From ab2fedcd02125dadb610a88cd44c0466927681d0 Mon Sep 17 00:00:00 2001 From: Max Horn Date: Fri, 2 Oct 2026 00:30:24 +0200 Subject: [PATCH] Give duplicate manual entries distinct labels GAPDoc derives each LaTeX label from the entry name plus its optional Label attribute, so 114 names documented more than once produced 309 "multiply defined" LaTeX warnings. Label all but one entry per name (keeping existing s pointing at the unlabelled one), drop literally duplicated entries, fix the ElementsOfIncidencStructure typo, and rename reused section labels. Also fix the BibTeX warning for Tits1959, whose issue number is really the volume. With the build now warning-free, re-enable warnings-as-errors in the docs workflow. Fixes #45 Assisted-by: Claude Code (Opus 5.5) --- .github/workflows/docs.yml | 2 - doc/affine.xml | 56 +++++++++--------- doc/classicalpolarspaces.xml | 80 +++++++++++++------------- doc/diagramgeometries.xml | 14 ++--- doc/fining.bib | 2 +- doc/gpolygons.xml | 72 ++++++++++++------------ doc/groups_app.xml | 4 +- doc/incidence_geometry.xml | 56 +++++++++--------- doc/morphisms.xml | 52 ++++++++--------- doc/morphisms_app.xml | 20 +++---- doc/polaritiesofps.xml | 8 +-- doc/projectivespaces.xml | 88 ++++++++++++++--------------- doc/projgroups.xml | 32 +++++------ doc/stab_orbs.xml | 10 ++-- doc/structure_app.xml | 2 +- doc/subgeometries.xml | 41 +++++++------- doc/varieties.xml | 106 +++++++++++++++++------------------ 17 files changed, 320 insertions(+), 325 deletions(-) diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml index c71e700..c4b069c 100644 --- a/.github/workflows/docs.yml +++ b/.github/workflows/docs.yml @@ -28,8 +28,6 @@ jobs: - uses: gap-actions/build-pkg-docs@v2 with: use-latex: 'true' - warnings-as-errors: 'false' - # Disabled due to a gazillion multiply defined label warnings - name: 'Upload documentation' uses: actions/upload-artifact@v7 with: diff --git a/doc/affine.xml b/doc/affine.xml index 0e604b3..38b2b5f 100644 --- a/doc/affine.xml +++ b/doc/affine.xml @@ -67,9 +67,9 @@ This category is a subcategory of IsIncidenceGeometry, and contains all f - + - + an affine space d must be a positive integer. In the first form, F is a field and the function returns the affine @@ -83,8 +83,8 @@ namely, the common abbreviation AG(d, q). - - + + the dimension of the affine space as (which is equal to its rank) @@ -94,7 +94,7 @@ namely, the common abbreviation AG(d, q). - + returns the base field for the affine space as @@ -105,7 +105,7 @@ namely, the common abbreviation AG(d, q). - + a vector space The underlying vector space of &agnq; is simply V(n,q). @@ -116,7 +116,7 @@ The underlying vector space of &agnq; is simply V(n,q). - + an affine space The ambient space of an affine space as is the affine space itself. Hence, simply as will be returned. @@ -133,7 +133,7 @@ Hence, simply as will be returned. - + a subspace of an affine space geo is an affine space, @@ -158,7 +158,7 @@ user is constructing an affine point. - + the collection of elements of the affine space as of type j For the affine space as of dimension d and the type j, 1 \leq j \leq d @@ -171,11 +171,11 @@ An error message is produced when the projective space ps has no elements Short names for ElementsOfIncidenceStructure - - - - - + + + + + The elements of ps of respective type 1, 2, 3, 4, and the hyperplanes An error message is produced when the projective space ps has no elements of a required type. @@ -187,9 +187,9 @@ An error message is produced when the projective space ps has no elements Incidence and containment - - - + + + true or false Recall that for affine spaces, incidence is symmetrized containment, where the whole affine space is @@ -203,7 +203,7 @@ for \in. The method for \* is using IsIncident. - + returns the ambient space of an element el of an affine space @@ -213,7 +213,7 @@ for \in. The method for \* is using IsIncident. - + returns the base field of an element el of an affine space @@ -223,7 +223,7 @@ for \in. The method for \* is using IsIncident. - + a subspace u and v are subspaces of an affine space. @@ -235,7 +235,7 @@ This function returns the span of the two subspaces. - + an affine subspace or the empty list u and v are subspaces of an affine space. @@ -261,7 +261,7 @@ The arguments u and v must be affine subspaces of a common affine - + a collection of affine subspaces @@ -287,7 +287,7 @@ with is the ambient space of v. Shadows of Affine Subspaces - + the subspaces of the affine space as of dimension type which are incident with v @@ -305,7 +305,7 @@ for affine spaces: Points(as,v), Points(v), Lines(v), etc. - + the subspaces of the affine space as of dimension type which are incident with each element of list @@ -336,7 +336,7 @@ subspace collections of affine spaces. - + an iterator for the given subspaces collection subs is a collection of subspaces of an affine space, such as @@ -348,7 +348,7 @@ subspace collections of affine spaces. - + an enumerator for the given subspaces collection subs is a collection of subspaces of an affine space, such as @@ -514,7 +514,7 @@ operation CollineationGroup. - + a group @@ -532,7 +532,7 @@ groups &agammalnq; and &aglnq; coincide. - + an element of an affine space diff --git a/doc/classicalpolarspaces.xml b/doc/classicalpolarspaces.xml index d6ca870..4161a33 100644 --- a/doc/classicalpolarspaces.xml +++ b/doc/classicalpolarspaces.xml @@ -100,8 +100,8 @@ symmetric bilinear forms are equivalent. Therefore, we call polar spaces with an underlying quadratic form in even characteristic also orthogonal polar spaces. - - + + a classical polar space form must be a sesquilinear or quadratic form created by use of the GAP package Forms. In the second variant, @@ -314,7 +314,7 @@ The following five operations always return polar spaces induced by one of the a - + a symplectic polar space This