# Types in Hecke

Relevant part of the OSCAR documentation: https://docs.oscar-system.org/dev/DeveloperDocumentation/styleguide/#Approved-abbreviations
The following types are exported in Hecke:

## Number field related

| old/current name | new name | export | description |
|-----------------------|----------|-------------|---|
| NumField | same | | Abstract type for number fields
| NumFieldElem | same | |
| SimpleNumField | same | | Abstract type for simple number field
| SimpleNumFieldElem | same | |
| NonSimpleNumField | same | | Abstract type nonsimple number field
| NonSimpleNumFieldElem | same | |
| AnticNumberField | AbsSimpleNumField | | Absolute simple number field (Nemo)|
| nf_elem | AbsSimpleNumFieldElem | | (Nemo) |
| NfAbsNS | AbsNonSimpleNumField | | Absolute non-simple number field |
| NfAbsNSElem | AbsNonSimpleNumFieldElem |
| NfRel | RelSimpleNumField | | Relative simple number field
| NfRelElem | RelSimpleNumFieldElem |
| NfRelNS | RelNonSimpleNumField | | Relative nonsimple number field
| NfRelNSElem | RelNonSimpleNumFieldElem |
| NfToNfMor | NumFieldMor | | Map between number fields
|
| NumFieldOrd | NumFieldOrder | | Abstract type for orders in number fields
| NumFieldOrdElem | NumFieldOrderElem |
| NumFieldOrdIdl | NumFieldOrderIdeal |
| NumFieldOrdFracIdl | NumFieldOrderFractionalIdeal | |
| NfAbsOrd | AbsNumFieldOrder | | Order in an absolute number field
| NfAbsOrdElem | AbsNumFieldOrderElem |
| NfAbsOrdSet | AbsNumFieldOrderSet | | Parent for the orders
| NfAbsOrdIdl | AbsNumFieldOrderIdeal | | Ideal of an order in an absolute number field
| NfAbsOrdIdlSet | AbsNumFieldOrderIdealSet | | Parent for ideals
| NfAbsOrdFracIdl | AbsNumFieldOrderFracionalIdeal | | Fractional ideal of an order in an absolute number field
| NfRelOrd | RelNumFieldOrder | | Order in a relative number field
| NfRelOrdElem | RelNumFieldOrderElem | |
| NfRelOrdIdl | RelNumFieldOrderIdeal | | Ideal of an order in a relative number field
| NfRelOrdFracIdl | RelNumFieldOrderFracionalIdeal | | Fractional ideal of an order in a relative number field
|
| NfOrd | AbsSimpleNumFieldOrder | | Alias, maybe delete
| NfOrdElem | AbsSimpleNumFieldOrder | | Alias, maybe delete
| NfOrdIdl | AbsSimpleNumFieldOrderIdeal | | Alias, maybe delete
| NfOrdQuoRing | AbsSimpleNumFieldOrderQuoRing | | Alias, maybe delete
| NfOrdQuoRingElem | AbsSimpleNumFieldOrderQuoRingElem | | Alias, maybe delete
|
| NumFieldEmbNfAbs | AbsSimpleNumFieldEmbedding | yes | |
| NumFieldEmbNfAbsNS | AbsNonSimpleNumFieldEmbedding | yes | |
| NumFieldEmbNfRel | RelSimpleNumFieldEmbedding | yes | |
| NumFieldEmbNfNS | RelNonSimpleNumFieldEmbedding | yes | |
|
| EmbeddedField | EmbeddedNumField | | Embedded number field
| EmbeddedElem | EmbeddedNumFieldElem | | Embedded number field element

