public void MorphismIsFunction()
{
Assert.Throws <ArgumentException>(() => Morphism.Create(
Product2.Create(1, true),
Product2.Create(1, false)
));
}
public void ApplyParameter_米田()
{
var mor = Morphism.Create(@"\yoneda_{#1?}\colon #1\rightarrow \widehat{#1}").TestSingle();
mor.Name.AsMathSequence().List.Count.Is(1);
mor.Name.AsMathSequence().List[0].IsMathToken(@"\yoneda");
mor.Name.AsMathSequence().Sub.IsMathToken("#1?");
mor.Source.IsMathToken("#1");
mor.Target.AsMathSequence().List.Count.Is(2);
mor.Target.AsMathSequence().List[0].IsMathToken(@"\widehat");
mor.Target.AsMathSequence().List[1].AsMathSequence().List.Count.Is(1);
mor.Target.AsMathSequence().List[1].AsMathSequence().List[0].IsMathToken("#1");
mor.Target.AsMathSequence().List[1].AsMathSequence().LeftBracket.TestToken("{");
mor.Target.AsMathSequence().List[1].AsMathSequence().RightBracket.TestToken("}");
var f = new MathObjectFactory(@"\yoneda_a").CreateSingle();
var parameters = new Dictionary <string, MathObject>();
mor.Name.IsSameType(f, parameters).IsTrue();
mor = mor.ApplyParameter(f, parameters, false).TestSingle();
mor.Name.AsMathSequence().List.Count.Is(1);
mor.Name.AsMathSequence().List[0].IsMathToken(@"\yoneda");
mor.Name.AsMathSequence().Sub.IsMathToken("a");
mor.Source.IsMathToken("a");
mor.Target.AsMathSequence().List.Count.Is(2);
mor.Target.AsMathSequence().List[0].IsMathToken(@"\widehat");
mor.Target.AsMathSequence().List[1].AsMathSequence().List.Count.Is(1);
mor.Target.AsMathSequence().List[1].AsMathSequence().List[0].IsMathToken("a");
mor.Target.AsMathSequence().List[1].AsMathSequence().LeftBracket.TestToken("{");
mor.Target.AsMathSequence().List[1].AsMathSequence().RightBracket.TestToken("}");
mor.Target.ToTokenString().TestString(@"\widehat{a}");
}
public void ApplyParameter_通常()
{
var mor = Morphism.Create(@"\theta^{#1}\colon F(#1)\rightarrow G#1").TestSingle();
mor.Name.AsMathSequence().List.Count.Is(1);
mor.Name.AsMathSequence().List[0].IsMathToken(@"\theta");
mor.Name.AsMathSequence().Sup.IsMathToken("#1");
mor.Source.AsMathSequence().List.Count.Is(2);
mor.Source.AsMathSequence().List[0].IsMathToken("F");
mor.Source.AsMathSequence().List[1].AsMathSequence().List.Count.Is(1);
mor.Source.AsMathSequence().List[1].AsMathSequence().List[0].IsMathToken("#1");
mor.Source.AsMathSequence().List[1].AsMathSequence().LeftBracket.TestToken("(");
mor.Source.AsMathSequence().List[1].AsMathSequence().RightBracket.TestToken(")");
mor.Target.AsMathSequence().List.Count.Is(2);
mor.Target.AsMathSequence().List[0].IsMathToken("G");
mor.Target.AsMathSequence().List[1].IsMathToken("#1");
var f = new MathObjectFactory(@"\theta^i").CreateSingle();
var parameters = new Dictionary <string, MathObject>();
mor.Name.IsSameType(f, parameters).IsTrue();
mor = mor.ApplyParameter(f, parameters, false).TestSingle();
mor.Name.AsMathSequence().List.Count.Is(1);
mor.Name.AsMathSequence().List[0].IsMathToken(@"\theta");
mor.Name.AsMathSequence().Sup.IsMathToken("i");
mor.Source.AsMathSequence().List.Count.Is(2);
mor.Source.AsMathSequence().List[0].IsMathToken("F");
mor.Source.AsMathSequence().List[1].AsMathSequence().List.Count.Is(1);
mor.Source.AsMathSequence().List[1].AsMathSequence().List[0].IsMathToken("i");
