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Make Example<2> construct minimal triangulations #97

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2e3ea5c
Preparation for new SFS constructions.
AlexHe98 Nov 9, 2025
9517735
More preparation.
AlexHe98 Nov 10, 2025
089f6ba
Private polygon() routine.
AlexHe98 Nov 10, 2025
7c451be
Make orientable() minimal.
AlexHe98 Nov 10, 2025
c1571be
Test and fix new version of orientable().
AlexHe98 Nov 10, 2025
8895bd6
Make LinkTest recognise another trefoil complement iso sig.
AlexHe98 Nov 10, 2025
72f68cc
Test that orientable() actually returns minimal triangulations.
AlexHe98 Nov 10, 2025
b54ddaa
Make nonOrientable() minimal.
AlexHe98 Nov 10, 2025
f75036e
Update python skeleton test that uses nonOrientable().
AlexHe98 Nov 10, 2025
71281f4
Merge branch 'master' into construct-sfs
AlexHe98 Nov 11, 2025
1420563
Merge branch 'main' into example-surfs
AlexHe98 Mar 8, 2026
3f02fa2
Remove code from separate unfinished feature.
AlexHe98 Mar 8, 2026
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105 changes: 105 additions & 0 deletions engine/testsuite/dim2/triangulation2.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -46,6 +46,20 @@ class Dim2Test : public TriangulationTest<2> {

// Closed non-orientable triangulations:
TestCase rp2 { Example<2>::rp2(), "RP^2" };
TestCase kb { Example<2>::nonOrientable(2, 0), "KB" };

// Minimal bounded orientable triangulations:
TestCase pants { Example<2>::orientable(0, 3), "Pair of pants" };
TestCase orPunc1 { Example<2>::orientable(2, 1),
"Or, g=2 + 1 puncture" };
TestCase orPunc3 { Example<2>::orientable(2, 3),
"Or, g=2 + 3 punctures" };

// Minimal bounded non-orientable triangulations:
TestCase norPunc1 { Example<2>::nonOrientable(2, 1),
"Non-or, g=2 + 1 puncture" };
TestCase norPunc3 { Example<2>::nonOrientable(2, 3),
"Non-or, g=2 + 3 punctures" };

// Disconnected triangulations (we build these in the constructor):
TestCase disjoint2 { {}, "Torus U Mobius" };
Expand All @@ -70,8 +84,16 @@ class Dim2Test : public TriangulationTest<2> {
f(s2Oct.tri, s2Oct.name);
f(torus2.tri, torus2.name);
f(rp2.tri, rp2.name);
f(kb.tri, kb.name);
f(disjoint2.tri, disjoint2.name);
f(disjoint3.tri, disjoint3.name);

// Minimal bounded triangulations.
f(pants.tri, pants.name);
f(orPunc1.tri, orPunc1.name);
f(orPunc3.tri, orPunc3.name);
f(norPunc1.tri, norPunc1.name);
f(norPunc3.tri, norPunc3.name);
}
};

Expand All @@ -93,26 +115,50 @@ TEST_F(Dim2Test, validity) {
verifyValid(s2Oct);
verifyValid(torus2);
verifyValid(rp2);
verifyValid(kb);
verifyValid(disjoint2);
verifyValid(disjoint3);

// Minimal bounded triangulations.
verifyValid(pants);
verifyValid(orPunc1);
verifyValid(orPunc3);
verifyValid(norPunc1);
verifyValid(norPunc3);
}
TEST_F(Dim2Test, connectivity) {
TriangulationTest<2>::connectivityGenericCases();

EXPECT_TRUE(s2Oct.tri.isConnected());
EXPECT_TRUE(torus2.tri.isConnected());
EXPECT_TRUE(rp2.tri.isConnected());
EXPECT_TRUE(kb.tri.isConnected());
EXPECT_FALSE(disjoint2.tri.isConnected());
EXPECT_FALSE(disjoint3.tri.isConnected());

