/*
      Objects to manage the interactions between the mesh data structures and the algebraic objects
*/
#pragma once
#include "petscsystypes.h"
#include <petscmat.h>
#include <petscdmtypes.h>
#include <petscdmlabel.h>
#include <petscfetypes.h>
#include <petscdstypes.h>
#include <petscdt.h>

/* SUBMANSEC = DM */

PETSC_EXTERN PetscErrorCode DMInitializePackage(void);

PETSC_EXTERN PetscClassId DM_CLASSID;

#define DMLOCATEPOINT_POINT_NOT_FOUND -367

/*J
   DMType - String with the name of a PETSc `DM`. These are all the `DM` provided by PETSc.

   Level: beginner

   Note:
   These can be used with `DMSetType()` or the options database key `-dm_type` to set the specific data structures and algorithms to use with a specific `DM`.
   But more commonly one calls directly a constructor for a particular `DMType` such as `DMDACreate()`

.seealso: [](ch_dmbase), `DMSetType()`, `DMCreate()`, `DM`, `DMDACreate()`
J*/
typedef const char *DMType;
#define DMDA        "da"
#define DMCOMPOSITE "composite"
#define DMSLICED    "sliced"
#define DMSHELL     "shell"
#define DMPLEX      "plex"
#define DMREDUNDANT "redundant"
#define DMPATCH     "patch"
#define DMMOAB      "moab"
#define DMNETWORK   "network"
#define DMFOREST    "forest"
#define DMP4EST     "p4est"
#define DMP8EST     "p8est"
#define DMSWARM     "swarm"
#define DMPRODUCT   "product"
#define DMSTAG      "stag"

PETSC_EXTERN const char *const       DMBoundaryTypes[];
PETSC_EXTERN const char *const       DMBoundaryConditionTypes[];
PETSC_EXTERN const char *const       DMBlockingTypes[];
PETSC_EXTERN PetscFunctionList       DMList;
PETSC_EXTERN DMGeneratorFunctionList DMGenerateList;
PETSC_EXTERN PetscFunctionList       DMGeomModelList;
PETSC_EXTERN PetscErrorCode          DMCreate(MPI_Comm, DM *);
PETSC_EXTERN PetscErrorCode          DMClone(DM, DM *);
PETSC_EXTERN PetscErrorCode          DMSetType(DM, DMType);
PETSC_EXTERN PetscErrorCode          DMGetType(DM, DMType *);
PETSC_EXTERN PetscErrorCode          DMRegister(const char[], PetscErrorCode (*)(DM));
PETSC_EXTERN PetscErrorCode          DMRegisterDestroy(void);

PETSC_EXTERN PetscErrorCode DMView(DM, PetscViewer);
PETSC_EXTERN PetscErrorCode DMLoad(DM, PetscViewer);
PETSC_EXTERN PetscErrorCode DMDestroy(DM *);
PETSC_EXTERN PetscErrorCode DMCreateGlobalVector(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMCreateLocalVector(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMGetLocalVector(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMRestoreLocalVector(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMGetGlobalVector(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMRestoreGlobalVector(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMClearGlobalVectors(DM);
PETSC_EXTERN PetscErrorCode DMClearLocalVectors(DM);
PETSC_EXTERN PetscErrorCode DMClearNamedGlobalVectors(DM);
PETSC_EXTERN PetscErrorCode DMClearNamedLocalVectors(DM);
PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *, Vec *);
PETSC_EXTERN PetscErrorCode DMCreateGradientMatrix(DM, DM, Mat *);
PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, PetscCtx), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, PetscCtx), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, PetscCtx), PetscErrorCode (*)(DM, Mat, DM, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, PetscCtx), PetscErrorCode (*)(DM, Mat, DM, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);

PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
PETSC_EXTERN PetscErrorCode DMGeomModelRegister(const char[], PetscErrorCode (*)(DM, PetscInt, PetscInt, const PetscScalar[], PetscScalar[]));
PETSC_EXTERN PetscErrorCode DMGeomModelRegisterAll(void);
PETSC_EXTERN PetscErrorCode DMGeomModelRegisterDestroy(void);
PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);

PETSC_EXTERN PetscErrorCode DMSetUp(DM);
PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
PETSC_EXTERN PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMDACreateAggregates()", ) PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, PetscCtx), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, PetscCtx), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);

/* Topology support */
PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt *[]);

/* Coordinate support */
PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
PETSC_EXTERN PetscErrorCode DMSetCellCoordinateField(DM, DMField);
PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
PETSC_EXTERN PetscErrorCode DMSetCoordinateDisc(DM, PetscFE, PetscBool, PetscBool);
PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);
PETSC_EXTERN PetscErrorCode DMSnapToGeomModel(DM, PetscInt, PetscInt, const PetscScalar[], PetscScalar[]);
PETSC_EXTERN PetscErrorCode DMSetSnapToGeomModel(DM, const char[]);

/* Periodicity support */
PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMGetSparseLocalize(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMSetSparseLocalize(DM, PetscBool);

/* block hook interface */
PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, PetscCtx), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, PetscCtx), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, PetscCtx), PetscCtx);
PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);

PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, PetscCtx);
PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscCtxDestroyFn *);
PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, PetscCtxRt);
PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);

PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], const PetscInt[], const PetscInt[], IS *, DM *);
PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS *[], DM *);
PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter *[], VecScatter *[], VecScatter *[]);

PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);

PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);

typedef struct NLF_DAAD *NLF;

#define DM_FILE_CLASSID 1211221

/* FEM support */
PETSC_EXTERN PetscErrorCode DMPrintCellIndices(PetscInt, const char[], PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode DMPrintCellVectorReal(PetscInt, const char[], PetscInt, const PetscReal[]);
PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);

PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));

PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
PETSC_EXTERN PetscErrorCode DMCreateSectionPermutation(DM, IS *, PetscBT *);
PETSC_EXTERN PetscErrorCode DMReorderSectionGetDefault(DM, DMReorderDefaultFlag *);
PETSC_EXTERN PetscErrorCode DMReorderSectionSetDefault(DM, DMReorderDefaultFlag);
PETSC_EXTERN PetscErrorCode DMReorderSectionGetType(DM, MatOrderingType *);
PETSC_EXTERN PetscErrorCode DMReorderSectionSetType(DM, MatOrderingType);
PETSC_EXTERN PetscErrorCode DMUseTensorOrder(DM, PetscBool);
static inline PETSC_DEPRECATED_FUNCTION(3, 23, 0, "DMGetLocalSection()", ) PetscErrorCode DMGetSection(DM dm, PetscSection *s)
{
  return DMGetLocalSection(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 23, 0, "DMSetLocalSection()", ) PetscErrorCode DMSetSection(DM dm, PetscSection s)
{
  return DMSetLocalSection(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetSection()", ) PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
{
  return DMGetLocalSection(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetSection()", ) PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
{
  return DMSetLocalSection(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetGlobalSection()", ) PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
{
  return DMGetGlobalSection(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetGlobalSection()", ) PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
{
  return DMSetGlobalSection(dm, s);
}

PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMGetSectionSF()", ) PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
{
  return DMGetSectionSF(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMSetSectionSF()", ) PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
{
  return DMSetSectionSF(dm, s);
}
static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMCreateSectionSF()", ) PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
{
  return DMCreateSectionSF(dm, l, g);
}
PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);

PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);

PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char[], PetscInt, PetscReal *);
PETSC_EXTERN PetscErrorCode DMGetOutputSequenceLength(DM, PetscViewer, const char[], PetscInt *);

PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode DMClearFields(DM);
PETSC_EXTERN PetscErrorCode DMCopyFields(DM, PetscInt, PetscInt, DM);
PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);

PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *, PetscDS *);
PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *, PetscDS *);
PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS, PetscDS);
PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *, PetscDS *);
PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS, PetscDS);
PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
PETSC_EXTERN PetscErrorCode DMClearDS(DM);
PETSC_EXTERN PetscErrorCode DMCopyDS(DM, PetscInt, PetscInt, DM);
PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
PETSC_EXTERN PetscErrorCode DMClearAuxiliaryVec(DM);

struct _n_DMInterpolationInfo {
  MPI_Comm   comm;
  PetscInt   dim;    /* The spatial dimension of points */
  PetscInt   nInput; /* The number of input points */
  PetscReal *points; /* The input point coordinates */
  PetscInt  *cells;  /* The cell containing each point */
  PetscInt   n;      /* The number of local points */
  Vec        coords; /* The point coordinates */
  PetscInt   dof;    /* The number of components to interpolate */
};
/*MC
  DMInterpolationInfo - Pointer to a structure for holding information about interpolation on a mesh

  Synopsis:
    comm     - The communicator
    dim      - The spatial dimension of points
    nInput   - The number of input points
    points[] - The input point coordinates
    cells[]  - The cell containing each point
    n        - The number of local points
    coords   - The point coordinates
    dof      - The number of components to interpolate

  Level: intermediate

.seealso: [](ch_dmbase), `DM`, `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
M*/
typedef struct _n_DMInterpolationInfo *DMInterpolationInfo;

PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);

PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
PETSC_EXTERN PetscErrorCode DMCreateLabelAtIndex(DM, PetscInt, const char[]);
PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);

/*E
   DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination `DM`s with the same name

   Values:
+  `DM_COPY_LABELS_REPLACE` - replace label in destination by label from source
.  `DM_COPY_LABELS_KEEP`    - keep destination label
-  `DM_COPY_LABELS_FAIL`    - generate an error

   Level: advanced

.seealso: [](ch_dmbase), `DMLabel`, `DM`, `DMCompareLabels()`, `DMRemoveLabel()`
E*/
typedef enum {
  DM_COPY_LABELS_REPLACE,
  DM_COPY_LABELS_KEEP,
  DM_COPY_LABELS_FAIL
} DMCopyLabelsMode;
PETSC_EXTERN const char *const DMCopyLabelsModes[];

PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char *[]);
PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode);
PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char *[]);

PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], PetscVoidFn *, PetscVoidFn *, void *, PetscInt *);
PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode DMHasBound(DM, PetscBool *);

PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectFieldLocal(DM, PetscReal, Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectFieldLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectFieldLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMProjectBdFieldLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);

PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);

PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, PetscCtx), PetscCtx, PetscCtxDestroyFn *);
PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, PetscCtx), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
PETSC_EXTERN PetscErrorCode DMMonitor(DM);

static inline PetscBool DMPolytopeTypeIsHybrid(DMPolytopeType ct)
{
  switch (ct) {
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return PETSC_TRUE;
  default:
    return PETSC_FALSE;
  }
}

static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct)
{
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return 0;
  case DM_POLYTOPE_SEGMENT:
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return 1;
  case DM_POLYTOPE_TRIANGLE:
  case DM_POLYTOPE_QUADRILATERAL:
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
  case DM_POLYTOPE_UNKNOWN_FACE:
    return 2;
  case DM_POLYTOPE_TETRAHEDRON:
  case DM_POLYTOPE_HEXAHEDRON:
  case DM_POLYTOPE_TRI_PRISM:
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
  case DM_POLYTOPE_PYRAMID:
  case DM_POLYTOPE_UNKNOWN_CELL:
    return 3;
  default:
    return -1;
  }
}

static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
{
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return 0;
  case DM_POLYTOPE_SEGMENT:
    return 2;
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return 2;
  case DM_POLYTOPE_TRIANGLE:
    return 3;
  case DM_POLYTOPE_QUADRILATERAL:
    return 4;
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return 4;
  case DM_POLYTOPE_TETRAHEDRON:
    return 4;
  case DM_POLYTOPE_HEXAHEDRON:
    return 6;
  case DM_POLYTOPE_TRI_PRISM:
    return 5;
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return 5;
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return 6;
  case DM_POLYTOPE_PYRAMID:
    return 5;
  default:
    return -1;
  }
}

static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
{
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return 1;
  case DM_POLYTOPE_SEGMENT:
    return 2;
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return 2;
  case DM_POLYTOPE_TRIANGLE:
    return 3;
  case DM_POLYTOPE_QUADRILATERAL:
    return 4;
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return 4;
  case DM_POLYTOPE_TETRAHEDRON:
    return 4;
  case DM_POLYTOPE_HEXAHEDRON:
    return 8;
  case DM_POLYTOPE_TRI_PRISM:
    return 6;
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return 6;
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return 8;
  case DM_POLYTOPE_PYRAMID:
    return 5;
  default:
    return -1;
  }
}

static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
{
  return dim == 0 ? DM_POLYTOPE_POINT : (dim == 1 ? DM_POLYTOPE_SEGMENT : (dim == 2 ? (simplex ? DM_POLYTOPE_TRIANGLE : DM_POLYTOPE_QUADRILATERAL) : (dim == 3 ? (simplex ? DM_POLYTOPE_TETRAHEDRON : DM_POLYTOPE_HEXAHEDRON) : DM_POLYTOPE_UNKNOWN)));
}

static inline PetscInt DMPolytopeTypeGetNumArrangements(DMPolytopeType ct)
{
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return 1;
  case DM_POLYTOPE_SEGMENT:
    return 2;
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return 2;
  case DM_POLYTOPE_TRIANGLE:
    return 6;
  case DM_POLYTOPE_QUADRILATERAL:
    return 8;
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return 4;
  case DM_POLYTOPE_TETRAHEDRON:
    return 24;
  case DM_POLYTOPE_HEXAHEDRON:
    return 48;
  case DM_POLYTOPE_TRI_PRISM:
    return 12;
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return 12;
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return 16;
  case DM_POLYTOPE_PYRAMID:
    return 8;
  default:
    return -1;
  }
}