function returns the symplectic polar space of dimension d @@ -328,7 +328,7 @@ over F for a field F or over GF(q) for a prime power - + a Hermitian polar space This function returns the Hermitian polar space of dimension d @@ -342,7 +342,7 @@ over F for a field F or over GF(q) for a prime power - + a parabolic quadric d must be an even positive integer. This function returns the parabolic quadric of dimension d @@ -356,7 +356,7 @@ over F for a field F or over GF(q) for a prime power - + a hyperbolic quadric d must be an odd positive integer. This function returns the hyperbolic quadric of dimension d @@ -370,7 +370,7 @@ over F for a field F or over GF(q) for a prime power - + an elliptic quadric d must be an odd positive integer. This function returns the elliptic quadric of dimension d @@ -400,7 +400,7 @@ as can be noted by the different printing of ps before and after executio - + a classical polar space the canonical polar space isometric to the given polar space P or the classical polar space with underlying form form. @@ -409,7 +409,7 @@ the classical polar space with underlying form form. - + a classical polar space the polar space induced by a standard form and similar to the given polar space P or the classical polar space with underlying form form. @@ -422,7 +422,7 @@ the classical polar space with underlying form form. Basic operations for finite classical polar spaces - + a vector space The polar space ps is the geometry associated with a sesquilinear or quadratic form f. The vector space on which f is acting is returned. @@ -433,7 +433,7 @@ The vector space on which f is acting is returned. - + the ambient projective space When ps is a polar space, this operation returns the ambient projective space, i.e. the @@ -445,8 +445,8 @@ underlying projective space of the sesquilinear or quadratic form that defines < - - + + the dimension of the ambient projective space of ps When ps is a polar space, an ambient projective space P is uniquely defined and can be asked using AmbientSpace. This operation and @@ -458,7 +458,7 @@ its synonym Dimension returns the dimension of P. - + the rank of ps When ps is a polar space, its rank, i.e. the number of different types, equals the Witt index of the defining sesquilinear or quadratic form. @@ -469,7 +469,7 @@ the Witt index of the defining sesquilinear or quadratic form. - + the base field of the polar space ps @@ -524,7 +524,7 @@ sense, but not as an element of the incidence geometry, and hence do in IsSubspaceOfClassicalPolarSpace. - + an element of the polar space geo Let ps be a polar space, and v is either a row vector (for points) or an mxn matrix (for an (m-1)-subspace of a polar space with an (n-1)-dimensional ambient projective space. @@ -539,7 +539,7 @@ defining ps. - + the trivial subspace in the projective ps The object returned by this operation is contained in @@ -552,8 +552,8 @@ incidence results in an error message. - - + + the projective dimension of a subspace of a polar space. The operation ProjectiveDimension is also applicable on the EmptySubspace @@ -565,7 +565,7 @@ is also applicable on the EmptySubspace - + the collection of elements of the projective space ps of type j For the projective space ps of dimension d and the type j, 1 \leq j \leq d @@ -576,7 +576,7 @@ this operation returns the collection of j-1 dimensional subspaces. - + returns the ambient space of an element el of a polar space This operation is also applicable on the trivial subspace. For a Lie geometry, the ambient space of @@ -588,7 +588,7 @@ an element is defined as the ambient space of the Lie geometry, i.e. a projectiv - + the homogeneous coordinates of the point p @@ -605,9 +605,9 @@ an element is defined as the ambient space of the Lie geometry, i.e. a projectiv Incidence and containment - - - + + + true or false Recall that for projective spaces, incidence is symmetrized containment, where the empty subspace and the @@ -620,7 +620,7 @@ of the geometry, but both the empty subspace and the whole projective space are - + an element u and v are elements of a projective or polar space. @@ -633,7 +633,7 @@ of the two subspaces. - + an element u and v are elements of a projective or polar space. @@ -665,7 +665,7 @@ in ps. Note that belonging to ps is a necessary condition for - + a polarity of a projective space ps must be a polar space. This operation returns, when possible a polarity of the ambient projective @@ -698,7 +698,7 @@ with the type of subspace: degenerate, symplectic, hermitian - + A subspace of a projective space Let el be an element of a classical polar space. The first version @@ -726,9 +726,9 @@ returns the pole of el with relation to the polar space ps. - - - + + + a finite field element or a list (of lists) of finite field elements This method passes form and the underlying vector or matrix of el1, when form is a quadratic form, @@ -752,8 +752,8 @@ are described in Section . The generic description o can be found in Section . - - + + the elements of type i incident with el. The second variant determines the type i from the position of str in the list returned by TypesOfElementsOfIncidenceStructurePlural @@ -765,7 +765,7 @@ the type i from the position of str in the list returned by - + the elements of type i incident with el, in other words, the type i shadow of the element el @@ -910,7 +910,7 @@ occur in certain cases, and will, as we will see in the following overview. - + the collineation group of the polar space ps In most cases, the full projective semisimilarity group is returned. For two-dimensional @@ -939,8 +939,8 @@ such a collection, then List(C) will use the enumerator to compute a list - - + + an enumerator for the collection C and a list with all elements of C The argument C is a collection of subspaces of a polar space. @@ -956,7 +956,7 @@ For all polar spaces an iterator is