mor.Source.AsMathSequence().List[1].AsMathSequence().LeftBracket.TestToken("(");
mor.Source.AsMathSequence().List[1].AsMathSequence().RightBracket.TestToken(")");
mor.Target.AsMathSequence().List.Count.Is(2);
mor.Target.AsMathSequence().List[0].IsMathToken("G");
mor.Target.AsMathSequence().List[1].IsMathToken("i");
f = new MathObjectFactory(@"\theta^{i}").CreateSingle();
parameters = new Dictionary <string, MathObject>();
mor.Name.IsSameType(f, parameters).IsTrue();
mor = mor.ApplyParameter(f, parameters, false).TestSingle();
mor.Name.AsMathSequence().List.Count.Is(1);
mor.Name.AsMathSequence().List[0].IsMathToken(@"\theta");
mor.Name.AsMathSequence().Sup.IsMathToken("i");
mor.Source.AsMathSequence().List.Count.Is(2);
mor.Source.AsMathSequence().List[0].IsMathToken("F");
mor.Source.AsMathSequence().List[1].AsMathSequence().List.Count.Is(1);
mor.Source.AsMathSequence().List[1].AsMathSequence().List[0].IsMathToken("i");
mor.Source.AsMathSequence().List[1].AsMathSequence().LeftBracket.TestToken("(");
mor.Source.AsMathSequence().List[1].AsMathSequence().RightBracket.TestToken(")");
mor.Target.AsMathSequence().List.Count.Is(2);
mor.Target.AsMathSequence().List[0].IsMathToken("G");
mor.Target.AsMathSequence().List[1].IsMathToken("i");
}
public void Apply()
{
var m = Morphism.Create(
Product2.Create("foo", 123),
Product2.Create("bar", 456),
Product2.Create("baz", 789)
);
Assert.Equal(123.ToOption(), m.Apply("foo"));
Assert.Equal(456.ToOption(), m.Apply("bar"));
Assert.Equal(789.ToOption(), m.Apply("baz"));
Assert.True(m.Apply("xyz").IsEmpty);
}
public void CreateThreeMorphism()
{
var xs = Morphism.Create(@"\Gamma, \Sigma\colon\theta\Rrightarrow\rho\colon f\Rightarrow g\colon a\rightarrow b").ToList();
xs.Count.Is(8);
xs[0].TestMorphism("f", "a", "b", MorphismType.OneMorphism);
xs[1].TestMorphism("g", "a", "b", MorphismType.OneMorphism);
xs[2].TestMorphism(@"\theta", "f", "g", MorphismType.TwoMorphism);
xs[3].TestMorphism("f", "a", "b", MorphismType.OneMorphism);
xs[4].TestMorphism("g", "a", "b", MorphismType.OneMorphism);
xs[5].TestMorphism(@"\rho", "f", "g", MorphismType.TwoMorphism);
xs[6].TestMorphism(@"\Gamma", @"\theta", @"\rho", MorphismType.ThreeMorphism);
xs[7].TestMorphism(@"\Sigma", @"\theta", @"\rho", MorphismType.ThreeMorphism);
}
public void DomainRange()
{
var m = Morphism.Create(
Product2.Create(1, true),
Product2.Create(2, true),
Product2.Create(3, false)
);
Assert.Equal(3, m.Domain.Count());
Assert.Contains(1, m.Domain);
Assert.Contains(2, m.Domain);
Assert.Contains(3, m.Domain);
Assert.Equal(2, m.Range.Count());
Assert.Contains(true, m.Range);
Assert.Contains(false, m.Range);
}
public void Create関手()
{
Morphism.Create(@"F\colon\cat{C}\rightarrow\cat{D}").TestSingle().TestMorphism("F", @"\cat{C}", @"\cat{D}", MorphismType.Functor);
Morphism.Create(@"U\colon\Ab\rightarrow\Set").TestSingle().TestMorphism("U", @"\Ab", @"\Set", MorphismType.Functor);
Morphism.Create(@"U\colon\Mod[R]\rightarrow\Ab").TestSingle().TestMorphism("U", @"\Mod[R]", @"\Ab", MorphismType.Functor);
var xs = Morphism.Create(@"\theta\colon F\Rightarrow G\colon\cat{C}\rightarrow\cat{D}").ToList();
xs.Count.Is(3);
xs[0].TestMorphism("F", @"\cat{C}", @"\cat{D}", MorphismType.Functor);