/* An arrangement is a face order combined with an orientation for each face */
static inline const PetscInt *DMPolytopeTypeGetArrangement(DMPolytopeType ct, PetscInt o)
{
  static const PetscInt pntArr[1 * 2] = {0, 0};
  /* a: swap */
  static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
                                             0, 0, 1, 0,
                                             /*  0: e */};
  /* a: swap first two
     b: swap last two */
  static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
                                             2, -1, 1, -1, 0, -1, /* -2: aba */
                                             1, -1, 0, -1, 2, -1, /* -1: a */
                                             0, 0,  1, 0,  2, 0,  /*  0: identity */
                                             1, 0,  2, 0,  0, 0,  /*  1: ba */
                                             2, 0,  0, 0,  1, 0,
                                             /*  2: ab */};
  /* a: forward cyclic permutation
     b: swap first and last pairs */
  static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
                                              0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
                                              3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
                                              2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
                                              0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
                                              1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
                                              2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
                                              3, 0,  0, 0,  1, 0,  2, 0,
                                              /*  3: a^3 */};
  /* r: rotate 180
     b: swap top and bottom segments */
  static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
                                              0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
                                              0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
                                              1, 0,  0, 0,  2, -1, 3, -1,
                                              /*  1: b */};
  /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
  static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
                                              3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
                                              3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
                                              2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
                                              2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
                                              2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
                                              1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
                                              1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
                                              1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
                                              0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
                                              0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
                                              0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
                                              0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
                                              0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
                                              0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
                                              1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
                                              1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
                                              1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
                                              2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
                                              2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
                                              2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
                                              3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
                                              3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
                                              3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
  /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
  static const PetscInt hexArr[48 * 6 * 2] = {
    2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
    4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
    5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
    3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
    3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
    4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
    2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
    5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
    4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
    5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
    3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
    2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
    1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
    1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
    5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
    1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
    4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
    3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
    1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
    2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
    0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
    0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
    0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
    0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
    0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
    0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
    0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
    0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
    2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
    1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
    3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
    4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
    1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
    5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
    1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
    1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
    2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
    3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
    5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
    4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
    5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
    2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
    4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
    3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
    3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
    5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
    4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
    2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
  };
  static const PetscInt tripArr[12 * 5 * 2] = {
    1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
    1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
    1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
    0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
    0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
    0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
    0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
    0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
    0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
    1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
    1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
    1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
  };
  /* a: rotate 120 about z
     b: swap top and bottom segments
     r: reflect */
  static const PetscInt ttriArr[12 * 5 * 2] = {
    1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
    1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
    1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
    0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
    0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
    0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
    0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
    0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
    0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
    1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
    1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
    1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
  };
  /* a: rotate 90 about z
     b: swap top and bottom segments
     r: reflect */
  static const PetscInt tquadArr[16 * 6 * 2] = {
    1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
    1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
    1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
    1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
    0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
    0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
    0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
    0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
    0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
    0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
    0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
    0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
    1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
    1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
    1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
    1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
  };
  static const PetscInt pyrArr[8 * 5 * 2] = {
    0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
    0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
    0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
    0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
    0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
    0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
    0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
    0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
  };
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return pntArr;
  case DM_POLYTOPE_SEGMENT:
    return &segArr[(o + 1) * 2 * 2];
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return &segArr[(o + 1) * 2 * 2];
  case DM_POLYTOPE_TRIANGLE:
    return &triArr[(o + 3) * 3 * 2];
  case DM_POLYTOPE_QUADRILATERAL:
    return &quadArr[(o + 4) * 4 * 2];
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return &tsegArr[(o + 2) * 4 * 2];
  case DM_POLYTOPE_TETRAHEDRON:
    return &tetArr[(o + 12) * 4 * 2];
  case DM_POLYTOPE_HEXAHEDRON:
    return &hexArr[(o + 24) * 6 * 2];
  case DM_POLYTOPE_TRI_PRISM:
    return &tripArr[(o + 6) * 5 * 2];
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return &ttriArr[(o + 6) * 5 * 2];
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return &tquadArr[(o + 8) * 6 * 2];
  case DM_POLYTOPE_PYRAMID:
    return &pyrArr[(o + 4) * 5 * 2];
  default:
    return PETSC_NULLPTR;
  }
}

