Adding simplify flag to group().

engine/triangulation/detail/algebra-impl.h

@@ -174,15 +174,27 @@ AbelianGroup TriangulationBase<dim>::homology() const {
 }
 
 template <int dim>
-const GroupPresentation& TriangulationBase<dim>::group() const {
-    if (fundGroup_.has_value())
-        return *fundGroup_;
-
+const GroupPresentation& TriangulationBase<dim>::group(bool simplify) const {
+    if (simplify) {
+        if (simplifiedFundGroup_)
+            return *simplifiedFundGroup_;
+        if (isEmpty())
+            return *(simplifiedFundGroup_ = GroupPresentation());
+        GroupPresentation ans =
+            fundGroup_ ? *fundGroup_ : unsimplifiedGroup();
+        ans.intelligentSimplify();
+        return *(simplifiedFundGroup_ = std::move(ans));
+    } else {
+        if (isEmpty())
+            return *(fundGroup_ = GroupPresentation());
+        return *(fundGroup_ = unsimplifiedGroup());
+    }
+}
+
+template <int dim>
+GroupPresentation TriangulationBase<dim>::unsimplifiedGroup() const {
     GroupPresentation ans;
-
-    if (isEmpty())
-        return *(fundGroup_ = std::move(ans));
-
+
     // Calculate a maximal forest in the dual 1-skeleton.
     ensureSkeleton();
 
@@ -199,7 +211,8 @@ const GroupPresentation& TriangulationBase<dim>::group() const {
     ans.addGenerator(nGens);
 
     // Find out which (dim-1)-face corresponds to which generator.
-    long* genIndex = new long[countFaces<dim-1>()];
+    std::unique_ptr<long[]> genIndex =
+        std::make_unique<long[]>(countFaces<dim-1>());
     long i = 0;
     for (Face<dim, dim-1>* f : faces<dim-1>())
         if (! (f->isBoundary() || f->inMaximalForest()))
@@ -234,11 +247,7 @@ const GroupPresentation& TriangulationBase<dim>::group() const {
         }
     }
 
-    // Tidy up.
-    delete[] genIndex;
-    ans.intelligentSimplify();
-
-    return *(fundGroup_ = std::move(ans));
+    return ans;
 }
 
 template <int dim>

engine/triangulation/detail/skeleton-impl.h

@@ -607,6 +607,7 @@ void TriangulationBase<dim>::clearBaseProperties() {
     // Clear properties.
     if (! topologyLock_) {
         fundGroup_.reset();
+        simplifiedFundGroup_.reset();
         H1_.reset();
     }
 }
@@ -634,6 +635,7 @@ void TriangulationBase<dim>::swapBaseData(TriangulationBase<dim>& other) {
     faces_.swap(other.faces_);
     nBoundaryFaces_.swap(other.nBoundaryFaces_);
     fundGroup_.swap(other.fundGroup_);
+    simplifiedFundGroup_.swap(other.simplifiedFundGroup_);
     H1_.swap(other.H1_);
 }
 

engine/triangulation/detail/triangulation.h

@@ -241,6 +241,12 @@ class TriangulationBase :
         mutable std::optional<GroupPresentation> fundGroup_;
             /**< Fundamental group of the triangulation.
                  This is std::nullopt if it has not yet been computed. */
+        mutable std::optional<GroupPresentation> simplifiedFundGroup_;
+            /**< Simplified fundamental group of the triangulation.
+                 It was either computed from fundGroup_ by
+                 GroupPresentation::intelligentSimplify or set by the
+                 user through setGroupPresentation.
+                 This is std::nullopt if it has not yet been computed. */
         mutable std::optional<AbelianGroup> H1_;
             /**< First homology group of the triangulation.
                  This is std::nullopt if it has not yet been computed. */
@@ -1327,7 +1333,8 @@ class TriangulationBase :
         /*@{*/
 