constructed using IteratorList(enum), - + an iterator C is a collection of subspaces of a polar space. @@ -967,7 +967,7 @@ For all polar spaces an iterator is constructed using IteratorList(enum), - + an Orb object or list diff --git a/doc/diagramgeometries.xml b/doc/diagramgeometries.xml index 27696d8..ba203f7 100644 --- a/doc/diagramgeometries.xml +++ b/doc/diagramgeometries.xml @@ -83,7 +83,7 @@ of l. - + true if and only if ele1 and ele2 are incident ele1 and ele2 must be two elements in the same coset geometry. @@ -171,7 +171,7 @@ The group element g must belong to AmbientGroup(AmbientGeometry(ele))< - + an element of a coset geometry This is an operation which returns the image of ele, an element of a coset incidence structure, under g, an element of AmbientGroup(AmbientGeometry(ele)). @@ -179,7 +179,7 @@ This is an operation which returns the image of ele, an element of a cose - + a flag of a coset geometry This is an operation which returns the image of flg, a flag of a coset incidence structure, under g, an element of AmbientGroup(AmbientGeometry(flg)). @@ -280,7 +280,7 @@ set \{i_1,i_2,\ldots ,i_k\} of fl. - + the residue of fl in AmbientGeometry(fl). This is a CosetGeometry method for the ResidueOfFlag operation given in Chapter . @@ -293,7 +293,7 @@ Note that the related operation CanonicalResidueOfFlag takes two a - + incidence graph of cg. cg must be a coset geometry. The graph returned is @@ -443,8 +443,8 @@ used to check flag-transitivity if needed. - - + + does not return anything but writes a file filename.ps diag must be a diagram. Writes a file filename.ps in the diff --git a/doc/fining.bib b/doc/fining.bib index d69f3bd..5b566b6 100644 --- a/doc/fining.bib +++ b/doc/fining.bib @@ -33,7 +33,7 @@ @article{Tits1959 Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, Mrclass = {Contributed Item}, Mrnumber = {1557095}, - Number = {2}, + Volume = {2}, Pages = {13--60}, Title = {Sur la trialit\'e et certains groupes qui s'en d\'eduisent}, Url = {http://www.numdam.org/item?id=PMIHES_1959__2__13_0}, diff --git a/doc/gpolygons.xml b/doc/gpolygons.xml index c1bd42b..496b28b 100644 --- a/doc/gpolygons.xml +++ b/doc/gpolygons.xml @@ -161,7 +161,7 @@ by GeneralisedPolygonByBlocks. - + a generalised polygon The argument pts, lns and inc are respectively a set of objects, a set of objects @@ -215,7 +215,7 @@ attribute and can be accessed by the operation IncidenceGraph. - + a graph The argument gp is a generalised polygon. This operation returns the incidence graph of @@ -256,7 +256,7 @@ for some generalised polygons, it is necessary to compute a collineation group f - + a group This attribute returns the full collineation group of the generalised polygon gp. @@ -346,9 +346,9 @@ as an attribute of gp. Normally, attributes of GAP objects are immutable. Collections of elements of generalised polygons - - - + + + a collection of elements of a generalised polygon gp is any generalised polygon, i is a natural number, necessarily 1 or 2. @@ -358,7 +358,7 @@ and Lines are the usual shortcuts. - + a number els is a collection of elements of a generalised polygon. This operation returns @@ -368,9 +368,9 @@ the number of element in els. Creating elements from objects and retrieving objects from elements - - - + + + a collection of elements of a generalised polygon To create elements in gp (of type type), one of the versions of @@ -385,8 +385,8 @@ can be used. Incidence - - + + true or false Let v and w be two elements of a generalised polygon. It is checked if @@ -396,7 +396,7 @@ the two elements are incident in their ambient geometry. - + a line of a generalised polygon or fail Let v and w be two elements of a generalised polygon. It is checked if @@ -413,7 +413,7 @@ generalised polygons that belong to IsLieGeometry, see + a point of a generalised polygon or fail Let v and w be two elements of a generalised polygon. It is checked if @@ -431,10 +431,10 @@ generalised polygons that belong to IsLieGeometry, see - - - + + + + A collection of elements geo is a generalised polygon, v must be an element of geo, @@ -605,7 +605,7 @@ of both generalised hexagons. - + Recall that the classical generalised hexagons are constructed as an object in IsLieGeometry. This makes most operations described in the appropriate chapters on Lie geometries, projective spaces and polar spaces applicable. @@ -614,8 +614,8 @@ described in the appropriate chapters on Lie geometries, projective spaces and p - - + + a generalised hexagon @@ -626,8 +626,8 @@ described in the appropriate chapters on Lie geometries, projective spaces and p - - + + a generalised hexagon @@ -650,7 +650,7 @@ vectors and matrices in different representations are allowed as argument. - + an element of a classical generalized hexagon The argument obj is one vector or a list of vectors from the underlying vector space of gh. @@ -663,14 +663,14 @@ vectors and matrices in different representations are allowed as argument. - + a vector or a matrix - + true or false @@ -681,8 +681,8 @@ vectors and matrices in different representations are allowed as argument. Span and meet of elements - - + + a subspace of a projective space x and y are two elements of a classical generalised hexagon. The operation Span returns the projective @@ -696,7 +696,7 @@ the operations Span and Meet behave as described in + a group of collineations gh is a classical generalised hexagon. This attribute returns the full collineation group, equipped with a nice monomorphism. @@ -821,10 +821,10 @@ demonstrated, and some categories are displayed. Representation of elements and underlying objects - - + + - + For technical reasons, the underlying objects of the elements of an elation generalised quadrangle constructed from a Kantor family, are not exactly the mathematical objects from the definition. However, these technicalities are almost