/* A vertex arrangement is a vertex order */
static inline const PetscInt *DMPolytopeTypeGetVertexArrangement(DMPolytopeType ct, PetscInt o)
{
  static const PetscInt pntVerts[1]      = {0};
  static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
  static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
  static const PetscInt quadVerts[8 * 4] = {2, 1, 0, 3, 1, 0, 3, 2, 0, 3, 2, 1, 3, 2, 1, 0, 0, 1, 2, 3, 1, 2, 3, 0, 2, 3, 0, 1, 3, 0, 1, 2};
  static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
  static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
                                            3, 1, 2, 0, /* -11: (14)     p21 */
                                            1, 2, 3, 0, /* -10: (1234)   p18 */
                                            3, 2, 0, 1, /*  -9: (1423)   p17 */
                                            2, 0, 3, 1, /*  -8: (1342)   p13 */
                                            0, 3, 2, 1, /*  -7: (24)     p14 */
                                            0, 1, 3, 2, /*  -6: (34)     p6  */
                                            1, 3, 0, 2, /*  -5: (1243)   p10 */
                                            3, 0, 1, 2, /*  -4: (1432    p9  */
                                            1, 0, 2, 3, /*  -3: (12)     p1  */
                                            0, 2, 1, 3, /*  -2: (23)     p2  */
                                            2, 1, 0, 3, /*  -1: (13)     p5  */
                                            0, 1, 2, 3, /*   0: ()       p0  */
                                            1, 2, 0, 3, /*   1: (123)    p4  */
                                            2, 0, 1, 3, /*   2: (132)    p3  */
                                            1, 0, 3, 2, /*   3: (12)(34) p7  */
                                            0, 3, 1, 2, /*   4: (243)    p8  */
                                            3, 1, 0, 2, /*   5: (143)    p11 */
                                            2, 3, 0, 1, /*   6: (13)(24) p16 */
                                            3, 0, 2, 1, /*   7: (142)    p15 */
                                            0, 2, 3, 1, /*   8: (234)    p12 */
                                            3, 2, 1, 0, /*   9: (14)(23) p23 */
                                            2, 1, 3, 0, /*  10: (134)    p19 */
                                            1, 3, 2, 0 /*  11: (124)    p20 */};
  static const PetscInt hexVerts[48 * 8] = {
    3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
    3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
    4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
    6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
    1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
    6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
    4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
    1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
    2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
    7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
    7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
    0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
    5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
    7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
    0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
    4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
    5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
    2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
    6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
    5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
    2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
    1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
    0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
    3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
    0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
    1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
    2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
    3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
    4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
    7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
    1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
    3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
    5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
    4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
    4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
    6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
    3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
    6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
    1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
    6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
    0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
    0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
    5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
    7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
    2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
    7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
    2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
    5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
  };
  static const PetscInt tripVerts[12 * 6] = {
    4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
    5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
    3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
    1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
    0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
    2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
    0, 1, 2, 3, 4, 5, /*  0: identity */
    1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
    2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
    4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
    3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
    5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
  };
  static const PetscInt ttriVerts[12 * 6] = {
    4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
    3, 5, 4, 0, 2, 1, /* -5: r b a */
    5, 4, 3, 2, 1, 0, /* -4: r b */
    1, 0, 2, 4, 3, 5, /* -3: r a^2 */
    0, 2, 1, 3, 5, 4, /* -2: r a */
    2, 1, 0, 5, 4, 3, /* -1: r */
    0, 1, 2, 3, 4, 5, /*  0: identity */
    1, 2, 0, 4, 5, 3, /*  1: a */
    2, 0, 1, 5, 3, 4, /*  2: a^2 */
    3, 4, 5, 0, 1, 2, /*  3: b */
    4, 5, 3, 1, 2, 0, /*  4: b a */
    5, 3, 4, 2, 0, 1, /*  5: b a^2 */
  };
  /* a: rotate 90 about z
     b: swap top and bottom segments
     r: reflect */
  static const PetscInt tquadVerts[16 * 8] = {
    6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
    5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
    4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
    7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
    2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
    1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
    0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
    3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
    0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
    1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
    2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
    3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
    4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
    5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
    6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
    7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
  };
  static const PetscInt pyrVerts[8 * 5] = {
    2, 1, 0, 3, 4, /* -4: Reflect bottom face */
    1, 0, 3, 2, 4, /* -3: Reflect bottom face */
    0, 3, 2, 1, 4, /* -2: Reflect bottom face */
    3, 2, 1, 0, 4, /* -1: Reflect bottom face */
    0, 1, 2, 3, 4, /*  0: identity */
    1, 2, 3, 0, 4, /*  1:  90 rotation about z */
    2, 3, 0, 1, 4, /*  2: 180 rotation about z */
    3, 0, 1, 2, 4, /*  3: 270 rotation about z */
  };
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return pntVerts;
  case DM_POLYTOPE_SEGMENT:
    return &segVerts[(o + 1) * 2];
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return &segVerts[(o + 1) * 2];
  case DM_POLYTOPE_TRIANGLE:
    return &triVerts[(o + 3) * 3];
  case DM_POLYTOPE_QUADRILATERAL:
    return &quadVerts[(o + 4) * 4];
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return &tsegVerts[(o + 2) * 4];
  case DM_POLYTOPE_TETRAHEDRON:
    return &tetVerts[(o + 12) * 4];
  case DM_POLYTOPE_HEXAHEDRON:
    return &hexVerts[(o + 24) * 8];
  case DM_POLYTOPE_TRI_PRISM:
    return &tripVerts[(o + 6) * 6];
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return &ttriVerts[(o + 6) * 6];
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return &tquadVerts[(o + 8) * 8];
  case DM_POLYTOPE_PYRAMID:
    return &pyrVerts[(o + 4) * 5];
  default:
    return PETSC_NULLPTR;
  }
}