         /**
-         * Returns the fundamental group of this triangulation.
+         * Returns the unsimplified or simplified (default) presentation of
+         * the fundamental group of this triangulation.
          *
          * The fundamental group is computed in the dual 2-skeleton.  This
          * means:
@@ -1350,6 +1357,15 @@ class TriangulationBase :
          *   barycentric subdivision is performed on a such a triangulation,
          *   the result of group() might change.
          *
+         * By default, the presentation will be simplified. The unsimplified
+         * presentation can be obtained by passing simplify = false as
+         * argument. In the unsimplified presentation, the generators
+         * correspond to those facet-pairings that are not dual to edges
+         * in the maximal forest in the dual 2-skeleton chosen by regina
+         * (those facet-pairings can be found by checking that neither
+         * Face<dim, dim-1>::isBoundary() nor
+         * Face<dim, dim-1>::inMaximalForest returns true).
+         *
          * Bear in mind that each time the triangulation changes, the
          * fundamental group will be deleted.  Thus the reference that is
          * returned from this routine should not be kept for later use.
@@ -1370,9 +1386,12 @@ class TriangulationBase :
          * fundamental group with fillings, call
          * SnapPeaTriangulation::fundamentalGroupFilled() instead.
          *
-         * \return the fundamental group.
+         * \param simplify \c true if the presentation should be simplified
+         * (default to \c true).
+         *
+         * \return A presentation of the fundamental group.
          */
-        const GroupPresentation& group() const;
+        const GroupPresentation& group(bool simplify = true) const;
         /**
          * An alias for group(), which returns the fundamental group of this
          * triangulation.
@@ -1394,9 +1413,9 @@ class TriangulationBase :
          * fundamental group with fillings, call
          * SnapPeaTriangulation::fundamentalGroupFilled() instead.
          *
-         * \return the fundamental group.
+         * \return a presentation of the fundamental group.
          */
-        const GroupPresentation& fundamentalGroup() const;
+        const GroupPresentation& fundamentalGroup(bool simplify = true) const;
         /**
          * Allows the specific presentation of the fundamental group to be
          * changed by some other (external) means.
@@ -3582,6 +3601,14 @@ class TriangulationBase :
         bool sameDegreesAt(const TriangulationBase& other,
             std::integer_sequence<int, useDim...>) const;
 
+        /**
+         * Computes unsimplified presentation of fundamental group.
+         *
+         * \return Unsimplified presentation of fundamental group.
+         */
+        GroupPresentation
+        unsimplifiedGroup() const;
+
     protected:
         /**
          * An object that facilitates both firing change events and
@@ -3828,6 +3855,7 @@ TriangulationBase<dim>::TriangulationBase(const TriangulationBase<dim>& src,
     // Clone properties:
     if (cloneProps) {
         fundGroup_ = src.fundGroup_;
+        simplifiedFundGroup_ = src.simplifiedFundGroup_;
         H1_ = src.H1_;
     }
 }
@@ -3842,6 +3870,7 @@ TriangulationBase<dim>::TriangulationBase(TriangulationBase<dim>&& src)
         calculatedSkeleton_(src.calculatedSkeleton_),
         orientable_(src.orientable_),
         fundGroup_(std::move(src.fundGroup_)),
+        simplifiedFundGroup_(std::move(src.simplifiedFundGroup_)),
         H1_(std::move(src.H1_)) {
     // For our simplices and skeletal components, we use swaps instead
     // of moves because we need to ensure that src's lists finish empty.
@@ -3910,6 +3939,7 @@ TriangulationBase<dim>& TriangulationBase<dim>::operator =
 
     // Clone properties:
     fundGroup_ = src.fundGroup_;
+    simplifiedFundGroup_ = src.simplifiedFundGroup_;
     H1_ = src.H1_;
 
     return *this;
@@ -3948,6 +3978,7 @@ TriangulationBase<dim>& TriangulationBase<dim>::operator =
     std::swap(calculatedSkeleton_, src.calculatedSkeleton_);
 
     fundGroup_ = std::move(src.fundGroup_);
+    simplifiedFundGroup_ = std::move(src.simplifiedFundGroup_);
     H1_ = std::move(src.H1_);
 