xs[1].TestMorphism("G", @"\cat{C}", @"\cat{D}", MorphismType.Functor);
xs[2].TestMorphism(@"\theta", "F", "G", MorphismType.TwoMorphism);
Morphism.Create(@"F\colon\opp{\cat{C}}\rightarrow\cat{D}").TestSingle().TestMorphism("F", @"\opp{\cat{C}}", @"\cat{D}", MorphismType.ContravariantFunctor);
Morphism.Create(@"G\colon\opp{\Set}\rightarrow\opp{\Cat}").TestSingle().TestMorphism("G", @"\opp{\Set}", @"\opp{\Cat}", MorphismType.Functor);
Morphism.Create(@"\Hom_{\cat{C}}(a, -)\colon \cat{C}\rightarrow\Set").TestSingle()
.TestMorphism(@"\Hom_{\cat{C}}(a,-)", @"\cat{C}", @"\Set", MorphismType.Functor);
}
public void 数二項演算_省略3()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = ExtensionsInTest.CreateDefaultMorphisms();
list.Add(Morphism.Create(@"\alpha^{#1?}_{#2?#3?#4?}\colon (#2#3)#4\rightarrow #2(#3#4)").TestSingle());
var tikz = new TikZDiagram("", -1, false, true, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\alpha",
@"((\encat{C}_{cd}\encat{D}_{c'd'})(\encat{C}_{bc}\encat{D}_{b'c'}))(\encat{C}_{ab}\encat{D}_{a'b'})",
@"(\encat{C}_{cd}\encat{D}_{c'd'})((\encat{C}_{bc}\encat{D}_{b'c'})(\encat{C}_{ab}\encat{D}_{a'b'}))"
).TestMorphism(@"\alpha",
@"((\encat{C}_{cd}\encat{D}_{c'd'})(\encat{C}_{bc}\encat{D}_{b'c'}))(\encat{C}_{ab}\encat{D}_{a'b'})",
@"(\encat{C}_{cd}\encat{D}_{c'd'})((\encat{C}_{bc}\encat{D}_{b'c'})(\encat{C}_{ab}\encat{D}_{a'b'}))",
MorphismType.Functor,
true
);
}
public void 数二項演算_省略1()
{
var dic = new Dictionary <TokenString, Morphism>()
{
{ "f".ToTokenString(), Morphism.Create(@"f\colon u\rightarrow v").TestSingle() },
{ "g".ToTokenString(), Morphism.Create(@"g\colon s\rightarrow t").TestSingle() },
};
var tikz = new TikZDiagram("", -1, false, true, true, dic, ExtensionsInTest.CreateDefaultMorphisms(), Array.Empty <Functor>());
tikz.CreateMorphism(@"f\otimes g")
.TestMorphism(@"f\otimes g", @"u\otimes s", @"v\otimes t", MorphismType.OneMorphism);
tikz.CreateMorphism(@"f\otimes g", @"u\otimes s", @"v\otimes t")
.TestMorphism(@"f\otimes g", @"u\otimes s", @"v\otimes t", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"f\otimes g", @"us", @"vt")
.TestMorphism(@"f\otimes g", @"us", @"vt", MorphismType.OneMorphism, true);
}
public void 数二項演算_省略しない()
{
var dic = new Dictionary <TokenString, Morphism>()
{
{ "f".ToTokenString(), Morphism.Create(@"f\colon u\rightarrow v").TestSingle() },
{ "g".ToTokenString(), Morphism.Create(@"g\colon s\rightarrow t").TestSingle() },
};
var tikz = CreateTikZDiagram(dic);
tikz.CreateMorphism(@"f\otimes g", @"us", @"vt")
.All(m =>
{
Console.WriteLine(m.ToString());
return(!m.Item1.Name.ToTokenString().Equals(@"f\otimes g") ||
!m.Item1.Source.ToTokenString().Equals(@"us") ||
!m.Item1.Target.ToTokenString().Equals(@"vt"));
}).IsTrue();
}
public void Create随伴()
{
var xs = Morphism.Create(@"F\dashv G\colon\cat{C}\rightarrow\cat{D}").ToList();
xs.Count.Is(2);
xs[0].TestMorphism("F", @"\cat{C}", @"\cat{D}", MorphismType.Functor);
xs[1].TestMorphism("G", @"\cat{D}", @"\cat{C}", MorphismType.Functor);
xs = Morphism.Create(@"f\dashv g\dashv h\dashv k\colon a\rightarrow b").ToList();
xs.Count.Is(4);
xs[0].TestMorphism("f", "a", "b", MorphismType.OneMorphism);
xs[1].TestMorphism("g", "b", "a", MorphismType.OneMorphism);
xs[2].TestMorphism("h", "a", "b", MorphismType.OneMorphism);