completely hidden for the user, except @@ -843,7 +843,7 @@ the base-point of an elation generalised quadrangle constructed from a Kantor fa Elation group and natural action on elements - + The attribute ElationGroup is naturally set upon creation of an elation generalised quadrangle from a Kantor family. The elements of the elation group act "naturally" on the elements of the elation generalised quadrangle. This @@ -1042,9 +1042,9 @@ completely. This attribute returns these q planes of &w5q;. Representation of elements and underlying objects - - - + + + The underlying objects of the elements of an elation generalised quadrangle in the category IsEGQByBLTSet are elements of the polar space &w5q; in its standard representation. These elements can be used as underlying diff --git a/doc/groups_app.xml b/doc/groups_app.xml index c6ce9d5..ad03a14 100644 --- a/doc/groups_app.xml +++ b/doc/groups_app.xml @@ -403,7 +403,7 @@ For this reason, CanonicalQuadraticForm is not an operation designed for -
+
Direct commands to construct the projective classical groups in FinInG As explained in Chapter , Section , we have assumed that @@ -622,7 +622,7 @@ The generators of this group are described explicitly in , Appe
-
+
Basis of the collineation groups The GenSS uses a function FindBasePointCandidates taking a group as one of the arguments. diff --git a/doc/incidence_geometry.xml b/doc/incidence_geometry.xml index f50d957..b01825d 100644 --- a/doc/incidence_geometry.xml +++ b/doc/incidence_geometry.xml @@ -103,9 +103,9 @@ generalised polygons have their own category, which is a subcategory of IsInc Main categories in IsIncidenceGeometry - - - + + + Within each category, several subcategories are declared. Subcategories of IsLieGeometry are discussed in Section and subcategories of IsGeneralisedPolygon are discussed in Chapter @@ -267,7 +267,7 @@ the general operation ElementsOfIncidenceStructure. - + a collection of elements inc must be an incidence structure, j must be a type of element of inc. This function returns all elements @@ -287,7 +287,7 @@ if inc has elements of the deduced type. - + a collection of elements inc must be an incidence structure, then this operation returns the collection of all elements of inc. Such a collection can e.g. be the range @@ -316,7 +316,7 @@ equal to 1,2,3,4, respectively. - + a positive integer inc must be an incidence structure, j must be a type of element of inc. This function returns the number of elements @@ -433,7 +433,7 @@ This operations simply returns the list of elements that define flag - + an integer This operations returns the number of elements that define flag @@ -455,7 +455,7 @@ This operations returns the number of elements that define flag - + an incidence structure This operations returns the ambient geometry of the flag @@ -466,7 +466,7 @@ This operations returns the ambient geometry of the flag - + an list of integers This operations returns the list of types of the elements defining flag @@ -477,8 +477,8 @@ This operations returns the list of types of the elements defining flag - - + + true or false An element is incident with a flag if and only if it is incident with all elements defining the flag. @@ -495,7 +495,7 @@ An element is incident with a flag if and only if it is incident with all elemen - + The collection of elements of type str or type j incident with v inc is an incidence structure, v must be an element of inc, str must @@ -523,9 +523,9 @@ and is a shortcut to ShadowOfElement(AmbientGeometry(v),v,j). - - - + + + The collection of elements of type str or type j incident with all elements of flag, or with all elements of list @@ -555,14 +555,14 @@ of the Category of G, the returned incidence structure is constructed usi Short names for ElementsIncidentWithElementOfIncidenceStructure - - - - - - - - + + + + + + + + The collections of elements of inc of respective type 1, 2, 3 and 4, that are incident with v @@ -687,8 +687,8 @@ the operation List. Main categories in IsLieGeometry - - + + In FinInG, a Lie geometry G refers to a geometry whose automorphism group is a (subgroup of a) group of Lie type. Generally spoken, one could say that a Lie geometry @@ -769,7 +769,7 @@ Lie geometries check whether the subspace of the vector space represents an elem - + the element of ig, represented by the subspace spanned by v or l, or returns the empty subspace. The first variant of this operation takes as second argument a vector of the underlying vector space of ig. @@ -785,7 +785,7 @@ argument. - + a CVEC object, which is the vector or matrix representing the element v The argument v must be an element, so it is not allowed that v is the empty subspace, @@ -813,7 +813,7 @@ use this method to test incidence between elements. More short names for ElementsIncidentWithElementOfIncidenceStructure - + Hyperplanes of an element of a Lie geometry the elements of type j-1 incident with v, which is an element of type j diff --git a/doc/morphisms.xml b/doc/morphisms.xml index bf33a45..5d60dac 100644 --- a/doc/morphisms.xml +++ b/doc/morphisms.xml @@ -130,7 +130,7 @@ polar spaces of the same kind that are induced by coordinate transformations. - + a geometry morphism The arguments ps1 and ps2 are equivalent polar spaces, i.e. up to @@ -181,9 +181,9 @@ quadric in &pg5q; with equation X_0X_5+X_1X_4+X_2X_3 - - - + + + a geometry morphism The argument f is a finite field, the argument q is a prime power. @@ -201,8 +201,8 @@ The returned geometry morphism has the lines of &pg3q; as source and the points - - + + a geometry morphism The argument quadric is a hyperbolic quadric in a 5 dimensional projective space. @@ -217,7 +217,7 @@ and the points of &qplus5q; as range. - + a geometry morphism The argument quadric is a hyperbolic quadric in a 5 dimensional projective space. @@ -243,9 +243,9 @@ and swapping the types.