     // Let src dispose of the original simplices and skeletal objects in
@@ -4966,9 +4997,10 @@ std::vector<Triangulation<dim>>
 }
 
 template <int dim>
-inline const GroupPresentation& TriangulationBase<dim>::fundamentalGroup()
+inline const GroupPresentation& TriangulationBase<dim>::fundamentalGroup(
+        const bool simplify)
         const {
-    return group();
+    return group(simplify);
 }
 
 template <int dim>

engine/triangulation/explicit/triangulation10.cpp

@@ -89,7 +89,7 @@ template MatrixInt TriangulationBase<10>::dualToPrimal<7>() const;
 template MatrixInt TriangulationBase<10>::dualToPrimal<8>() const;
 template MatrixInt TriangulationBase<10>::dualToPrimal<9>() const;
 
-template const GroupPresentation& TriangulationBase<10>::group() const;
+template const GroupPresentation& TriangulationBase<10>::group(bool) const;
 
 template void TriangulationBase<10>::calculateSkeleton();
 template void TriangulationBase<10>::cloneSkeleton(

engine/triangulation/explicit/triangulation11.cpp

@@ -93,7 +93,7 @@ template MatrixInt TriangulationBase<11>::dualToPrimal<8>() const;
 template MatrixInt TriangulationBase<11>::dualToPrimal<9>() const;
 template MatrixInt TriangulationBase<11>::dualToPrimal<10>() const;
 
-template const GroupPresentation& TriangulationBase<11>::group() const;
+template const GroupPresentation& TriangulationBase<11>::group(bool) const;
 
 template void TriangulationBase<11>::calculateSkeleton();
 template void TriangulationBase<11>::cloneSkeleton(

engine/triangulation/explicit/triangulation12.cpp

@@ -97,7 +97,7 @@ template MatrixInt TriangulationBase<12>::dualToPrimal<9>() const;
 template MatrixInt TriangulationBase<12>::dualToPrimal<10>() const;
 template MatrixInt TriangulationBase<12>::dualToPrimal<11>() const;
 
-template const GroupPresentation& TriangulationBase<12>::group() const;
+template const GroupPresentation& TriangulationBase<12>::group(bool) const;
 
 template void TriangulationBase<12>::calculateSkeleton();
 template void TriangulationBase<12>::cloneSkeleton(

engine/triangulation/explicit/triangulation13.cpp

@@ -101,7 +101,7 @@ template MatrixInt TriangulationBase<13>::dualToPrimal<10>() const;
 template MatrixInt TriangulationBase<13>::dualToPrimal<11>() const;
 template MatrixInt TriangulationBase<13>::dualToPrimal<12>() const;
 
-template const GroupPresentation& TriangulationBase<13>::group() const;
+template const GroupPresentation& TriangulationBase<13>::group(bool) const;
 
 template void TriangulationBase<13>::calculateSkeleton();
 template void TriangulationBase<13>::cloneSkeleton(

engine/triangulation/explicit/triangulation14.cpp

@@ -105,7 +105,7 @@ template MatrixInt TriangulationBase<14>::dualToPrimal<11>() const;
 template MatrixInt TriangulationBase<14>::dualToPrimal<12>() const;
 template MatrixInt TriangulationBase<14>::dualToPrimal<13>() const;
 
-template const GroupPresentation& TriangulationBase<14>::group() const;
+template const GroupPresentation& TriangulationBase<14>::group(bool) const;
 
 template void TriangulationBase<14>::calculateSkeleton();
 template void TriangulationBase<14>::cloneSkeleton(

engine/triangulation/explicit/triangulation15.cpp

@@ -109,7 +109,7 @@ template MatrixInt TriangulationBase<15>::dualToPrimal<12>() const;
 template MatrixInt TriangulationBase<15>::dualToPrimal<13>() const;
 template MatrixInt TriangulationBase<15>::dualToPrimal<14>() const;
 