## Algebras related

| old/current name | new name | export | description |
|-----------------------|----------|-------------|---|
| AbsAlgAss | FinDimAssociativeAlgebra | | Abstract type for associative algebras (unitary) |
| AbsAlgAssElem | FinDimAssociativeAlgebraElem | |
| AlgAss | StructureConstantAlgebra | | Finite dimensional algebra with structure constants
| AlgAssElem | AssociativeAlgebraElem | | Element in a finite-dimensional associative algebra
| AlgGrp | GroupAlgebra | | Group algebra over finite group
| AlgGrpElem | GroupAlgebraElem | | Element of group algebra over finite field
| AlgMat | MatAlgebra | | Matrix algebra
| AlgMatElem | MatAlgebraElem | | Element of Matrix Algebra
| AlgQuat | QuaternionAlgebra |

## Something with groups

| old/current name | new name | export | description |
|-----------------------|----------|-------------|---|
| GrpAbFinGen | FinGenAbGroup | | Finitely generated abelian group
| GrpAbFinGenElem | FinGenAbGroupElem | | Finitely generated abelian group element
| GrpAbFinGenMap | FinGenAbGroupHom | | Morphism between finitely generated abelian groups
| GrpAbToGrpGenMor | FinGenAbGroupToGroupHom | | Map from finitely generated abelian group to a group described by multiplication table
| GrpGen | MultTableGroup | | Group described by multiplication table
| GrpGenElem | MultTableGroupElem | | Element of group with multiplication table
| GrpGenToGrpAbMor | MultTableGroupToGroupHom | | Map from group described by multiplication table to finitely generated abelian group
| GrpGenToGrpGenMor | MultTableGroupHom | | Endomorphism from group described by multiplication table

## Rest

| old/current name | new name | export | description |
|-----------------------|----------|-------------|---|
| AbstractLat | | | Lattices in quadratic or hermitian spaces
| AbstractSpace | | | Quadratic or hermitian space
| AbstractSpaceMor | | | Map between quadratic or hermitian spaces
| AbstractSpaceRes | | | Restriction of scalars for the maps
| BigComplex | | | Complex numbers as pairs of BigFloat. @claus: Do we still need this?
| ClassField | | | Class field of number fields
| ComplexOfMorphisms | | | Some homological algebra thing
| CyclotomicExt | | no | Cyclotomic extension
| Divisor | | no | (Absolute) function field divisor
| Divisors | | yes | Iterator object over divisors
| EllCrv | EllipticCurve | | Elliptic curve
| EllCrvPt | EllipticCurvePoint | | Point on elliptic curve
|
| FacElem | | | Factorized element
| FacElemMon | | | Monoid of factorized things
| FactorBase | | no | Internal class group thing
| FakeFmpqMat | | | Rational matrix as a pair. Should be internal, but basis matrix returns this.
| FakeFmpqMatSpace | | | Parent for FakeFmpqMat
| FunFldDiff | | no | Differential of function field
| GenOrdFracIdl | | | Fractional ideal in a generic order
| HermGenus | | | Hermitian genus
| HermLat | | | Hermitian lattice
| HermLocalGenus | | | Hermitian local genus
| HypellCrv | | | Hyperelliptic curve
| HypellCrvPt | | | Point on hyperelliptic curve
| IdealSet | | | Parent for ideals
| InfPlc | | | Infinite place of number field
| Isogeny | | | Isogeny between elliptic curves
| KInftyElem | | no | Localization of $K[X]$ at the "infinite place"
| KInftyRing | | no | Element of some localization
| KodairaSymbol | | | Kodaira symbol of elliptic curve
| Line | | no | Internal type for Line of polygon
| MSet | | | Multiset
| Map | | | Coming from AA?
| MapFromFunc | | | Map given by julia functions
| MapRayClassGrp | | | Map describing ray class group
| NewtonPolygon | | | NewtonPolygon
| OrdLoc | | | Localiation of a number field order
| OrdLocElem | | | Element of localization of number field
| Plc | | | Some abstract overtype for places of number fields?
| Polygon | | | Some type for Polygon
| PrimeIdealsSet | | | Prime ideal iterator of number field
| PrimesSet | | | Prime number iterator
| QuadBin | | | Binary quadratic form
| QuadGenus | | | Quadratic genus
| QuadLat | | | Quadratic lattice
| QuadLocalGenus | | | Quadratic local genus
| SMat | | | Sparse matrix
| SMatSpace | | | Parent of sparse matrices
| SRow | | | Sparse row
| TorQuadModule | | | Torsion quadratic module
| TorQuadModuleElem | | | Torsion quadratic module element
| TorQuadModuleMor | | | Morphism between [...]
| VecSpaceRes | | | Some restriction map L^m -> K^n, if L is a finite extesion of K
| ZZGenus | | | Genus of ZZ-lattices
| ZZLat | | | Quadratic Z-lattice
| ZZLocalGenus | | | Local genus of quadratic Z-lattices
| ZpnGModule | | no | Finitely generated $\mathbf{Z}/\mathbf{Z}n[G]$-modules