/* This is orientation o1 acting on orientation o2 */
static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
{
  static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
  static const PetscInt triMult[6 * 6]   = {0, 2, 1, -3, -1, -2, 1, 0, 2, -2, -3, -1, 2, 1, 0, -1, -2, -3, -3, -2, -1, 0, 1, 2, -2, -1, -3, 1, 2, 0, -1, -3, -2, 2, 0, 1};
  static const PetscInt quadMult[8 * 8]  = {0,  3,  2,  1,  -4, -1, -2, -3, 1,  0,  3,  2,  -3, -4, -1, -2, 2,  1,  0,  3,  -2, -3, -4, -1, 3,  2,  1,  0,  -1, -2, -3, -4,
                                            -4, -3, -2, -1, 0,  1,  2,  3,  -3, -2, -1, -4, 1,  2,  3,  0,  -2, -1, -4, -3, 2,  3,  0,  1,  -1, -4, -3, -2, 3,  0,  1,  2};
  static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
  static const PetscInt tetMult[24 * 24] = {
    3,   2,   7,   0,   5,   10,  9,   8,   1,   6,   11,  4,   -12, -7,  -5,  -9,  -10, -2,  -6,  -1,  -11, -3,  -4,  -8,  4,   0,   8,   1,   3,   11,  10,  6,   2,   7,   9,   5,   -11, -9,  -4,  -8,  -12, -1,  -5,  -3,  -10, -2,  -6,  -7,
    5,   1,   6,   2,   4,   9,   11,  7,   0,   8,   10,  3,   -10, -8,  -6,  -7,  -11, -3,  -4,  -2,  -12, -1,  -5,  -9,  0,   8,   4,   3,   11,  1,   6,   2,   10,  9,   5,   7,   -9,  -4,  -11, -12, -1,  -8,  -3,  -10, -5,  -6,  -7,  -2,
    1,   6,   5,   4,   9,   2,   7,   0,   11,  10,  3,   8,   -8,  -6,  -10, -11, -3,  -7,  -2,  -12, -4,  -5,  -9,  -1,  2,   7,   3,   5,   10,  0,   8,   1,   9,   11,  4,   6,   -7,  -5,  -12, -10, -2,  -9,  -1,  -11, -6,  -4,  -8,  -3,
    6,   5,   1,   9,   2,   4,   0,   11,  7,   3,   8,   10,  -6,  -10, -8,  -3,  -7,  -11, -12, -4,  -2,  -9,  -1,  -5,  7,   3,   2,   10,  0,   5,   1,   9,   8,   4,   6,   11,  -5,  -12, -7,  -2,  -9,  -10, -11, -6,  -1,  -8,  -3,  -4,
    8,   4,   0,   11,  1,   3,   2,   10,  6,   5,   7,   9,   -4,  -11, -9,  -1,  -8,  -12, -10, -5,  -3,  -7,  -2,  -6,  9,   11,  10,  6,   8,   7,   3,   5,   4,   0,   2,   1,   -3,  -1,  -2,  -6,  -4,  -5,  -9,  -7,  -8,  -12, -10, -11,
    10,  9,   11,  7,   6,   8,   4,   3,   5,   1,   0,   2,   -2,  -3,  -1,  -5,  -6,  -4,  -8,  -9,  -7,  -11, -12, -10, 11,  10,  9,   8,   7,   6,   5,   4,   3,   2,   1,   0,   -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9,  -10, -11, -12,
    -12, -11, -10, -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   10,  11,  -11, -10, -12, -8,  -7,  -9,  -5,  -4,  -6,  -2,  -1,  -3,  1,   2,   0,   4,   5,   3,   7,   8,   6,   10,  11,  9,
    -10, -12, -11, -7,  -9,  -8,  -4,  -6,  -5,  -1,  -3,  -2,  2,   0,   1,   5,   3,   4,   8,   6,   7,   11,  9,   10,  -9,  -5,  -1,  -12, -2,  -4,  -3,  -11, -7,  -6,  -8,  -10, 3,   10,  8,   0,   7,   11,  9,   4,   2,   6,   1,   5,
    -8,  -4,  -3,  -11, -1,  -6,  -2,  -10, -9,  -5,  -7,  -12, 4,   11,  6,   1,   8,   9,   10,  5,   0,   7,   2,   3,   -7,  -6,  -2,  -10, -3,  -5,  -1,  -12, -8,  -4,  -9,  -11, 5,   9,   7,   2,   6,   10,  11,  3,   1,   8,   0,   4,
    -3,  -8,  -4,  -6,  -11, -1,  -9,  -2,  -10, -12, -5,  -7,  6,   4,   11,  9,   1,   8,   0,   10,  5,   3,   7,   2,   -2,  -7,  -6,  -5,  -10, -3,  -8,  -1,  -12, -11, -4,  -9,  7,   5,   9,   10,  2,   6,   1,   11,  3,   4,   8,   0,
    -1,  -9,  -5,  -4,  -12, -2,  -7,  -3,  -11, -10, -6,  -8,  8,   3,   10,  11,  0,   7,   2,   9,   4,   5,   6,   1,   -6,  -2,  -7,  -3,  -5,  -10, -12, -8,  -1,  -9,  -11, -4,  9,   7,   5,   6,   10,  2,   3,   1,   11,  0,   4,   8,
    -5,  -1,  -9,  -2,  -4,  -12, -11, -7,  -3,  -8,  -10, -6,  10,  8,   3,   7,   11,  0,   4,   2,   9,   1,   5,   6,   -4,  -3,  -8,  -1,  -6,  -11, -10, -9,  -2,  -7,  -12, -5,  11,  6,   4,   8,   9,   1,   5,   0,   10,  2,   3,   7,
  };
  static const PetscInt hexMult[48 * 48] = {
    18,  2,   5,   22,  21,  8,   16,  0,   13,  6,   11,  3,   15,  9,   4,   23,  12,  1,   19,  10,  7,   20,  14,  17,  -24, -10, -20, -16, -12, -21, -4,  -5,  -18, -13, -15, -8,  -2,  -11, -14, -7,  -3,  -22, -6,  -17, -19, -9,  -1,  -23,
    8,   20,  19,  2,   5,   23,  0,   17,  11,  1,   15,  7,   13,  4,   10,  18,  3,   14,  21,  9,   12,  22,  6,   16,  -23, -13, -17, -7,  -8,  -19, -16, -12, -22, -2,  -14, -5,  -10, -15, -11, -4,  -20, -9,  -21, -3,  -6,  -18, -24, -1,
    2,   17,  23,  8,   0,   19,  5,   20,  1,   11,  9,   14,  12,  6,   3,   16,  10,  7,   22,  15,  13,  21,  4,   18,  -22, -14, -19, -5,  -15, -17, -10, -2,  -23, -12, -13, -7,  -16, -8,  -4,  -11, -24, -3,  -18, -9,  -1,  -21, -20, -6,
    21,  5,   2,   16,  18,  0,   22,  8,   4,   12,  3,   11,  14,  7,   13,  20,  6,   10,  17,  1,   9,   23,  15,  19,  -21, -8,  -18, -15, -4,  -24, -12, -14, -20, -7,  -16, -10, -11, -2,  -5,  -13, -6,  -19, -3,  -23, -22, -1,  -9,  -17,
    16,  8,   0,   21,  22,  2,   18,  5,   12,  4,   1,   10,  9,   15,  6,   19,  13,  11,  23,  3,   14,  17,  7,   20,  -20, -16, -24, -10, -2,  -18, -11, -7,  -21, -14, -8,  -15, -12, -4,  -13, -5,  -9,  -23, -1,  -19, -17, -3,  -6,  -22,
    5,   19,  20,  0,   8,   17,  2,   23,  10,  3,   7,   15,  6,   12,  11,  22,  1,   9,   16,  14,  4,   18,  13,  21,  -19, -5,  -22, -14, -16, -23, -8,  -11, -17, -4,  -7,  -13, -15, -10, -12, -2,  -21, -6,  -20, -1,  -9,  -24, -18, -3,
    22,  0,   8,   18,  16,  5,   21,  2,   6,   13,  10,  1,   7,   14,  12,  17,  4,   3,   20,  11,  15,  19,  9,   23,  -18, -15, -21, -8,  -11, -20, -2,  -13, -24, -5,  -10, -16, -4,  -12, -7,  -14, -1,  -17, -9,  -22, -23, -6,  -3,  -19,
    0,   23,  17,  5,   2,   20,  8,   19,  3,   10,  14,  9,   4,   13,  1,   21,  11,  15,  18,  7,   6,   16,  12,  22,  -17, -7,  -23, -13, -10, -22, -15, -4,  -19, -11, -5,  -14, -8,  -16, -2,  -12, -18, -1,  -24, -6,  -3,  -20, -21, -9,
    10,  13,  6,   1,   11,  12,  3,   4,   8,   0,   22,  18,  19,  23,  5,   15,  2,   21,  9,   16,  17,  7,   20,  14,  -16, -24, -10, -20, -23, -8,  -19, -6,  -15, -3,  -21, -18, -22, -17, -9,  -1,  -14, -12, -7,  -4,  -11, -13, -5,  -2,
    1,   4,   12,  10,  3,   6,   11,  13,  0,   8,   16,  21,  17,  20,  2,   14,  5,   18,  7,   22,  19,  9,   23,  15,  -15, -21, -8,  -18, -17, -10, -22, -3,  -16, -6,  -24, -20, -19, -23, -1,  -9,  -5,  -4,  -13, -12, -2,  -7,  -14, -11,