// Minimal bounded triangulations.
EXPECT_TRUE(pants.tri.isConnected());
EXPECT_TRUE(orPunc1.tri.isConnected());
EXPECT_TRUE(orPunc3.tri.isConnected());
EXPECT_TRUE(norPunc1.tri.isConnected());
EXPECT_TRUE(norPunc3.tri.isConnected());
}
TEST_F(Dim2Test, orientability) {
TriangulationTest<2>::orientabilityGenericCases();

EXPECT_TRUE(s2Oct.tri.isOrientable());
EXPECT_TRUE(torus2.tri.isOrientable());
EXPECT_FALSE(rp2.tri.isOrientable());
EXPECT_FALSE(kb.tri.isOrientable());
EXPECT_FALSE(disjoint2.tri.isOrientable());
EXPECT_FALSE(disjoint3.tri.isOrientable());

// Minimal bounded triangulations.
EXPECT_TRUE(pants.tri.isOrientable());
EXPECT_TRUE(orPunc1.tri.isOrientable());
EXPECT_TRUE(orPunc3.tri.isOrientable());
EXPECT_FALSE(norPunc1.tri.isOrientable());
EXPECT_FALSE(norPunc3.tri.isOrientable());
}
TEST_F(Dim2Test, orientedExamples) {
// Ensure that the orientable Example<2> constructions are oriented.
Expand All @@ -128,6 +174,11 @@ TEST_F(Dim2Test, orientedExamples) {
EXPECT_TRUE(Example<2>::orientable(5, 3).isOriented());
EXPECT_TRUE(Example<2>::sphereOctahedron().isOriented());
EXPECT_TRUE(Example<2>::disc().isOriented());

// Minimal bounded triangulations.
EXPECT_TRUE(pants.tri.isOriented());
EXPECT_TRUE(orPunc1.tri.isOriented());
EXPECT_TRUE(orPunc3.tri.isOriented());
}

TEST_F(Dim2Test, eulerChar) {
Expand All @@ -136,26 +187,50 @@ TEST_F(Dim2Test, eulerChar) {
EXPECT_EQ(s2Oct.tri.eulerCharTri(), 2);
EXPECT_EQ(torus2.tri.eulerCharTri(), -2);
EXPECT_EQ(rp2.tri.eulerCharTri(), 1);
EXPECT_EQ(kb.tri.eulerCharTri(), 0);
EXPECT_EQ(disjoint2.tri.eulerCharTri(), 0);
EXPECT_EQ(disjoint3.tri.eulerCharTri(), 2);

// Minimal bounded triangulations.
EXPECT_EQ(pants.tri.eulerCharTri(), -1);
EXPECT_EQ(orPunc1.tri.eulerCharTri(), -3);
EXPECT_EQ(orPunc3.tri.eulerCharTri(), -5);
EXPECT_EQ(norPunc1.tri.eulerCharTri(), -1);
EXPECT_EQ(norPunc3.tri.eulerCharTri(), -3);
}
TEST_F(Dim2Test, boundaryBasic) {
TriangulationTest<2>::boundaryBasicGenericCases();

verifyBoundaryBasic(s2Oct, {}, {}, {});
verifyBoundaryBasic(torus2, {}, {}, {});
verifyBoundaryBasic(rp2, {}, {}, {});
verifyBoundaryBasic(kb, {}, {}, {});
verifyBoundaryBasic(disjoint2, {0}, {}, {});
verifyBoundaryBasic(disjoint3, {0, 0}, {}, {});

// Minimal bounded triangulations.
verifyBoundaryBasic(pants, {0, 0, 0}, {}, {});
verifyBoundaryBasic(orPunc1, {0}, {}, {});
verifyBoundaryBasic(orPunc3, {0, 0, 0}, {}, {});
verifyBoundaryBasic(norPunc1, {0}, {}, {});
verifyBoundaryBasic(norPunc3, {0, 0, 0}, {}, {});
}
TEST_F(Dim2Test, vertexLinksBasic) {
TriangulationTest<2>::vertexLinksBasicGenericCases();

verifyVertexLinksBasic(s2Oct, 6, 0);
verifyVertexLinksBasic(torus2, 1, 0);
verifyVertexLinksBasic(rp2, 2, 0);
verifyVertexLinksBasic(kb, 1, 0);
verifyVertexLinksBasic(disjoint2, 1, 1);
verifyVertexLinksBasic(disjoint3, 4, 2);

