public void 数3()
{
var mor = ToMorphismHelp(@"M^{#1#2#3}", @"\bicat{B}(#2, #3)\times\bicat{B}(#1, #2)", @"\bicat{B}(#1, #3)", MorphismType.Bifunctor);
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
mor,
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"M^{abc}")
.TestMorphism(@"M^{abc}", @"\bicat{B}(b, c)\times\bicat{B}(a, b)", @"\bicat{B}(a, c)", MorphismType.Bifunctor);
tikz.CreateMorphism(@"M^{abc}", @"\bicat{B}(b, c)\times\bicat{B}(a, b)", @"\bicat{B}(a, c)")
.TestMorphism(@"M^{abc}", @"\bicat{B}(b, c)\times\bicat{B}(a, b)", @"\bicat{B}(a, c)", MorphismType.Bifunctor, true);
tikz.CreateMorphism(@"M^{ace}")
.TestMorphism(@"M^{ace}", @"\bicat{B}(c, e)\times\bicat{B}(a, c)", @"\bicat{B}(a, e)", MorphismType.Bifunctor);
tikz.CreateMorphism(@"M^{abb}")
.TestMorphism(@"M^{abb}", @"\bicat{B}(b, b)\times\bicat{B}(a, b)", @"\bicat{B}(a, b)", MorphismType.Bifunctor);
tikz.CreateMorphism(@"M^{Fa, Fb, Fc}")
.TestMorphism(@"M^{Fa, Fb, Fc}", @"\bicat{B}(Fb, Fc)\times\bicat{B}(Fa, Fb)", @"\bicat{B}(Fa, Fc)", MorphismType.Bifunctor);
}
public void 数LeftUnitor2()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
ToMorphismHelp(@"\lambda^{#1?}_{#2?}", @"\id_{#3?}\ocmp #2", @"#2", MorphismType.OneMorphism)
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\lambda_f", @"\id_b\ocmp f", "f")
.TestMorphism(@"\lambda_f", @"\id_b\ocmp f", @"f", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\lambda_f", @"\id\ocmp f", "f")
.TestMorphism(@"\lambda_f", @"\id\ocmp f", @"f", MorphismType.OneMorphism, true);
}
public void 数二項演算()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = ExtensionsInTest.CreateDefaultMorphisms();
list.Add(ToMorphismHelp(@"\rho^{#1?}_{#2?}", @"#2\otimes\Vunit", @"#2", MorphismType.OneMorphism));
list.Add(ToMorphismHelp(@"\rho^{#1?}_{#2?}", @"#2\Vunit", @"#2", MorphismType.OneMorphism));
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\rho^{ab}_x\otimes\rho_u", @"(x\otimes \Vunit)\otimes (u\otimes \Vunit)", @"x\otimes u")
.TestMorphism(@"\rho^{ab}_x\otimes\rho_u", @"(x\otimes \Vunit)\otimes (u\otimes \Vunit)", @"x\otimes u", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\id\otimes\rho^{ab}_x", @"a\otimes (x\otimes \Vunit)", @"a \otimes x")
.TestMorphism(@"\id\otimes\rho^{ab}_x", @"a\otimes (x\otimes \Vunit)", @"a \otimes x", MorphismType.OneMorphism, true);
}
public void Morphism二項演算_省略()
{
var mor1 = ToMorphismHelp(@"f", "a", "b", MorphismType.OneMorphism);
var mor2 = ToMorphismHelp(@"g", "s", "t", MorphismType.OneMorphism);
var mor3 = ToMorphismHelp(@"X", @"\test{A}", @"\test{B}", MorphismType.OneMorphism);
var mor4 = ToMorphismHelp(@"Y", @"\test{C}", @"\test{D}", MorphismType.OneMorphism);
var mor5 = ToMorphismHelp(@"\beta_i", "Fi", "Gi", MorphismType.OneMorphism);
var mor6 = ToMorphismHelp(@"\gamma_j", "Kj", "Lj", MorphismType.OneMorphism);
var mor7 = ToMorphismHelp(@"\sigma", "P", "Q", MorphismType.NaturalTransformation);
var mor8 = ToMorphismHelp(@"\tau", "R", "S", MorphismType.NaturalTransformation);
var dic = new Dictionary <TokenString, Morphism>()
{
{ mor1.Name.ToTokenString(), mor1 },
{ mor2.Name.ToTokenString(), mor2 },
{ mor3.Name.ToTokenString(), mor3 },
{ mor4.Name.ToTokenString(), mor4 },
{ mor5.Name.ToTokenString(), mor5 },
{ mor6.Name.ToTokenString(), mor6 },
{ mor7.Name.ToTokenString(), mor7 },
{ mor8.Name.ToTokenString(), mor8 },
};
var tikz = new TikZDiagram("", -1, false, true, true, dic, ExtensionsInTest.CreateDefaultMorphisms(), ExtensionsInTest.CreateDefaultFunctors().ToList());
var mor = tikz.CreateMorphism(@"f\otimes g", @"as", @"bt");
mor.TestMorphism(@"f\otimes g", @"as", @"bt", MorphismType.OneMorphism, true);
mor = tikz.CreateMorphism(@"X\otimes Y", @"(\test{A})(\test{C})", @"(\test{B})(\test{D})");