xs[3].TestMorphism("k", "b", "a", MorphismType.OneMorphism);
xs = Morphism.Create(@"L_0\dashv R^1\colon\cat{C}\rightarrow\cat{D}").ToList();
xs.Count.Is(2);
xs[0].TestMorphism("L_{0}", @"\cat{C}", @"\cat{D}", MorphismType.Functor);
xs[1].TestMorphism("R^{1}", @"\cat{D}", @"\cat{C}", MorphismType.Functor);
}
public void 数st()
{
var dic = new Dictionary <TokenString, Morphism>()
{
{ "F".ToTokenString(), Morphism.Create(@"F\colon\encat{A}\rightarrow\encat{B}").TestSingle() }
};
var list = new List <Morphism>()
{
ToMorphismHelp(@"#1_{#2#3}", @"#1s(#2, #3)", @"#1t(#1#2, #1#3)", MorphismType.OneMorphism)
};
var func = ExtensionsInTest.CreateDefaultFunctors().ToList();
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, func);
tikz.CreateMorphism(@"F_{ab}")
.TestMorphism(@"F_{ab}", @"\encat{A}(a, b)", @"\encat{B}(Fa, Fb)", MorphismType.Functor);
tikz.CreateMorphism(@"F_{ab}", @"\encat{A}(a, b)", @"\encat{B}(Fa, Fb)")
.TestMorphism(@"F_{ab}", @"\encat{A}(a, b)", @"\encat{B}(Fa, Fb)", MorphismType.Functor, true);
}
public void Create変数()
{
var mor = Morphism.Create(@"\theta^{#1}\colon F(#1)\rightarrow G#1").TestSingle();
mor.Name.AsMathSequence().List.Count.Is(1);
mor.Name.AsMathSequence().List[0].IsMathToken(@"\theta");
mor.Name.AsMathSequence().Sup.IsMathToken("#1");
mor.Source.AsMathSequence().List.Count.Is(2);
mor.Source.AsMathSequence().List[0].IsMathToken("F");
mor.Source.AsMathSequence().List[1].AsMathSequence().List.Count.Is(1);
mor.Source.AsMathSequence().List[1].AsMathSequence().List[0].IsMathToken("#1");
mor.Source.AsMathSequence().List[1].AsMathSequence().LeftBracket.TestToken("(");
mor.Source.AsMathSequence().List[1].AsMathSequence().RightBracket.TestToken(")");
mor.Target.AsMathSequence().List.Count.Is(2);
mor.Target.AsMathSequence().List[0].IsMathToken("G");
mor.Target.AsMathSequence().List[1].IsMathToken("#1");
var xs = Morphism.Create(@"\test{#1}{#2s}\colon F#1\rightarrow G#1").ToArray();
xs.Length.Is(0);
}
public void Create通常()
{
Morphism.Create(@"f\colon a\rightarrow b").TestSingle().TestMorphism("f", "a", "b", MorphismType.OneMorphism);
Morphism.Create(@" g \colon u \rightarrow v ").TestSingle().TestMorphism("g", "u", "v", MorphismType.OneMorphism);
Morphism.Create(@"\test\colon \test\rightarrow\testtest").TestSingle()
.TestMorphism(@"\test", @"\test", @"\testtest", MorphismType.OneMorphism);
Morphism.Create(@"\test^{\test}\colon \test\test\rightarrow\testtest\test").TestSingle()
.TestMorphism(@"\test ^{\test }", @"\test\test", @"\testtest\test", MorphismType.OneMorphism);
var xs = Morphism.Create(@"f, g\colon a\rightarrow b").ToList();
xs.Count.Is(2);
xs[0].TestMorphism("f", "a", "b", MorphismType.OneMorphism);
xs[1].TestMorphism("g", "a", "b", MorphismType.OneMorphism);
Morphism.Create(@"\eta_a\colon \id_{\cat{C}}(a)\rightarrow GF(a)").TestSingle()
.TestMorphism(@"\eta_a", @"\id_{\cat{C}}(a)", "GF(a)", MorphismType.OneMorphism);
}
public void 数2()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
Morphism.Create(@"m_{#1#2} \colon \encat{A}(#1, #2) \rightarrow \encat{B}(G#1, G#2)").TestSingle()
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"m_{ab}")
.TestMorphism(@"m_{ab}", @"\encat{A}(a, b)", @"\encat{B}(Ga, Gb)", MorphismType.Functor);
