet &RAQ;
|
||||
@ -22,14 +20,7 @@ DeclareInfoClass("InfoRAQ");
|
||||
# new, non-conflicting terms.
|
||||
|
||||
#! @Chapter basic
|
||||
#! In order to build up and define one-sided quasigroups, racks, and
|
||||
#! quandles, &RAQ; must define several lower-level objects and properties,
|
||||
#! which are documented in this section. Although logically they come before
|
||||
#! the domain constructors and operations, they are presented afterwards
|
||||
#! because it's rare that one needs to use them directly when working with
|
||||
#! &RAQ;.
|
||||
#! @Section elements
|
||||
#! @SectionTitle Categories of elements
|
||||
#! @Description An element <C>x</C> with the property
|
||||
#! that for all elements <C>y</C> and <C>z</C> in its family, <C>x*(y*z) =
|
||||
#! (x*y)*(x*z)</C>.
|
||||
@ -46,7 +37,6 @@ DeclareCategory("IsRSelfDistElement", IsMultiplicativeElement);
|
||||
DeclareCategoryCollections("IsRSelfDistElement");
|
||||
|
||||
#! @Section collections
|
||||
#! @SectionTitle Categories of collections
|
||||
#! @Description A collection which satisfies the left self-distributive
|
||||
#! property (see the description of
|
||||
#! <Ref Filt="IsLSelfDistElement" Label="for IsMultiplicativeElement"/>)
|
||||
@ -80,11 +70,13 @@ InstallTrueMethod(IsElementwiseIdempotent, IsIdempotentCollection);
|
||||
#! (i.e., <C>IsLSelfDistributive(obj)</C> is true).
|
||||
#! @Arguments obj
|
||||
#! @ItemType Filt
|
||||
#! @Returns true or false
|
||||
DeclareSynonym("IsLeftRack", IsLeftQuasigroup and IsLSelfDistributive);
|
||||
#! @Description Tests whether <A>obj</A> is a right rack, by definition
|
||||
#! precisely that it is a right quasigroup and right self-distributive.
|
||||
#! @Arguments obj
|
||||
#! @ItemType Filt
|
||||
#! @Returns true or false
|
||||
DeclareSynonym("IsRightRack", IsRightQuasigroup and IsRSelfDistributive);
|
||||
|
||||
#! @Description Tests whether <A>obj</A> is a left quandle, which by definition
|
||||
@ -93,20 +85,18 @@ DeclareSynonym("IsRightRack", IsRightQuasigroup and IsRSelfDistributive);
|
||||
#! (i.e., <C>IsElementwiseIdempotent(obj)</C> is true).
|
||||
#! @Arguments obj
|
||||
#! @ItemType Filt
|
||||
#! @Returns true or false
|
||||
DeclareSynonym("IsLeftQuandle", IsLeftRack and IsElementwiseIdempotent);
|
||||
|
||||
#! @Description Tests whether <A>obj</A> is a right quandle, by definition
|
||||
#! precisely that it is a right rack and every element is idempotent.
|
||||
#! @Arguments obj
|
||||
#! @ItemType Filt
|
||||
#! @Returns true or false
|
||||
DeclareSynonym("IsRightQuandle", IsRightRack and IsElementwiseIdempotent);
|
||||
|
||||
#! @Chapter construct
|
||||
#! @Section from_scratch
|
||||
#! @SectionTitle Direct constructors
|
||||
#! All of the functions in this section produce magmas (of one of the
|
||||
#! categories with which &RAQ; is concerned) from data of other (non-domain)
|
||||
#! types.
|
||||
#! @BeginAutoDoc
|
||||
#! @BeginGroup basic_constructors
|
||||
#! @GroupTitle Basic constructors (from generators)
|
||||
@ -123,13 +113,13 @@ DeclareSynonym("IsRightQuandle", IsRightRack and IsElementwiseIdempotent);
|
||||
#! quotients on the specified side must exist; racks must also satisfy the
|
||||
#! appropriate self-distributive law; and quandles must also have every
|
||||
#! element idempotent.
|
||||
#! @Returns a magma of the named category
|
||||
#! @Returns a magma of the designated category
|
||||
#! @GroupInitialArguments [family], [generators]
|
||||
DeclareGlobalFunction("LeftQuasigroup");
|
||||
DeclareGlobalFunction("RightQuasigroup");
|
||||
DeclareGlobalFunction("LeftRack");
|
||||
DeclareGlobalFunction("RightRack");
|
||||
DeclareGlobalFunction("LeftQuandle");
|
||||
DeclareGlobalFunction("RightQuasigroup");
|
||||
DeclareGlobalFunction("RightRack");
|
||||
DeclareGlobalFunction("RightQuandle");
|
||||
#! @EndGroup
|
||||
#! @BeginGroup unchecked_basic_constructors
|
||||
@ -144,10 +134,10 @@ DeclareGlobalFunction("RightQuandle");
|
||||
#! @Returns a magma of the named category
|
||||
#! @GroupInitialArguments family, generators
|
||||
DeclareGlobalFunction("LeftQuasigroupNC");
|
||||
DeclareGlobalFunction("RightQuasigroupNC");
|
||||
DeclareGlobalFunction("LeftRackNC");
|
||||
DeclareGlobalFunction("RightRackNC");
|
||||
DeclareGlobalFunction("LeftQuandleNC");
|
||||
DeclareGlobalFunction("RightQuasigroupNC");
|
||||
DeclareGlobalFunction("RightRackNC");
|
||||
DeclareGlobalFunction("RightQuandleNC");
|
||||
#! @EndGroup
|
||||
#! @EndAutoDoc
|
||||
|
||||
@ -9,6 +9,15 @@ TestDirectory(tst_path,
|
||||
testOptions := rec(compareFunction := "uptowhitespace"))
|
||||
);
|
||||
|
||||
# Now make sure the manual tests are up to date
|
||||
|
||||
doc_path := DirectoriesPackageLibrary("RAQ", "doc");
|
||||
makedoc_file := Filename(doc_path, "makedoc.g");
|
||||
|
||||
RAQ_makedoc_no_quit := true;
|
||||
Info(InfoRAQ, 1, "Generating RAQ documentation..\n\n");
|
||||
Read(makedoc_file);
|
||||
|
||||
auto_file := Filename(tst_path, "AutoDoc_tests.g");
|
||||
|
||||
if auto_file <> fail then
|
||||
|
||||
Loading…
Reference in New Issue
Block a user