// Minimal bounded triangulations.
verifyVertexLinksBasic(pants, 0, 3);
verifyVertexLinksBasic(orPunc1, 0, 1);
verifyVertexLinksBasic(orPunc3, 0, 3);
verifyVertexLinksBasic(norPunc1, 0, 1);
verifyVertexLinksBasic(norPunc3, 0, 3);
}
TEST_F(Dim2Test, orient) {
testManualCases(TriangulationTest<2>::verifyOrient);
Expand Down Expand Up @@ -215,17 +290,34 @@ TEST_F(Dim2Test, homologyH1) {
EXPECT_EQ(s2Oct.tri.homology<1>(), regina::AbelianGroup());
EXPECT_EQ(torus2.tri.homology<1>(), regina::AbelianGroup(4));
EXPECT_EQ(rp2.tri.homology<1>(), regina::AbelianGroup(0, {2}));
EXPECT_EQ(kb.tri.homology<1>(), regina::AbelianGroup(1, {2}));
EXPECT_EQ(disjoint2.tri.homology<1>(), regina::AbelianGroup(3));
EXPECT_EQ(disjoint3.tri.homology<1>(), regina::AbelianGroup(2, {2}));

// Minimal bounded triangulations.
EXPECT_EQ(pants.tri.homology<1>(), regina::AbelianGroup(2));
EXPECT_EQ(orPunc1.tri.homology<1>(), regina::AbelianGroup(4));
EXPECT_EQ(orPunc3.tri.homology<1>(), regina::AbelianGroup(6));
EXPECT_EQ(norPunc1.tri.homology<1>(), regina::AbelianGroup(2));
EXPECT_EQ(norPunc3.tri.homology<1>(), regina::AbelianGroup(4));
}
TEST_F(Dim2Test, fundGroup) {
TriangulationTest<2>::fundGroupGenericCases();

EXPECT_EQ(s2Oct.tri.group().recogniseGroup(), "0");
EXPECT_EQ(torus2.tri.group().recogniseGroup(), "");
EXPECT_EQ(rp2.tri.group().recogniseGroup(), "Z_2");
EXPECT_EQ(kb.tri.group().recogniseGroup(),
"Z~Z w/monodromy a ↦ a^-1");

// We cannot call group() on disjoint triangulations.

// Minimal bounded triangulations.
EXPECT_EQ(pants.tri.group().recogniseGroup(), "Free(2)");
EXPECT_EQ(orPunc1.tri.group().recogniseGroup(), "Free(4)");
EXPECT_EQ(orPunc3.tri.group().recogniseGroup(), "Free(6)");
EXPECT_EQ(norPunc1.tri.group().recogniseGroup(), "Free(2)");
EXPECT_EQ(norPunc3.tri.group().recogniseGroup(), "Free(4)");
}
TEST_F(Dim2Test, chainComplex) {
testManualCases(TriangulationTest<2>::verifyChainComplex);
Expand All @@ -239,3 +331,16 @@ TEST_F(Dim2Test, dualToPrimal) {
TEST_F(Dim2Test, copyMove) {
testManualCases(TriangulationTest<2>::verifyCopyMove);
}
TEST_F(Dim2Test, minimalSize) {
// Check that promises of minimality are fulfilled.
EXPECT_EQ(Example<2>::orientable(0, 0).size(), 2);
EXPECT_EQ(Example<2>::orientable(0, 1).size(), 1);
EXPECT_EQ(torus2.tri.size(), 6);
EXPECT_EQ(rp2.tri.size(), 2);
EXPECT_EQ(kb.tri.size(), 2);
EXPECT_EQ(pants.tri.size(), 5);
EXPECT_EQ(orPunc1.tri.size(), 7);
EXPECT_EQ(orPunc3.tri.size(), 13);
EXPECT_EQ(norPunc1.tri.size(), 3);
EXPECT_EQ(norPunc3.tri.size(), 9);
}
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