tikz.CreateMorphism(@"m_{ab}", @"\encat{A}(a, b)", @"\encat{B}(Ga, Gb)")
.TestMorphism(@"m_{ab}", @"\encat{A}(a, b)", @"\encat{B}(Ga, Gb)", MorphismType.Functor, true);
tikz.CreateMorphism(@"m_{{Fa}{Fb}}")
.TestMorphism(@"m_{{Fa}{Fb}}", @"\encat{A}(Fa, Fb)", @"\encat{B}(GFa, GFb)", MorphismType.Functor);
tikz.CreateMorphism(@"m_{{Fa}{Fb}}", @"\encat{A}(Fa, Fb)", @"\encat{B}(GFa, GFb)")
.TestMorphism(@"m_{{Fa}{Fb}}", @"\encat{A}(Fa, Fb)", @"\encat{B}(GFa, GFb)", MorphismType.Functor, true);
}
public void CreateHom()
{
Morphism.Create(@"f\in\Hom(a,b)").TestSingle().TestMorphism("f", "a", "b", MorphismType.OneMorphism);
Morphism.Create(@"f\in\Hom_{\cat{C}}(a,b)").TestSingle().TestMorphism("f", "a", "b", MorphismType.OneMorphism);
Morphism.Create(@" g \in \Hom _{\cat{C}} ( c , d )").TestSingle().TestMorphism("g", "c", "d", MorphismType.OneMorphism);
Morphism.Create(@"\test\in\Hom(a, b)").TestSingle().TestMorphism(@"\test", "a", "b", MorphismType.OneMorphism);
Morphism.Create(@"\test\test\in\Hom_{\cat{C}}(a, b)").TestSingle().TestMorphism(@"\test \test", "a", "b", MorphismType.OneMorphism);
Morphism.Create(@"\mor{f}\in\Hom(a, b)").TestSingle().TestMorphism(@"\mor {f}", "a", "b", MorphismType.OneMorphism);
var xs = Morphism.Create(@"K, L\in\Hom_{\Cat[\moncat{V}]}(\encat{C}, \encat{D})").ToList();
xs.Count.Is(2);
xs[0].TestMorphism(@"K", @"\encat {C}", @"\encat {D}", MorphismType.Functor);
xs[1].TestMorphism(@"L", @"\encat {C}", @"\encat {D}", MorphismType.Functor);
xs = Morphism.Create(@"s, t\in\Hom_{\Cat}(\Set, \Mod[R])").ToList();
xs.Count.Is(2);
xs[0].TestMorphism("s", "\\Set", "\\Mod [R]", MorphismType.Functor);
xs[1].TestMorphism("t", "\\Set", "\\Mod [R]", MorphismType.Functor);
Morphism.Create(@"f\in\Hom(a_i, c^b)").TestSingle().TestMorphism("f", "a_{i}", "c^{b}", MorphismType.OneMorphism);
}
public void CreateTwoMorphism()
{
Morphism.Create(@"\theta\colon F\Rightarrow G").TestSingle().TestMorphism(@"\theta", "F", "G", MorphismType.TwoMorphism);
Morphism.Create(@"\theta_i\colon Fi\rightarrow Gi").TestSingle().TestMorphism(@"\theta _{i}", "Fi", "Gi", MorphismType.OneMorphism);
Morphism.Create(@"\theta\colon F\Rightarrow G").TestSingle().TestMorphism(@"\theta", "F", "G", MorphismType.TwoMorphism);
Morphism.Create(@"\Gamma\colon\theta\Rrightarrow\rho").TestSingle().TestMorphism(@"\Gamma", @"\theta", @"\rho", MorphismType.ThreeMorphism);
var xs = Morphism.Create(@"\alpha, \beta, \gamma\colon F\Rightarrow G\colon A\rightarrow B").ToList();
xs.Count.Is(5);
xs[0].TestMorphism("F", "A", "B", MorphismType.OneMorphism);
xs[1].TestMorphism("G", "A", "B", MorphismType.OneMorphism);
xs[2].TestMorphism(@"\alpha", "F", "G", MorphismType.TwoMorphism);
xs[3].TestMorphism(@"\beta", "F", "G", MorphismType.TwoMorphism);
xs[4].TestMorphism(@"\gamma", "F", "G", MorphismType.TwoMorphism);
xs = Morphism.Create(@"\theta\colon F\Rightarrow G\colon C\rightarrow D").ToList();
xs.Count.Is(3);
xs[0].TestMorphism("F", @"C", @"D", MorphismType.OneMorphism);
xs[1].TestMorphism("G", @"C", @"D", MorphismType.OneMorphism);
xs[2].TestMorphism(@"\theta", "F", "G", MorphismType.TwoMorphism);
}
public void Morphismでない()
{
Morphism.Create(@"a").Count().Is(0);
Morphism.Create(@"\cat{C}").Count().Is(0);
}