There are also some (a lot of?) non-exported types like AbsAlgAssMor and AlgAss(Abs|Rel)Ord*

## Renaming script

The script is consistent with the above table as of 31-01-2024 15:15

#!/bin/sh
#

# some settings that avoid weirdness in sed when it tries to
# adapt to your locale (e.g. if your system uses German as system language)
export LANG=C
export LC_CTYPE=C
export LC_ALL=C

# Files to modify (default uses all files known to git,
# but obviously you can modify it)
FILES=$(git ls-files)

# on macOS, you may need to change the following
SED_I="sed -i"
#SED_I="gsed -i"
#SED_I="sed -i ''"

# from https://github.com/Nemocas/AbstractAlgebra.jl/pull/1574

$SED_I \
-e "s;\bMatAlgElem\b;MatRingElem;g" \
-e "s;\bMatAlgebra\b;MatRing;g" \
-e "s;\bMatrixAlgebra\b;matrix_ring;g" \
$FILES

# from https://hackmd.io/nRnyfrSxTVe5CzXidB1cBQ?both#Nemo

$SED_I \
-e "s;\bFlintPadicField\b;PadicField;g" \
-e "s;\bpadic\b;PadicFieldElem;g" \
-e "s;\bFlintQadicField\b;QadicField;g" \
-e "s;\bqadic\b;QadicFieldElem;g" \
-e "s;\barb_poly\b;ArbPolyRingElem;g" \
-e "s;\barb_mat\b;ArbMatrix;g" \
-e "s;\barb\b;ArbFieldElem;g" \
-e "s;\bacb_poly\b;AcbPolyRingElem;g" \
-e "s;\bacb_mat\b;AcbMatrix;g" \
-e "s;\bacb\b;AcbFieldElem;g" \
-e "s;\bca\b;CalciumFieldElem;g" \
-e "s;\bLoc\b;LocalizedEuclideanRing;g" \
-e "s;\bLocElem\b;LocalizedEuclideanRingElem;g" \
-e "s;\blll_ctx\b;LLLContext;g" \
-e "s;\bqqbar\b;QQBarFieldElem;g" \
-e "s;\bCalciumQQBarField\b;QQBarField;g" \
-e "s;\bFlintQQiField\b;QQiField;g" \
-e "s;\bfmpqi\b;QQiFieldElem;g" \
-e "s;\bFlintZZiRing\b;ZZiRing;g" \
-e "s;\bfmpzi\b;ZZiRingElem;g" \
-e "s;\bfmpzUnitRange\b;ZZRingElemUnitRange;g" \
$FILES
#-e "s;\bCalciumField\b;CalciumField;g" \ # no change
#-e "s;\bFac\b;;g" \ # to be decided