-template const GroupPresentation& TriangulationBase<15>::group() const;
+template const GroupPresentation& TriangulationBase<15>::group(bool) const;
 
 template void TriangulationBase<15>::calculateSkeleton();
 template void TriangulationBase<15>::cloneSkeleton(

engine/triangulation/explicit/triangulation2.cpp

@@ -58,7 +58,7 @@ template MatrixInt TriangulationBase<2>::dualBoundaryMap<2>() const;
 template MatrixInt TriangulationBase<2>::dualToPrimal<0>() const;
 template MatrixInt TriangulationBase<2>::dualToPrimal<1>() const;
 
-template const GroupPresentation& TriangulationBase<2>::group() const;
+template const GroupPresentation& TriangulationBase<2>::group(bool) const;
 
 template void TriangulationBase<2>::calculateSkeleton();
 template void TriangulationBase<2>::cloneSkeleton(const TriangulationBase<2>&);

engine/triangulation/explicit/triangulation3.cpp

@@ -62,7 +62,7 @@ template MatrixInt TriangulationBase<3>::dualToPrimal<0>() const;
 template MatrixInt TriangulationBase<3>::dualToPrimal<1>() const;
 template MatrixInt TriangulationBase<3>::dualToPrimal<2>() const;
 
-template const GroupPresentation& TriangulationBase<3>::group() const;
+template const GroupPresentation& TriangulationBase<3>::group(bool) const;
 
 template void TriangulationBase<3>::calculateSkeleton();
 template void TriangulationBase<3>::cloneSkeleton(const TriangulationBase<3>&);

engine/triangulation/explicit/triangulation4.cpp

@@ -66,7 +66,7 @@ template MatrixInt TriangulationBase<4>::dualToPrimal<1>() const;
 template MatrixInt TriangulationBase<4>::dualToPrimal<2>() const;
 template MatrixInt TriangulationBase<4>::dualToPrimal<3>() const;
 
-template const GroupPresentation& TriangulationBase<4>::group() const;
+template const GroupPresentation& TriangulationBase<4>::group(bool) const;
 
 template void TriangulationBase<4>::calculateSkeleton();
 template void TriangulationBase<4>::cloneSkeleton(const TriangulationBase<4>&);

engine/triangulation/explicit/triangulation5.cpp

@@ -68,7 +68,7 @@ template MatrixInt TriangulationBase<5>::dualToPrimal<2>() const;
 template MatrixInt TriangulationBase<5>::dualToPrimal<3>() const;
 template MatrixInt TriangulationBase<5>::dualToPrimal<4>() const;
 
-template const GroupPresentation& TriangulationBase<5>::group() const;
+template const GroupPresentation& TriangulationBase<5>::group(bool) const;
 
 template void TriangulationBase<5>::calculateSkeleton();
 template void TriangulationBase<5>::cloneSkeleton(const TriangulationBase<5>&);

engine/triangulation/explicit/triangulation6.cpp

@@ -72,7 +72,7 @@ template MatrixInt TriangulationBase<6>::dualToPrimal<3>() const;
 template MatrixInt TriangulationBase<6>::dualToPrimal<4>() const;
 template MatrixInt TriangulationBase<6>::dualToPrimal<5>() const;
 
-template const GroupPresentation& TriangulationBase<6>::group() const;
+template const GroupPresentation& TriangulationBase<6>::group(bool) const;
 
 template void TriangulationBase<6>::calculateSkeleton();
 template void TriangulationBase<6>::cloneSkeleton(const TriangulationBase<6>&);

engine/triangulation/explicit/triangulation7.cpp

@@ -76,7 +76,7 @@ template MatrixInt TriangulationBase<7>::dualToPrimal<4>() const;
 template MatrixInt TriangulationBase<7>::dualToPrimal<5>() const;
 template MatrixInt TriangulationBase<7>::dualToPrimal<6>() const;
 