- - - + + + a geometry morphism The operation allows the construction of the duality between &w3q; and &q4q;, @@ -279,7 +279,7 @@ and the duality between the same GQs, yields a duality from each of these GQs it - + a geometry morphism It is checked whether the base field of gq is a field of characteristic 2 and whether @@ -320,7 +320,7 @@ be equivalent as geometries. An Intertwiner is not implemented for this geometry - + a geometry morphism The arguments geom1 and geom2 are projective spaces of @@ -378,9 +378,9 @@ of choosing a different basis is shown. - - - + + + a geometry morphism This operation comes in four flavours. For the first flavour, the argument geom1 is a projective @@ -409,7 +409,7 @@ automorphism of order two, corresponding with the Frobenius automorphism. Embeddings of polar spaces - + a geometry morphism The arguments geom1 and geom2 both polar spaces, and v is an element of a projective space. @@ -424,8 +424,8 @@ An Intertwiner is not implemented for this geometry morphism. - - + + a geometry morphism The arguments geom1 and geom2 are projective or polar spaces with an underlying vector @@ -610,12 +610,12 @@ The possible embeddings are listed in the following table. - - - - - - + + + + + + a geometry morphism ps1 is a polar space over a field extension L of f2, basis is a @@ -640,8 +640,8 @@ symplectic generalised quadrangle over \mathrm{GF}(9 - - + + a geometry morphism If ps1 and ps2 are two polar spaces which are suitable for field diff --git a/doc/morphisms_app.xml b/doc/morphisms_app.xml index 5693113..dd8649f 100644 --- a/doc/morphisms_app.xml +++ b/doc/morphisms_app.xml @@ -22,12 +22,12 @@ This appendix gives more (technical) information on the low level functions for Low level functions for morphisms -

+
Field reduction and vector spaces - + a vector The argument f2 is a subfield of f1 and v is vector @@ -43,7 +43,7 @@ the length of v is a multiple of the degree of the field extension. - + a matrix Let K be the field &gfq; and let L be the field &gfqt;. @@ -94,8 +94,8 @@ Blows up a projective space pg with respect to the standard basis of the - - + + a subspace of a projective space The first flavour blows up a subspace of a projective space with respect to the basis using @@ -136,7 +136,7 @@ and relies on the following three operations. - + a quadratic form Let f be quadratic form determining a polar space over the field L This operation returns @@ -149,7 +149,7 @@ in Section . - + a bilinear form Let f be bilinear form determining a polar space over the field L This operation returns @@ -162,7 +162,7 @@ in Section . - + a hermitian form Let f be bilinear form determining a polar space over the field L This operation returns @@ -180,7 +180,7 @@ in Section . Low level functions - + The first operation can also take a matrix representing a line of &pg3q; as argument. @@ -202,7 +202,7 @@ in Section . - + IsomorphismPolarSpacesNC is the version of IsomorphismPolarSpaces where no checks are built in, and which is only applicable when the two polar spaces are equivalent. As no checks are built in, this operation is to diff --git a/doc/polaritiesofps.xml b/doc/polaritiesofps.xml index 56791ce..f12326e 100644 --- a/doc/polaritiesofps.xml +++ b/doc/polaritiesofps.xml @@ -108,7 +108,7 @@ objects in the category IsPolarityOfProjectiveSpace, which is a subcategory of the category IsProjGrpElWithFrobWithPSIsom. - + a polarity of a projective space The underlying correlation of the projective space is constructed using matrix mat, field f, the identity @@ -122,7 +122,7 @@ induce a polarity. - + a polarity of a projective space The underlying correlation of @@ -142,7 +142,7 @@ hermitian form. - + a polarity of a projective space The polarity of the projective space is constructed using a non-degenerate sesquilinear form form. It is checked whether the given @@ -185,7 +185,7 @@ error message is returned. - + a field The base field over which the polarity phi was constructed. diff --git a/doc/projectivespaces.xml b/doc/projectivespaces.xml index e20a1f4..709a785 100644 --- a/doc/projectivespaces.xml +++ b/doc/projectivespaces.xml @@ -51,7 +51,7 @@ We refer the reader to - + a projective space @@ -67,9 +67,9 @@ namely, the common abbreviation PG(d, q). - + - + the projective dimension of the projective space ps @@ -90,7 +90,7 @@ namely, the common abbreviation PG(d, q). - + a vector space If ps is a projective space of dimension n over the field of order @@ -103,7 +103,7 @@ vector space over the field of order q. - + a projective space The ambient space of a projective space ps is the projective space itself. Hence, simply ps will be returned. @@ -128,7 +128,7 @@ incidence geometry, and hence do in FinInG not belong to the category IsSubspaceOfProjectiveSpace. - + an element geo is a projective space, and v is either a row vector (for points) or an m \times @@ -156,7 +156,7 @@ incidence results in an error message. - + the projective dimension of a subspace of a projective space. The operation ProjectiveDimension is also applicable on the EmptySubspace. @@ -168,7 +168,7 @@ is also applicable on the EmptySubspace. - + the collection of elements of the projective space ps of type j For the projective space ps of dimension d and the type j (where 1 \leq j \leq d), @@ -181,11 +181,11 @@ An error message is produced when the projective space ps has no elements Short names for ElementsOfIncidenceStructure - - - - - + + + + + The elements of ps of respective type 1, 2, 3, 4, and the hyperplanes An error message is produced when the projective space ps has no elements of a required type. @@ -197,9 +197,9 @@ An error message is produced when the projective space ps has no elements Incidence and containment - - - + + + true or false Recall that for projective spaces, incidence is symmetrized containment, where the empty subspace and the @@ -264,7 +264,7 @@ list of