mor.TestMorphism(@"X\otimes Y", @"(\test{A})(\test{C})", @"(\test{B})(\test{D})", MorphismType.OneMorphism, true);
mor = tikz.CreateMorphism(@"\beta_i\otimes\gamma_j", @"(Fi)(Kj)", @"(Gi)(Lj)");
mor.TestMorphism(@"\beta_i\otimes\gamma_j", @"(Fi)(Kj)", @"(Gi)(Lj)", MorphismType.OneMorphism, true);
mor = tikz.CreateMorphism(@"\sigma_a\otimes\tau_b", @"(Pa)(Rb)", @"(Qa)(Sb)");
mor.TestMorphism(@"\sigma_a\otimes\tau_b", @"(Pa)(Rb)", @"(Qa)(Sb)", MorphismType.OneMorphism, true);
mor = tikz.CreateMorphism(@"(\sigma_a\otimes\tau_b)\otimes\beta_i", @"((Pa)(Rb))(Fi)", @"((Qa)(Sb))(Gi)");
mor.TestMorphism(@"(\sigma_a\otimes\tau_b)\otimes\beta_i", @"((Pa)(Rb))(Fi)", @"((Qa)(Sb))(Gi)",
MorphismType.OneMorphism, true);
mor = tikz.CreateMorphism(@"\sigma_a\otimes(\tau_b\otimes\beta_i)", @"(Pa)((Rb)(Fi))", @"(Qa)((Sb)(Gi))");
mor.TestMorphism(@"\sigma_a\otimes (\tau_b\otimes\beta_i)", @"(Pa)((Rb)(Fi))", @"(Qa)((Sb)(Gi))",
MorphismType.OneMorphism, true);
}
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 数RightUnitor()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
ToMorphismHelp(@"\rho^{#1?}_{#2?}", @"#2\otimes\Vunit", @"#2", MorphismType.OneMorphism)
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\rho_x", @"\Vunit\otimes x", null)
.TestMorphism(@"\rho_x", @"x\otimes \Vunit", @"x", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\rho_x^{-1}", "x", @"x\otimes\Vunit")
.TestMorphism(@"\rho_x^{-1}", "x", @"x\otimes \Vunit", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\rho_{u\otimes v}", @"(u\otimes v)\otimes \Vunit", @"u\otimes v")
.TestMorphism(@"\rho_{u\otimes v}", @"(u\otimes v)\otimes \Vunit", @"u\otimes v", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\rho", @"x\otimes \Vunit", "x")
.TestMorphism(@"\rho", @"x\otimes \Vunit", @"x", MorphismType.OneMorphism, true);
}
public void 数Associator_NotNull()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
ToMorphismHelp(@"\alpha^{#1}_{#2#3#4}", @"(#2\otimes #3)\otimes #4", @"#2\otimes (#3\otimes #4)", MorphismType.OneMorphism)
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\alpha^{abcd}_{uvw}")
.TestMorphism(@"\alpha^{abcd}_{uvw}", @"(u\otimes v)\otimes w", @"u\otimes(v\otimes w)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\alpha^x_{u, v\otimes w, x}")
.TestMorphism(@"\alpha^x_{u, v\otimes w, x}", @"(u\otimes (v\otimes w))\otimes x", @"u\otimes((v\otimes w)\otimes x)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"(\alpha_{abc}^x)^{-1}")
.TestMorphism(@"(\alpha_{abc}^x)^{-1}", @"a\otimes(b\otimes c)", @"(a\otimes b)\otimes c", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\alpha^x_{Fu, Fv, Fw}")
.TestMorphism(@"\alpha^x_{Fu, Fv, Fw}", @"(Fu\otimes Fv)\otimes Fw", @"Fu\otimes(Fv\otimes Fw)", 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 数ab()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
ToMorphismHelp(@"\ev", @"[#1a, #2]\otimes #1b", @"#2", MorphismType.OneMorphism)
};
var func = ExtensionsInTest.CreateDefaultFunctors().ToList();
func.Add(Functor.Create("F#1", "G#1"));
func.Add(Functor.Create("X", "Y"));
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, func);
tikz.CreateMorphism(@"\ev", @"[u, v]\otimes u", @"v")
.TestMorphism(@"\ev", @"[u, v]\otimes u", @"v", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\ev", @"[X, v]\otimes Y", @"v")
.TestMorphism(@"\ev", @"[X, v]\otimes Y", @"v", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\ev", @"[Fu, v]\otimes Gu", @"v")
.TestMorphism(@"\ev", @"[Fu, v]\otimes Gu", @"v", MorphismType.OneMorphism, true);
}
public void 数1()
{
var mor = ToMorphismHelp(@"\test{#1}", "F(#1)", "G(#1)", MorphismType.OneMorphism);
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
mor,