    14,  10,  3,   9,   7,   1,   15,  11,  17,  23,  0,   5,   16,  22,  20,  6,   19,  8,   12,  2,   21,  4,   18,  13,  -14, -19, -5,  -22, -3,  -13, -9,  -20, -7,  -21, -23, -17, -6,  -1,  -24, -18, -12, -16, -2,  -8,  -10, -4,  -11, -15,
    7,   3,   10,  15,  14,  11,  9,   1,   20,  19,  5,   0,   18,  21,  17,  4,   23,  2,   13,  8,   22,  6,   16,  12,  -13, -17, -7,  -23, -9,  -14, -3,  -24, -5,  -18, -22, -19, -1,  -6,  -20, -21, -2,  -10, -12, -15, -16, -11, -4,  -8,
    13,  14,  15,  12,  4,   9,   6,   7,   21,  22,  23,  20,  2,   0,   18,  3,   16,  17,  1,   19,  8,   11,  5,   10,  -12, -9,  -11, -6,  -21, -4,  -24, -22, -2,  -23, -3,  -1,  -20, -18, -19, -17, -16, -14, -15, -13, -5,  -8,  -10, -7,
    6,   9,   7,   4,   12,  14,  13,  15,  16,  18,  17,  19,  0,   2,   22,  1,   21,  23,  3,   20,  5,   10,  8,   11,  -11, -6,  -12, -9,  -20, -2,  -18, -17, -4,  -19, -1,  -3,  -21, -24, -23, -22, -8,  -7,  -10, -5,  -13, -16, -15, -14,
    3,   12,  4,   11,  1,   13,  10,  6,   2,   5,   21,  16,  23,  19,  0,   9,   8,   22,  15,  18,  20,  14,  17,  7,   -10, -20, -16, -24, -22, -15, -17, -1,  -8,  -9,  -18, -21, -23, -19, -3,  -6,  -13, -2,  -5,  -11, -4,  -14, -7,  -12,
    20,  16,  18,  23,  17,  21,  19,  22,  14,  15,  4,   6,   3,   1,   7,   0,   9,   12,  2,   13,  11,  5,   10,  8,   -9,  -11, -6,  -12, -14, -3,  -13, -10, -1,  -8,  -2,  -4,  -7,  -5,  -16, -15, -23, -20, -22, -18, -24, -19, -17, -21,
    11,  6,   13,  3,   10,  4,   1,   12,  5,   2,   18,  22,  20,  17,  8,   7,   0,   16,  14,  21,  23,  15,  19,  9,   -8,  -18, -15, -21, -19, -16, -23, -9,  -10, -1,  -20, -24, -17, -22, -6,  -3,  -7,  -11, -14, -2,  -12, -5,  -13, -4,
    9,   11,  1,   14,  15,  3,   7,   10,  23,  17,  2,   8,   21,  18,  19,  13,  20,  5,   4,   0,   16,  12,  22,  6,   -7,  -23, -13, -17, -1,  -5,  -6,  -21, -14, -20, -19, -22, -9,  -3,  -18, -24, -11, -8,  -4,  -16, -15, -2,  -12, -10,
    19,  21,  22,  17,  23,  16,  20,  18,  9,   7,   12,  13,  1,   3,   15,  2,   14,  4,   0,   6,   10,  8,   11,  5,   -6,  -12, -9,  -11, -7,  -1,  -5,  -15, -3,  -16, -4,  -2,  -14, -13, -8,  -10, -19, -21, -17, -24, -18, -23, -22, -20,
    15,  1,   11,  7,   9,   10,  14,  3,   19,  20,  8,   2,   22,  16,  23,  12,  17,  0,   6,   5,   18,  13,  21,  4,   -5,  -22, -14, -19, -6,  -7,  -1,  -18, -13, -24, -17, -23, -3,  -9,  -21, -20, -4,  -15, -11, -10, -8,  -12, -2,  -16,
    4,   15,  14,  6,   13,  7,   12,  9,   18,  16,  20,  23,  5,   8,   21,  11,  22,  19,  10,  17,  0,   3,   2,   1,   -4,  -1,  -2,  -3,  -24, -12, -21, -19, -11, -17, -6,  -9,  -18, -20, -22, -23, -15, -5,  -16, -7,  -14, -10, -8,  -13,
    17,  18,  16,  19,  20,  22,  23,  21,  7,   9,   6,   4,   10,  11,  14,  5,   15,  13,  8,   12,  1,   0,   3,   2,   -3,  -4,  -1,  -2,  -13, -9,  -14, -16, -6,  -15, -12, -11, -5,  -7,  -10, -8,  -22, -24, -23, -21, -20, -17, -19, -18,
    12,  7,   9,   13,  6,   15,  4,   14,  22,  21,  19,  17,  8,   5,   16,  10,  18,  20,  11,  23,  2,   1,   0,   3,   -2,  -3,  -4,  -1,  -18, -11, -20, -23, -12, -22, -9,  -6,  -24, -21, -17, -19, -10, -13, -8,  -14, -7,  -15, -16, -5,
    23,  22,  21,  20,  19,  18,  17,  16,  15,  14,  13,  12,  11,  10,  9,   8,   7,   6,   5,   4,   3,   2,   1,   0,   -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9,  -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24,
    -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   10,  11,  12,  13,  14,  15,  16,  17,  18,  19,  20,  21,  22,  23,
    -13, -8,  -10, -14, -7,  -16, -5,  -15, -23, -22, -20, -18, -9,  -6,  -17, -11, -19, -21, -12, -24, -3,  -2,  -1,  -4,  1,   2,   3,   0,   17,  10,  19,  22,  11,  21,  8,   5,   23,  20,  16,  18,  9,   12,  7,   13,  6,   14,  15,  4,
    -18, -19, -17, -20, -21, -23, -24, -22, -8,  -10, -7,  -5,  -11, -12, -15, -6,  -16, -14, -9,  -13, -2,  -1,  -4,  -3,  2,   3,   0,   1,   12,  8,   13,  15,  5,   14,  11,  10,  4,   6,   9,   7,   21,  23,  22,  20,  19,  16,  18,  17,
    -5,  -16, -15, -7,  -14, -8,  -13, -10, -19, -17, -21, -24, -6,  -9,  -22, -12, -23, -20, -11, -18, -1,  -4,  -3,  -2,  3,   0,   1,   2,   23,  11,  20,  18,  10,  16,  5,   8,   17,  19,  21,  22,  14,  4,   15,  6,   13,  9,   7,   12,
    -16, -2,  -12, -8,  -10, -11, -15, -4,  -20, -21, -9,  -3,  -23, -17, -24, -13, -18, -1,  -7,  -6,  -19, -14, -22, -5,  4,   21,  13,  18,  5,   6,   0,   17,  12,  23,  16,  22,  2,   8,   20,  19,  3,   14,  10,  9,   7,   11,  1,   15,
    -20, -22, -23, -18, -24, -17, -21, -19, -10, -8,  -13, -14, -2,  -4,  -16, -3,  -15, -5,  -1,  -7,  -11, -9,  -12, -6,  5,   11,  8,   10,  6,   0,   4,   14,  2,   15,  3,   1,   13,  12,  7,   9,   18,  20,  16,  23,  17,  22,  21,  19,
    -10, -12, -2,  -15, -16, -4,  -8,  -11, -24, -18, -3,  -9,  -22, -19, -20, -14, -21, -6,  -5,  -1,  -17, -13, -23, -7,  6,   22,  12,  16,  0,   4,   5,   20,  13,  19,  18,  21,  8,   2,   17,  23,  10,  7,   3,   15,  14,  1,   11,  9,
    -12, -7,  -14, -4,  -11, -5,  -2,  -13, -6,  -3,  -19, -23, -21, -18, -9,  -8,  -1,  -17, -15, -22, -24, -16, -20, -10, 7,   17,  14,  20,  18,  15,  22,  8,   9,   0,   19,  23,  16,  21,  5,   2,   6,   10,  13,  1,   11,  4,   12,  3,
    -21, -17, -19, -24, -18, -22, -20, -23, -15, -16, -5,  -7,  -4,  -2,  -8,  -1,  -10, -13, -3,  -14, -12, -6,  -11, -9,  8,   10,  5,   11,  13,  2,   12,  9,   0,   7,   1,   3,   6,   4,   15,  14,  22,  19,  21,  17,  23,  18,  16,  20,
    -4,  -13, -5,  -12, -2,  -14, -11, -7,  -3,  -6,  -22, -17, -24, -20, -1,  -10, -9,  -23, -16, -19, -21, -15, -18, -8,  9,   19,  15,  23,  21,  14,  16,  0,   7,   8,   17,  20,  22,  18,  2,   5,   12,  1,   4,   10,  3,   13,  6,   11,
    -7,  -10, -8,  -5,  -13, -15, -14, -16, -17, -19, -18, -20, -1,  -3,  -23, -2,  -22, -24, -4,  -21, -6,  -11, -9,  -12, 10,  5,   11,  8,   19,  1,   17,  16,  3,   18,  0,   2,   20,  23,  22,  21,  7,   6,   9,   4,   12,  15,  14,  13,
    -14, -15, -16, -13, -5,  -10, -7,  -8,  -22, -23, -24, -21, -3,  -1,  -19, -4,  -17, -18, -2,  -20, -9,  -12, -6,  -11, 11,  8,   10,  5,   20,  3,   23,  21,  1,   22,  2,   0,   19,  17,  18,  16,  15,  13,  14,  12,  4,   7,   9,   6,
    -8,  -4,  -11, -16, -15, -12, -10, -2,  -21, -20, -6,  -1,  -19, -22, -18, -5,  -24, -3,  -14, -9,  -23, -7,  -17, -13, 12,  16,  6,   22,  8,   13,  2,   23,  4,   17,  21,  18,  0,   5,   19,  20,  1,   9,   11,  14,  15,  10,  3,   7,