coefficients of the equation defining the hyperplane as an algebraic var - + returns the ambient space of an element el of a projective space This operation is also applicable on the empty subspace and the whole space. @@ -275,7 +275,7 @@ This operation is also applicable on the empty subspace and the whole space. - + returns the base field of an element el of a projective space This operation is also applicable on the trivial subspace and the whole space. @@ -287,7 +287,7 @@ This operation is also applicable on the trivial subspace and the whole space. - + a random element from the collection elements The collection elements is an object in the category IsElementsOfIncidenceStructure, @@ -301,7 +301,7 @@ latter information can be derived e.g. using AmbientSpace and Type - + the first variant returns a random element of type i of the projective space ps. The second variant returns a random element of a random type of the projective space ps @@ -314,7 +314,7 @@ The second variant returns a random element of a random type of the projective s - + an element or the empty subspace or the whole space When u and v are elements of a projective space. @@ -334,7 +334,7 @@ variant of this operation. - + an element or the empty subspace or the whole space When u and v are elements of a projective space. @@ -353,7 +353,7 @@ variant of this operation. We remark that the result of a Meet operation - + the flag of the projective space ps, determined by the subspaces of ps in the list els. When els is empty, the empty flag is returned. @@ -365,14 +365,14 @@ the empty flag is returned. - + return true if flag is the empty flag - + true if flag is a chamber @@ -388,8 +388,8 @@ the empty flag is returned. Shadows of Projective Subspaces - - + + the elements of type i incident with el. The second variant determines the type i from the position of str in the list returned by TypesOfElementsOfIncidenceStructurePlural @@ -401,8 +401,8 @@ the type i from the position of str in the list returned by - - + + the type i shadow elements of the flag flag, i.e. the elements of type i incident with all elements of flag. The second variant determines the type i from the position of str in the list @@ -416,7 +416,7 @@ returned by TypesOfElementsOfIncidenceStructurePlural. - + the elements of type i incident with el, in other words, the type i shadow of the element el @@ -431,16 +431,16 @@ also performs the checking. Short names for ElementsIncidentWithElementOfIncidenceStructure - - - - - - - - - - + + + + + + + + + + The elements of the incidence geometry of the according type. If ps is not given as an argument, it is deduced from v as its ambient geometry. @@ -457,7 +457,7 @@ ambient geometry. Enumerating subspaces of a projective space - + an iterator for the collection subspaces We refer to the GAP operation for the definition of an iterator. @@ -469,7 +469,7 @@ We refer to the GAP operation for the definition of an it - + an enumerator for the collection subspaces For complete collections of subspaces of a given type of a projective space, currently, no non-trivial enumerator is installed, @@ -482,8 +482,8 @@ be used as an enumerator, but this might be time consuming. - - + + the complete list of elements in the collection subspaces The operation List will return a complete list, the operation AsList will return an orb object, diff --git a/doc/projgroups.xml b/doc/projgroups.xml index 0057f4a..2a1dc8b 100644 --- a/doc/projgroups.xml +++ b/doc/projgroups.xml @@ -307,7 +307,7 @@ semilinear maps from projectivities inside the category of collineations of a pr Correlations and collineations - + @@ -334,7 +334,7 @@ category IsProjGrpElWithFrobWithPSIsom. - + a projectivity of a projective space The argument mat must be a nonsingular matrix over the finite field f. In the second variant, the size of the nonsingular matrix mat @@ -349,13 +349,11 @@ belongs to IsProjGrpElWithFrob! - - - - - + + + - + mat is a nonsingular matrix, frob is a field automorphism, f is a field, and pg is a projective space. This function @@ -407,10 +405,10 @@ This operation returns the standard duality of the projective space ps - - - - + + + + mat is a nonsingular matrix, frob is a field automorphism, f @@ -470,7 +468,7 @@ This function returns the matrix that was used to construct g. - + a field g is a projectivity, collineation or correlation of a projective space. @@ -509,7 +507,7 @@ companion isomorphism of the projective space which defines g. - + g is a projectivity, collineation or correlation of a projective space. This function returns the order of g. @@ -612,7 +610,7 @@ This operation returns the correlations and collineations of &pgnq;. Basic operations for projective groups - + a field g must be a projective group. This function finds the base field of the vector space on which the group acts. @@ -620,7 +618,7 @@ the base field of the vector space on which the group acts. - + a number g must be a projective group. This function finds the dimension of the vector space on which the group acts. @@ -858,7 +856,7 @@ identity mapping is returned. - + A group of elations The first version returns the group of elations with with given axis axis and centre centre. diff --git a/doc/stab_orbs.xml b/doc/stab_orbs.xml index 8f7ae3a..0cf6038 100644 --- a/doc/stab_orbs.xml +++ b/doc/stab_orbs.xml @@ -55,7 +55,7 @@ a set (and therefore it might be necessary to apply Set on a collection o - + The orbits of the group g on set under the action of act. The set is a set of elements of a projective space, the group g is a subgroup of the collineation group @@ -197,8 +197,8 @@ functions are applicable on the projective groups implemented in FinInG Action functions - - + + a element of a Lie geometry @@ -230,7 +230,7 @@ suitable action domain. An easy example is the permutation action of the full co group of a projective space on its points.