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\test a")
.TestMorphism(@"\test a", "F(a)", "G(a)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\test{x}")
.TestMorphism(@"\test{x}", "F(x)", "G(x)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\test{x^i_j}")
.TestMorphism(@"\test{x^i_j}", "F(x^i_j)", "G(x^i_j)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\test{\alpha\beta}")
.TestMorphism(@"\test{\alpha\beta}", @"F(\alpha\beta)", @"G(\alpha\beta)", MorphismType.OneMorphism);
}
public void 数二項演算_省略2()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = ExtensionsInTest.CreateDefaultMorphisms();
list.Add(ToMorphismHelp(@"\rho^{#1?}_{#2?}", @"#2\otimes\Vunit", @"#2", MorphismType.OneMorphism));
list.Add(ToMorphismHelp(@"\rho^{#1?}_{#2?}", @"#2\Vunit", @"#2", MorphismType.OneMorphism));
list.Add(ToMorphismHelp(@"\lambda^{#1?}_{#2?}", @"\Vunit #2", @"#2", MorphismType.OneMorphism));
var tikz = new TikZDiagram("", -1, false, true, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\rho^{ab}_x\otimes\rho_u", @"(x\Vunit)(u\Vunit)", @"xu")
.TestMorphism(@"\rho^{ab}_x\otimes\rho_u", @"(x\Vunit)(u\Vunit)", @"xu", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\id\otimes\rho^{ab}_x", @"a(x\Vunit)", @"ax")
.TestMorphism(@"\id\otimes\rho^{ab}_x", @"a(x\Vunit)", @"ax", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\lambda\otimes(\id\otimes\rho)", @"(\Vunit a)(s(x\Vunit))", @"a(sx)")
.TestMorphism(@"\lambda\otimes(\id\otimes\rho)", @"(\Vunit a)(s(x\Vunit))", @"a(sx)", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\lambda", @"\Vunit \encat{C}_{ab}", @"\encat{C}_{ab}")
.TestMorphism(@"\lambda", @"\Vunit \encat{C}_{ab}", @"\encat{C}_{ab}", MorphismType.Functor, true);
tikz.CreateMorphism(@"\id\otimes\rho",
@"\encat{C}_{st}(\encat{C}_{xz}\Vunit)",
@"\encat{C}_{st}\encat{C}_{xz}")
.TestMorphism(@"\id\otimes\rho",
@"\encat{C}_{st}(\encat{C}_{xz}\Vunit)",
@"\encat{C}_{st}\encat{C}_{xz}", MorphismType.Functor, true);
tikz.CreateMorphism(@"\lambda\otimes(\id\otimes\rho)",
@"(\Vunit \encat{C}_{ab})(\encat{C}_{st}(\encat{C}_{xz}\Vunit))",
@"\encat{C}_{ab}(\encat{C}_{st}\encat{C}_{xz})")
.TestMorphism(@"\lambda\otimes(\id\otimes\rho)",
@"(\Vunit \encat{C}_{ab})(\encat{C}_{st}(\encat{C}_{xz}\Vunit))",
@"\encat{C}_{ab}(\encat{C}_{st}\encat{C}_{xz})", MorphismType.Functor, true);
}
public void 数Associator_Null()
{
var dic = new Dictionary <TokenString, Morphism>();
var list = new List <Morphism>()
{
ToMorphismHelp(@"\alpha^{#1?}_{#2?#3?#4?}", @"(#2\otimes #3)\otimes #4", @"#2\otimes (#3\otimes #4)", MorphismType.OneMorphism)
};
var tikz = new TikZDiagram("", -1, false, false, true, dic, list, Array.Empty <Functor>());
tikz.CreateMorphism(@"\alpha_{uvw}", @"(u\otimes v)\otimes w", null)
.TestMorphism(@"\alpha_{uvw}", @"(u\otimes v)\otimes w", @"u\otimes(v\otimes w)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\alpha_{u, v\otimes w, x}")
.TestMorphism(@"\alpha_{u, v\otimes w, x}", @"(u\otimes (v\otimes w))\otimes x", @"u\otimes((v\otimes w)\otimes x)", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\alpha_{abc}^{-1}", @"a\otimes(b\otimes c)")
.TestMorphism(@"\alpha_{abc}^{-1}", @"a\otimes(b\otimes c)", @"(a\otimes b)\otimes c", MorphismType.OneMorphism);
tikz.CreateMorphism(@"\alpha", @"(u\otimes v)\otimes w", @"u\otimes (v\otimes w)")
.TestMorphism(@"\alpha", @"(u\otimes v)\otimes w", @"u\otimes(v\otimes w)", MorphismType.OneMorphism, true);
tikz.CreateMorphism(@"\alpha", @"(\encat{A}\otimes \encat{B})\otimes \encat{C}", @"\encat{A}\otimes (\encat{B}\otimes \encat{C})")
.TestMorphism(@"\alpha", @"(\encat{A}\otimes \encat{B})\otimes \encat{C}", @"\encat{A}\otimes(\encat{B}\otimes \encat{C})", MorphismType.Functor, true);
}