    -15, -11, -4,  -10, -8,  -2,  -16, -12, -18, -24, -1,  -6,  -17, -23, -21, -7,  -20, -9,  -13, -3,  -22, -5,  -19, -14, 13,  18,  4,   21,  2,   12,  8,   19,  6,   20,  22,  16,  5,   0,   23,  17,  11,  15,  1,   7,   9,   3,   10,  14,
    -2,  -5,  -13, -11, -4,  -7,  -12, -14, -1,  -9,  -17, -22, -18, -21, -3,  -15, -6,  -19, -8,  -23, -20, -10, -24, -16, 14,  20,  7,   17,  16,  9,   21,  2,   15,  5,   23,  19,  18,  22,  0,   8,   4,   3,   12,  11,  1,   6,   13,  10,
    -11, -14, -7,  -2,  -12, -13, -4,  -5,  -9,  -1,  -23, -19, -20, -24, -6,  -16, -3,  -22, -10, -17, -18, -8,  -21, -15, 15,  23,  9,   19,  22,  7,   18,  5,   14,  2,   20,  17,  21,  16,  8,   0,   13,  11,  6,   3,   10,  12,  4,   1,
    -1,  -24, -18, -6,  -3,  -21, -9,  -20, -4,  -11, -15, -10, -5,  -14, -2,  -22, -12, -16, -19, -8,  -7,  -17, -13, -23, 16,  6,   22,  12,  9,   21,  14,  3,   18,  10,  4,   13,  7,   15,  1,   11,  17,  0,   23,  5,   2,   19,  20,  8,
    -23, -1,  -9,  -19, -17, -6,  -22, -3,  -7,  -14, -11, -2,  -8,  -15, -13, -18, -5,  -4,  -21, -12, -16, -20, -10, -24, 17,  14,  20,  7,   10,  19,  1,   12,  23,  4,   9,   15,  3,   11,  6,   13,  0,   16,  8,   21,  22,  5,   2,   18,
    -6,  -20, -21, -1,  -9,  -18, -3,  -24, -11, -4,  -8,  -16, -7,  -13, -12, -23, -2,  -10, -17, -15, -5,  -19, -14, -22, 18,  4,   21,  13,  15,  22,  7,   10,  16,  3,   6,   12,  14,  9,   11,  1,   20,  5,   19,  0,   8,   23,  17,  2,
    -17, -9,  -1,  -22, -23, -3,  -19, -6,  -13, -5,  -2,  -11, -10, -16, -7,  -20, -14, -12, -24, -4,  -15, -18, -8,  -21, 19,  15,  23,  9,   1,   17,  10,  6,   20,  13,  7,   14,  11,  3,   12,  4,   8,   22,  0,   18,  16,  2,   5,   21,
    -22, -6,  -3,  -17, -19, -1,  -23, -9,  -5,  -13, -4,  -12, -15, -8,  -14, -21, -7,  -11, -18, -2,  -10, -24, -16, -20, 20,  7,   17,  14,  3,   23,  11,  13,  19,  6,   15,  9,   10,  1,   4,   12,  5,   18,  2,   22,  21,  0,   8,   16,
    -3,  -18, -24, -9,  -1,  -20, -6,  -21, -2,  -12, -10, -15, -13, -7,  -4,  -17, -11, -8,  -23, -16, -14, -22, -5,  -19, 21,  13,  18,  4,   14,  16,  9,   1,   22,  11,  12,  6,   15,  7,   3,   10,  23,  2,   17,  8,   0,   20,  19,  5,
    -9,  -21, -20, -3,  -6,  -24, -1,  -18, -12, -2,  -16, -8,  -14, -5,  -11, -19, -4,  -15, -22, -10, -13, -23, -7,  -17, 22,  12,  16,  6,   7,   18,  15,  11,  21,  1,   13,  4,   9,   14,  10,  3,   19,  8,   20,  2,   5,   17,  23,  0,
    -19, -3,  -6,  -23, -22, -9,  -17, -1,  -14, -7,  -12, -4,  -16, -10, -5,  -24, -13, -2,  -20, -11, -8,  -21, -15, -18, 23,  9,   19,  15,  11,  20,  3,   4,   17,  12,  14,  7,   1,   10,  13,  6,   2,   21,  5,   16,  18,  8,   0,   22,
  };
  static const PetscInt tripMult[12 * 12] = {
    1,  0,  2,  3,  5,  4,  -6, -4, -5, -2, -3, -1, 0,  2,  1,  4,  3,  5,  -5, -6, -4, -3, -1, -2, 2,  1,  0,  5,  4,  3,  -4, -5, -6, -1, -2, -3, 4,  3,  5,  0,  2,  1,  -3, -1, -2, -5, -6, -4,
    3,  5,  4,  1,  0,  2,  -2, -3, -1, -6, -4, -5, 5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  -4, -6, -5, -2, -1, -3, 1,  2,  0,  5,  3,  4,
    -5, -4, -6, -1, -3, -2, 2,  0,  1,  4,  5,  3,  -3, -2, -1, -6, -5, -4, 3,  4,  5,  0,  1,  2,  -1, -3, -2, -5, -4, -6, 4,  5,  3,  2,  0,  1,  -2, -1, -3, -4, -6, -5, 5,  3,  4,  1,  2,  0,
  };
  static const PetscInt ttriMult[12 * 12] = {
    0,  2,  1,  3,  5,  4,  -6, -4, -5, -3, -1, -2, 1,  0,  2,  4,  3,  5,  -5, -6, -4, -2, -3, -1, 2,  1,  0,  5,  4,  3,  -4, -5, -6, -1, -2, -3, 3,  5,  4,  0,  2,  1,  -3, -1, -2, -6, -4, -5,
    4,  3,  5,  1,  0,  2,  -2, -3, -1, -5, -6, -4, 5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  -5, -4, -6, -2, -1, -3, 1,  2,  0,  4,  5,  3,
    -4, -6, -5, -1, -3, -2, 2,  0,  1,  5,  3,  4,  -3, -2, -1, -6, -5, -4, 3,  4,  5,  0,  1,  2,  -2, -1, -3, -5, -4, -6, 4,  5,  3,  1,  2,  0,  -1, -3, -2, -4, -6, -5, 5,  3,  4,  2,  0,  1,
  };
  static const PetscInt tquadMult[16 * 16] = {
    0,  3,  2,  1,  4,  7,  6,  5,  -8, -5, -6, -7, -4, -1, -2, -3, 1,  0,  3,  2,  5,  4,  7,  6,  -7, -8, -5, -6, -3, -4, -1, -2, 2,  1,  0,  3,  6,  5,  4,  7,  -6, -7, -8, -5, -2, -3, -4, -1, 3, 2, 1, 0,
    7,  6,  5,  4,  -5, -6, -7, -8, -1, -2, -3, -4, 4,  7,  6,  5,  0,  3,  2,  1,  -4, -1, -2, -3, -8, -5, -6, -7, 5,  4,  7,  6,  1,  0,  3,  2,  -3, -4, -1, -2, -7, -8, -5, -6, 6,  5,  4,  7,  2, 1, 0, 3,
    -2, -3, -4, -1, -6, -7, -8, -5, 7,  6,  5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -7, -8, -8, -7, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  6,  7,  -7, -6, -5, -8, -3, -2, -1, -4, 1, 2, 3, 0,
    5,  6,  7,  4,  -6, -5, -8, -7, -2, -1, -4, -3, 2,  3,  0,  1,  6,  7,  4,  5,  -5, -8, -7, -6, -1, -4, -3, -2, 3,  0,  1,  2,  7,  4,  5,  6,  -4, -3, -2, -1, -8, -7, -6, -5, 4,  5,  6,  7,  0, 1, 2, 3,
    -3, -2, -1, -4, -7, -6, -5, -8, 5,  6,  7,  4,  1,  2,  3,  0,  -2, -1, -4, -3, -6, -5, -8, -7, 6,  7,  4,  5,  2,  3,  0,  1,  -1, -4, -3, -2, -5, -8, -7, -6, 7,  4,  5,  6,  3,  0,  1,  2,
  };
  static const PetscInt pyrMult[8 * 8] = {
    0, 3, 2, 1, -4, -1, -2, -3, 1, 0, 3, 2, -3, -4, -1, -2, 2, 1, 0, 3, -2, -3, -4, -1, 3, 2, 1, 0, -1, -2, -3, -4, -4, -3, -2, -1, 0, 1, 2, 3, -3, -2, -1, -4, 1, 2, 3, 0, -2, -1, -4, -3, 2, 3, 0, 1, -1, -4, -3, -2, 3, 0, 1, 2,
  };
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return 0;
  case DM_POLYTOPE_SEGMENT:
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return segMult[(o1 + 1) * 2 + o2 + 1];
  case DM_POLYTOPE_TRIANGLE:
    return triMult[(o1 + 3) * 6 + o2 + 3];
  case DM_POLYTOPE_QUADRILATERAL:
    return quadMult[(o1 + 4) * 8 + o2 + 4];
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return tsegMult[(o1 + 2) * 4 + o2 + 2];
  case DM_POLYTOPE_TETRAHEDRON:
    return tetMult[(o1 + 12) * 24 + o2 + 12];
  case DM_POLYTOPE_HEXAHEDRON:
    return hexMult[(o1 + 24) * 48 + o2 + 24];
  case DM_POLYTOPE_TRI_PRISM:
    return tripMult[(o1 + 6) * 12 + o2 + 6];
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return ttriMult[(o1 + 6) * 12 + o2 + 6];
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return tquadMult[(o1 + 8) * 16 + o2 + 8];
  case DM_POLYTOPE_PYRAMID:
    return pyrMult[(o1 + 4) * 8 + o2 + 4];
  default:
    return 0;
  }
}