-template const GroupPresentation& TriangulationBase<7>::group() const;
+template const GroupPresentation& TriangulationBase<7>::group(bool) const;
 
 template void TriangulationBase<7>::calculateSkeleton();
 template void TriangulationBase<7>::cloneSkeleton(const TriangulationBase<7>&);

engine/triangulation/explicit/triangulation8.cpp

@@ -80,7 +80,7 @@ template MatrixInt TriangulationBase<8>::dualToPrimal<5>() const;
 template MatrixInt TriangulationBase<8>::dualToPrimal<6>() const;
 template MatrixInt TriangulationBase<8>::dualToPrimal<7>() const;
 
-template const GroupPresentation& TriangulationBase<8>::group() const;
+template const GroupPresentation& TriangulationBase<8>::group(bool) const;
 
 template void TriangulationBase<8>::calculateSkeleton();
 template void TriangulationBase<8>::cloneSkeleton(const TriangulationBase<8>&);

engine/triangulation/explicit/triangulation9.cpp

@@ -84,7 +84,7 @@ template MatrixInt TriangulationBase<9>::dualToPrimal<6>() const;
 template MatrixInt TriangulationBase<9>::dualToPrimal<7>() const;
 template MatrixInt TriangulationBase<9>::dualToPrimal<8>() const;
 
-template const GroupPresentation& TriangulationBase<9>::group() const;
+template const GroupPresentation& TriangulationBase<9>::group(bool) const;
 
 template void TriangulationBase<9>::calculateSkeleton();
 template void TriangulationBase<9>::cloneSkeleton(const TriangulationBase<9>&);

python/dim2/triangulation2.cpp

@@ -228,12 +228,14 @@ void addTriangulation2(pybind11::module_& m) {
         .def("isConnected", &Triangulation<2>::isConnected,
             rbase::isConnected)
         .def("group", &Triangulation<2>::group,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal, rbase::group)
         .def("fundamentalGroup", &Triangulation<2>::fundamentalGroup,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal,
             rbase::fundamentalGroup)
         .def("setGroupPresentation",
-             &Triangulation<2>::setGroupPresentation,
+            &Triangulation<2>::setGroupPresentation,
             rbase::setGroupPresentation)
         .def("simplifiedFundamentalGroup", // deprecated
             &Triangulation<2>::setGroupPresentation,

python/dim3/triangulation3.cpp

@@ -316,8 +316,10 @@ void addTriangulation3(pybind11::module_& m) {
         .def("isConnected", &Triangulation<3>::isConnected,
             rbase::isConnected)
         .def("group", &Triangulation<3>::group,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal, rbase::group)
         .def("fundamentalGroup", &Triangulation<3>::fundamentalGroup,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal,
             rbase::fundamentalGroup)
         .def("setGroupPresentation",

python/dim4/triangulation4.cpp

@@ -256,8 +256,10 @@ void addTriangulation4(pybind11::module_& m) {
         .def("isConnected", &Triangulation<4>::isConnected,
             rbase::isConnected)
         .def("group", &Triangulation<4>::group,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal, rbase::group)
         .def("fundamentalGroup", &Triangulation<4>::fundamentalGroup,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal,
             rbase::fundamentalGroup)
         .def("setGroupPresentation",

python/generic/triangulation-bindings.h

@@ -188,8 +188,10 @@ void addTriangulation(pybind11::module_& m, const char* name) {
         .def("eulerCharTri", &Triangulation<dim>::eulerCharTri,
             rbase::eulerCharTri)
         .def("group", &Triangulation<dim>::group,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal, rbase::group)
         .def("fundamentalGroup", &Triangulation<dim>::fundamentalGroup,
+            pybind11::arg("simplify") = true,
             pybind11::return_value_policy::reference_internal,
             rbase::fundamentalGroup)
         .def("setGroupPresentation",

python/testsuite/refs.out

@@ -44,6 +44,9 @@ g0^6 g1 g0^-1 g1 g0 g1^-1
 g0^6
 g0^7
 
+g1^-1 g0 g1 g2 g0^-1
+g0 g2 g1 g2^-1
+
 foo
 foo
 foo