# from https://hackmd.io/ONVPdlfARgWzkfkNkcJkgA

# Number field related

$SED_I \
-e "s;\bAnticNumberField\b;AbsSimpleNumField;g" \
-e "s;\bnf_elem\b;AbsSimpleNumFieldElem;g" \
-e "s;\bNfAbsNS\b;AbsNonSimpleNumField;g" \
-e "s;\bNfAbsNSElem\b;AbsNonSimpleNumFieldElem;g" \
-e "s;\bNfRel\b;RelSimpleNumField;g" \
-e "s;\bNfRelElem\b;RelSimpleNumFieldElem;g" \
-e "s;\bNfRelNS\b;RelNonSimpleNumField;g" \
-e "s;\bNfRelNSElem\b;RelNonSimpleNumFieldElem;g" \
-e "s;\bNfToNfMor\b;NumFieldMor;g" \
-e "s;\bNumFieldOrd\b;NumFieldOrder;g" \
-e "s;\bNumFieldOrdElem\b;NumFieldOrderElem;g" \
-e "s;\bNumFieldOrdIdl\b;NumFieldOrderIdeal;g" \
-e "s;\bNumFieldOrdFracIdl\b;NumFieldOrderFractionalIdeal;g" \
-e "s;\bNfAbsOrd\b;AbsNumFieldOrder;g" \
-e "s;\bNfAbsOrdElem\b;AbsNumFieldOrderElem;g" \
-e "s;\bNfAbsOrdSet\b;AbsNumFieldOrderSet;g" \
-e "s;\bNfAbsOrdIdl\b;AbsNumFieldOrderIdeal;g" \
-e "s;\bNfAbsOrdIdlSet\b;AbsNumFieldOrderIdealSet;g" \
-e "s;\bNfAbsOrdFracIdl\b;AbsNumFieldOrderFractionalIdeal;g" \
-e "s;\bNfAbsOrdFracIdlSet\b;AbsNumFieldOrderFractionalIdealSet;g" \
-e "s;\bNfRelOrd\b;RelNumFieldOrder;g" \
-e "s;\bNfRelOrdElem\b;RelNumFieldOrderElem;g" \
-e "s;\bNfRelOrdIdl\b;RelNumFieldOrderIdeal;g" \
-e "s;\bNfRelOrdFracIdl\b;RelNumFieldOrderFractionalIdeal;g" \
-e "s;\bNfAbsNSToNfAbsNS\b;NumFieldAut{AbsNonSimpleNumField};g" \
-e "s;\bNfToNfMor\b;NumFieldAut{AbsSimpleNumField};g" \
-e "s;\bNumFieldMor\b;NumFieldHom;g" \
-e "s;\bNfAbsToNfAbsNS\b;NumFieldHom{AbsSimpleNumField, AbsNonSimpleNumField};g" \
-e "s;\bNfToNfRel\b;NumFieldHom{AbsSimpleNumField, RelSimpleNumField{AbsSimpleNumFieldElem}};g" \
-e "s;\bNfRelToNfRelMor_nf_elem_nf_elem\b;NumFieldHom{RelSimpleNumField{AbsSimpleNumFieldElem}, RelSimpleNumField{AbsSimpleNumFieldElem}};g" \
-e "s;\bNfRelToNf\b;NumFieldHom{RelSimpleNumField{AbsSimpleNumFieldElem}, AbsSimpleNumField};g" \
-e "s;\bNfRelNSToNfRelNSMor_nf_elem\b;NumFieldHom{RelNonSimpleNumField{AbsSimpleNumFieldElem}, RelNonSimpleNumField{AbsSimpleNumFieldElem}};g" \
-e "s;\bNfRelToNfRelNSMor_nf_elem\b;NumFieldHom{RelSimpleNumField{AbsSimpleNumFieldElem}, RelNonSimpleNumField{AbsSimpleNumFieldElem}};g" \
-e "s;\bNfOrd\b;AbsSimpleNumFieldOrder;g" \
-e "s;\bNfOrdElem\b;AbsSimpleNumFieldOrderElem;g" \
-e "s;\bNfOrdIdl\b;AbsSimpleNumFieldOrderIdeal;g" \
-e "s;\bNfOrdFracIdlSet\b;AbsSimpleNumFieldOrderFractionalIdealSet;g" \
-e "s;\bNfOrdFracIdl\b;AbsSimpleNumFieldOrderFractionalIdeal;g" \
-e "s;\bNfOrdQuoRing\b;AbsSimpleNumFieldOrderQuoRing;g" \
-e "s;\bNfOrdQuoRingElem\b;AbsSimpleNumFieldOrderQuoRingElem;g" \
-e "s;\bNumFieldEmbNfAbs\b;AbsSimpleNumFieldEmbedding;g" \
-e "s;\bNumFieldEmbNfAbsNS\b;AbsNonSimpleNumFieldEmbedding;g" \
-e "s;\bNumFieldEmbNfRel\b;RelSimpleNumFieldEmbedding;g" \
-e "s;\bNumFieldEmbNfNS\b;RelNonSimpleNumFieldEmbedding;g" \
$FILES
#-e "s;\bNfOrd\b;;g" \  # Alias, maybe delete \
#-e "s;\bNfOrdElem\b;;g" \ # Alias, maybe delete \
#-e "s;\bNfOrdIdl\b;;g" \ # Alias, maybe delete \
#-e "s;\bNfOrdQuoRing\b;;g" \ # Alias, maybe delete \ 
#-e "s;\bNfOrdQuoRingElem\b;;g" \ # Alias, maybe delete \