/* This is orientation o1 acting on orientation o2^{-1} */
static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
{
  static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
  static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
  static const PetscInt tetInv[24]   = {-9, -11, -4, -12, -5, -7, -6, -8, -10, -3, -2, -1, 0, 2, 1, 3, 8, 10, 6, 11, 4, 9, 5, 7};
  static const PetscInt hexInv[48]   = {-17, -18, -20, -19, -22, -21, -23, -24, -15, -16, -14, -13, -11, -12, -10, -9, -8, -5, -6, -7, -4, -3, -2, -1, 0, 3, 2, 1, 6, 5, 4, 9, 8, 7, 10, 11, 12, 13, 14, 15, 17, 16, 19, 18, 21, 20, 23, 22};
  static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
  static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
  static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
  static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
  switch (ct) {
  case DM_POLYTOPE_POINT:
    return 0;
  case DM_POLYTOPE_SEGMENT:
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    return DMPolytopeTypeComposeOrientation(ct, o1, o2);
  case DM_POLYTOPE_TRIANGLE:
    return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
  case DM_POLYTOPE_QUADRILATERAL:
    return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    return DMPolytopeTypeComposeOrientation(ct, o1, o2);
  case DM_POLYTOPE_TETRAHEDRON:
    return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
  case DM_POLYTOPE_HEXAHEDRON:
    return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
  case DM_POLYTOPE_TRI_PRISM:
    return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
    return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
  case DM_POLYTOPE_PYRAMID:
    return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
  default:
    return 0;
  }
}

PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);