- + A group homomorphism This is a generic GAP function, and returns a homomorphism to a "better" representation. @@ -238,7 +238,7 @@ This is a generic GAP function, and returns a homomorphism to a "better" represe - + A permutation group group is a projective group. The object this operation returns is actually equivalent with Image(NiceMonomorphism(group)). diff --git a/doc/structure_app.xml b/doc/structure_app.xml index 7dae9c5..7ada097 100644 --- a/doc/structure_app.xml +++ b/doc/structure_app.xml @@ -18,7 +18,7 @@ groups_app.xml FinInG package documentation This appendix gives more (technical) information on structure of FinInG. --> - + The structure of FinInG

The different components diff --git a/doc/subgeometries.xml b/doc/subgeometries.xml index 4e69f80..6d1f86b 100644 --- a/doc/subgeometries.xml +++ b/doc/subgeometries.xml @@ -112,7 +112,7 @@ A subspace of a subgeometry belongs to the category IsSubspaceOfSubgeometryOf - + a subgeometry of pg This operation returns the subgeometry of pg induced by the standard frame over the subfield subfield. Alternatively, a prime power q can be used as the order of the @@ -150,7 +150,7 @@ in list belong to the same projective space. - + a subgeometry of pg The argument pg is a projective space which is not a subgeometry itself, the argument @@ -177,8 +177,8 @@ so pg may not be a subgeometry itself. If the specified subfield equals t Underlying vector space and ambient projective space - - + + Let P be a projective space over the field F. Let sub be a subgeometry of P over the subfield F'. The underlying vector space of sub @@ -206,9 +206,9 @@ of points, and it is also a set in the GAP sense, i.e. an ordered list without d Projective dimension and rank - - - + + + an integer If sub is a subgeometry of a projective space, then it is a projective space @@ -222,15 +222,14 @@ see also . Underlying algebraic structures - - + -the first operation returns a vector space, the second and third operations return a finite field +a finite field -The operations UnderlyingVectorSpace and BaseField are defined for -projective spaces, see and . +The operation BaseField is defined for +projective spaces, see . For a subgeometry of a projective space sub with ambient space ps, -these operations return UnderlyingVectorSpace(ps), BaseField(ps) respectively. +it returns BaseField(ps). The operation SubfieldOfSubgeometry returns the subfield over which sub is defined. <#Include SYSTEM "../examples/include/subgeometries_underlyingstructures.include"> @@ -262,7 +261,7 @@ this collineation is known in the literature as the Baer involution of the subge Constructing elements of a subgeometry - + a subspace of a subgeometry sub is a subgeometry of a projective space, and v is either a row vector @@ -290,7 +289,7 @@ Note that the set S can be obtained using UnderlyingObject, see - + an incidence geometry For el an element of a subgeometry P, which is also a projective space, this operation @@ -300,9 +299,9 @@ returns P. Flags - - - + + + true or false These operations are defined for projective spaces and so they are also applicable to subgeometries. @@ -326,9 +325,9 @@ the projective space isomorphic to P'. Groups of collineations - - - + + + a group of collineations diff --git a/doc/varieties.xml b/doc/varieties.xml index d440d1c..f7192da 100644 --- a/doc/varieties.xml +++ b/doc/varieties.xml @@ -31,7 +31,7 @@ The package FinInG also contains the Veronese varieties algebraic variety in FinInG is an algebraic variety in a projective space or affine space, defined by a list of polynomials over a finite field. - + an algebraic variety The argument space is an affine or projective space over a finite field F, the argument pring is a multivariate polynomial ring defined over @@ -49,7 +49,7 @@ An algebraic variety in FinInG is an algebraic variety - + an affine or projective space The argument var is an algebraic variety. This attribute returns the affine or projective space in which the variety var was defined. @@ -57,10 +57,10 @@ An algebraic variety in FinInG is an algebraic variety - + a list of points - The argument var is an algebraic variety. This operation returns the list of points of the of the algebraic variety var whose coordinates satisfy the of the algebraic variety var. + The argument var is an algebraic variety. This operation returns the list of points of the of the algebraic variety var whose coordinates satisfy the of the algebraic variety var. <#Include SYSTEM "../examples/include/varieties_points.include"> @@ -68,18 +68,18 @@ An algebraic variety in FinInG is an algebraic variety - + an iterator The argument pts is the set of of an algebraic variety var. This operation returns an iterator for the points of an algebraic variety. - - + + true or false - The argument x is a point of the of an algebraic variety . This operation also works for a point x and the collection pts returned by . + The argument x is a point of the of an algebraic variety . This operation also works for a point x and the collection pts returned by . @@ -91,9 +91,9 @@ An algebraic variety in FinInG is an algebraic variety A projective variety in FinInG is an algebraic variety in a projective space defined by a list of homogeneous polynomials over a finite field. - - - + + + a projective algebraic variety @@ -113,9 +113,9 @@ attribute installed. Furthermore, we provide a method for PolarSpace taking as an argument a projective algebraic variety. - - - + + + a hermitian variety in a projective space For the first two methods, the argument pg is a projective space, pring