# Algebras related

$SED_I \
-e "s;\bAbsAlgAss\b;AbstractAssociativeAlgebra;g" \
-e "s;\bAbsAlgAssElem\b;AbstractAssociativeAlgebraElem;g" \
-e "s;\bAlgAss\b;StructureConstantAlgebra;g" \
-e "s;\bAlgAssElem\b;AssociativeAlgebraElem;g" \
-e "s;\bAlgGrp\b;GroupAlgebra;g" \
-e "s;\bAlgGrpElem\b;GroupAlgebraElem;g" \
-e "s;\bAlgMat\b;MatAlgebra;g" \
-e "s;\bAlgMatElem\b;MatAlgebraElem;g" \
-e "s;\bAlgQuat\b;QuaternionAlgebra;g" \
$FILES

# Something with groups

$SED_I \
-e "s;\bGrpAbFinGen\b;FinGenAbGroup;g" \
-e "s;\bGrpAbFinGenElem\b;FinGenAbGroupElem;g" \
-e "s;\bGrpAbFinGenMap\b;FinGenAbGroupHom;g" \
-e "s;\bGrpAbToGrpGenMor\b;FinGenAbGroupToGroupHom;g" \
-e "s;\bGrpGen\b;MultTableGroup;g" \
-e "s;\bGrpGenElem\b;MultTableGroupElem;g" \
-e "s;\bGrpGenToGrpAbMor\b;MultTableGroupToGroupHom;g" \
-e "s;\bGrpGenToGrpGenMor\b;MultTableGroupHom;g" \
$FILES

# Rest

$SED_I \
-e "s;\bEllCrv\b;EllipticCurve;g" \
-e "s;\bEllCrvPt\b;EllipticCurvePoint;g" \
-e "s;\bEmbeddedField\b;EmbeddedNumField;g" \
-e "s;\bEmbeddedElem\b;EmbeddedNumFieldElem;g" \
$FILES
# -e "s;\bAbstractLat\b;;g"\ #Lattices in quadratic or hermitian spaces
# -e "s;\bAbstractSpace\b;;g"\ #Quadratic or hermitian space
# -e "s;\bAbstractSpaceMor\b;;g"\ #Map between quadratic or hermitian spaces
# -e "s;\bAbstractSpaceRes\b;;g"\ #Restriction of scalars for the maps
# -e "s;\bBigComplex\b;;g"\ #Complex numbers as pairs of BigFloat. @claus: Do we still need this?
# -e "s;\bClassField\b;;g"\ #Class field of number fields
# -e "s;\bComplexOfMorphisms\b;;g"\ #Some homological algebra thing
# -e "s;\bCyclotomicExt\b;;g"\ #Cyclotomic extension
# -e "s;\bDivisor\b;;g"\ #(Absolute) function field divisor
# -e "s;\bDivisors\b;;g"\ # Iterator object over divisors
# -e "s;\bFacElem\b;;g" \ # Factorized element
# lots more undecided things