is a polynomial ring, @@ -144,11 +144,11 @@ and the argument q is a prime power. This function returns the hermitian - - - - - + + + + + a quadratic variety in a projective space In the first two methods, the argument pg is a projective space, pring is a polynomial ring, @@ -253,7 +253,7 @@ When the argument var is a , this returns t - + a hermitian form If the argument var is a , this returns the associated hermitian form. @@ -262,7 +262,7 @@ If the argument var is a , this returns the - + the argument var is a projective algebraic variety. When its list of defining polynomial contains exactly one polynomial, depending on its degree, the operation QuadraticFormByPolynomial or HermitianFormByPolynomial is used to compute @@ -282,9 +282,9 @@ An affine variety in FinInG is an algebraic variety in - - - + + + an affine algebraic variety The argument ag is an affine space over a finite field F, the @@ -329,7 +329,7 @@ A geometry map is a map from a set of elements of a geometry to a set of - + the image of an element of the source under a geometry map The argument gm is a geometry map, the element x is an element of the of the geometry map gm. @@ -346,10 +346,10 @@ A Segre variety in FinInG is a projective algebraic va - - - - + + + + a Segre variety The argument listofpgs is a list of projective spaces defined over the same finite field, say [PG(n_1-1,q) [PG(n<sub>1 </sub>-1,q), PG(n_2-1,q) PG(n<sub>2 </sub>-1,q), ..., PG(n_k-1,q)] PG(n<sub>k </sub>-1,q)]. The operation also takes as input the list of dimensions (listofdims) and a finite field field (e.g. @@ -361,19 +361,19 @@ A Segre variety in FinInG is a projective algebraic va - + the points of a Segre variety - The argument sv is a Segre variety. This operation returns a set of points of the of the Segre variety. This set of points corresponds to the image of the . + The argument sv is a Segre variety. This operation returns a set of points of the of the Segre variety. This set of points corresponds to the image of the . - - - - - + + + + + a geometry map The argument listofpgs is a list of projective spaces defined over the same finite field, say [PG(n_1-1,q) [PG(n<sub>1 </sub>-1,q), PG(n_2-1,q) PG(n<sub>2 </sub>-1,q), ..., PG(n_k-1,q)] PG(n<sub>k </sub>-1,q)]. The operation also takes as input the list of dimensions (listofdims) and a finite field field (e.g. @@ -389,7 +389,7 @@ A Segre variety in FinInG is a projective algebraic va - + the source of a Segre map The argument sm is a . This operation returns the cartesian product of the list consisting of the pointsets of the projective spaces that were used to construct the . @@ -405,8 +405,8 @@ A Veronese variety in FinInG is a projective algebraic - - + + a Veronese variety The argument pg is a projective space defined over a finite field, say PG(n-1,q). The operation also takes as input the dimension and a finite field field (e.g. [n-1,q]). @@ -420,17 +420,17 @@ A Veronese variety in FinInG is a projective algebraic - + the points of a Veronese variety - The argument vv is a Veronese variety. This operation returns a set of points of the of the Veronese variety. This set of points corresponds to the image of the . + The argument vv is a Veronese variety. This operation returns a set of points of the of the Veronese variety. This set of points corresponds to the image of the . - - - + + + a geometry map The argument pg is a projective space defined over a finite field, say PG(n-1,q). The operation also takes as input the dimension and a finite field field (e.g. [n-1,q]). @@ -444,7 +444,7 @@ A Veronese variety in FinInG is a projective algebraic - + the source of a Veronese map The argument vm is a . This operation returns the pointset of the projective space that was used to construct the . @@ -459,8 +459,8 @@ A Veronese variety in FinInG is a projective algebraic A Grassmann variety in FinInG is a projective algebraic variety in a projective space over a finite field. The set of points that lie on this variety is the image of the Grassmann map. - - + + a Grassmann variety The argument pg is a projective space defined over a finite field, say PG(n,q), and argument k is an integer (k at least 1 and at most n-2) and denotes the projective dimension determining the Grassmann Variety. The operation also takes as input the set subspaces of subspaces of a projective space, or the dimension k, the dimension n and the size q of the finite field (k at least 1 and at most n-2). @@ -469,17 +469,17 @@ A Grassmann variety in FinInG is a projective algebrai - + the points of a Grassmann variety - The argument gv is a Grassmann variety. This operation returns a set of points of the of the Grassmann variety. This set of points corresponds to the image of the . + The argument gv is a Grassmann variety. This operation returns a set of points of the of the Grassmann variety. This set of points corresponds to the image of the . - - - + + + a geometry map The argument pg is a projective space defined over a finite field, say PG(n,q), and argument k is an integer (k at least 1 and at most n-2), and denotes the projective dimension determining the Grassmann Variety. The operation also takes as input the set subspaces of subspaces of a projective space, or the dimension k, the dimension n and the size q of the finite field (k at least 1 and at most n-2). @@ -490,7 +490,7 @@ A Grassmann variety in FinInG is a projective algebrai - + the source of a Grassmann map The argument gm is a . This operation returns the set of subspaces of the projective space that was used to construct the .