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-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html - -[dependencies] -num = "0.3.1" -nalgebra = "0.27.1" -num-complex = "0.3.1" -rayon = "1.5.1" - -[profile.release] -debug = true diff --git a/fractal_dimension/bai_finch_rust/src/main.rs b/fractal_dimension/bai_finch_rust/src/main.rs deleted file mode 100644 index 792004a..0000000 --- a/fractal_dimension/bai_finch_rust/src/main.rs +++ /dev/null @@ -1,271 +0,0 @@ -#![allow(dead_code)] - -use num_complex::Complex64; - -type F = f64; -type Matrix2x2 = nalgebra::SMatrix; -type MatrixBig = nalgebra::DMatrix; -type MatrixBigr = nalgebra::DMatrix; - -const G: Matrix2x2 = Matrix2x2::new( - Complex64::new(2.0 / 12.0, -2.0 / 12.0), - Complex64::new(-1.0 / 12.0, -5.0 / 12.0), - Complex64::new(4.0 / 12.0, -4.0 / 12.0), - Complex64::new(-2.0 / 12.0, -10.0 / 12.0), -); - -const R: Matrix2x2 = Matrix2x2::new( - Complex64::new(-6.0 / 12.0, 8.0 / 12.0), - Complex64::new(0.0, 11.0 / 12.0), - Complex64::new(0.0, 4.0 / 12.0), - Complex64::new(-6.0 / 12.0, -8.0 / 12.0), -); - -const NC: usize = 5; -const K0: i32 = 100; -const LC: usize = 3; -const NC2: usize = NC * NC; -const UPPER_BOUND: i32 = 10_000; - -fn fancy_l(q: f64) -> MatrixBigr { - let mut fancy_l = MatrixBigr::zeros(NC2, NC2); - for m in 0..NC { - for n in 0..NC { - for r in 0..NC { - for s in 0..NC { - if m <= n { - let mut sum_m = Complex64::new(0.0, 0.0); - for k in 1..K0 { - sum_m += normal_m(k, q, n as i32, s as i32) - * normal_m(k as i32, q, m as i32, r as i32).conj(); - } - let sum_f = (0..=LC) - .map(|l: usize| -> Complex64 { - zeta(l as f64 + 2.0 * q, K0) - * (0..=l) - .map(|lp| { - normal_f(q, m as i32, r as i32, (l - lp) as i32) - * normal_f(q, n as i32, s as i32, lp as i32).conj() - }) - .sum::() - }) - .sum::(); - fancy_l[(m * NC + n, r * NC + s)] = 2.0 * (sum_m.re + sum_f.re); - } else { - fancy_l[(m * NC + n, r * NC + s)] = fancy_l[(n * NC + m, s * NC + r)]; - } - } - } - } - } - fancy_l - // MatrixBigr::from_diagonal_element(NC2, NC2, 2.0) * (fancy_m(q) + fancy_f(q)).map(|z| z.re) -} - -fn integral_choose(n: i32, k: i32) -> f64 { - match k.cmp(&0) { - std::cmp::Ordering::Less => 0.0, - std::cmp::Ordering::Equal => 1.0, - std::cmp::Ordering::Greater => (0..k).map(|i| (n - i) as f64 / (k - i) as f64).product(), - } -} - -fn non_integral_choose(q: f64, k: i32) -> f64 { - match k.cmp(&0) { - std::cmp::Ordering::Less => 0.0, - std::cmp::Ordering::Equal => 1.0, - std::cmp::Ordering::Greater => (0..k).map(|i| (q - i as f64) / (k - i) as f64).product(), - } -} - -fn normal_f(q: f64, n: i32, s: i32, l: i32) -> Complex64 { - let r11 = R[(0, 0)]; - let r12 = R[(0, 1)]; - let r21 = R[(1, 0)]; - let r22 = R[(1, 1)]; - - let g11 = G[(0, 0)]; - let g12 = G[(0, 1)]; - let g21 = G[(1, 0)]; - let g22 = G[(1, 1)]; - (0..=s) - .into_iter() - .map(|j: i32| -> Complex64 { - non_integral_choose(-n as f64 - q, j) - * integral_choose(n, s - j) - * (0..=j) - .map(|l1: i32| -> Complex64 { - (0..=(s - j)) - .map(|l3: i32| -> Complex64 { - (0..=(n - s + j)) - .map(|l4: i32| -> Complex64 { - integral_choose(j, l1) - * non_integral_choose( - -n as f64 - q - j as f64, - l - l1 - l3 - l4, - ) - * integral_choose(s - j, l3) - * integral_choose(n - s + j, l4) - * r21.powi(l1) - * r22.powi(l - l1 - l3 - l4) - * r11.powi(l3) - * r12.powi(l4) - * g21.powi(j - l1) - * g22.powf( - -n as f64 - q - j as f64 - l as f64 - + l1 as f64 - + l3 as f64 - + l4 as f64, - ) - * g11.powi(s - j - l3) - * g12.powi(n - s + j - l4) - }) - .sum() - }) - .sum() - }) - .sum::() - }) - .sum() -} - -fn zeta(s: f64, k0: i32) -> f64 { - (k0..=UPPER_BOUND) - .into_iter() - .map(|j| (j as f64).powf(-s)) - .sum::() - - (UPPER_BOUND as f64).powf(1.0 - s) / (1.0 - s) -} - -fn fancy_f(q: f64) -> MatrixBig { - let mut fancy_f = MatrixBig::zeros(NC2, NC2); - for m in 0..NC { - for n in 0..NC { - for r in 0..NC { - for s in 0..NC { - if m <= n { - fancy_f[(m * NC + n, r * NC + s)] = (0..=LC) - .map(|l: usize| -> Complex64 { - zeta(l as f64 + 2.0 * q, K0) - * (0..=l) - .map(|lp| { - normal_f(q, m as i32, r as i32, (l - lp) as i32) - * normal_f(q, n as i32, s as i32, lp as i32).conj() - }) - .sum::() - }) - .sum::(); - } else { - fancy_f[(m * NC + n, r * NC + s)] = - fancy_f[(n * NC + m, s * NC + r)].conj(); - } - } - } - } - } - fancy_f -} - -fn normal_m(k: i32, q: f64, n: i32, s: i32) -> Complex64 { - let ak = R + Matrix2x2::from_diagonal_element(Complex64::new(k as f64, 0.0)) * G; - let a11 = ak[(0, 0)]; - let a12 = ak[(0, 1)]; - let a21 = ak[(1, 0)]; - let a22 = ak[(1, 1)]; - - (0..=s) - .into_iter() - .map(|j| { - non_integral_choose(-n as f64 - q, j) - * integral_choose(n, s - j) - * a21.powi(j) - * a22.powf(-n as f64 - q - j as f64) - * a11.powi(s - j) - * a12.powi(n - s + j) - }) - .sum() -} - -fn fancy_m(q: f64) -> MatrixBig { - let mut fancy_m = MatrixBig::zeros(NC2, NC2); - for m in 0..NC { - for n in 0..NC { - for r in 0..NC { - for s in 0..NC { - if m <= n { - let mut sum = Complex64::new(0.0, 0.0); - for k in 1..K0 { - sum += normal_m(k, q, n as i32, s as i32) - * normal_m(k as i32, q, m as i32, r as i32).conj(); - } - fancy_m[(m * NC + n, r * NC + s)] = sum; - } else { - fancy_m[(m * NC + n, r * NC + s)] = - fancy_m[(n * NC + m, s * NC + r)].conj(); - } - } - } - } - } - fancy_m -} - -fn secant_method(f: fn(F) -> F, target: F, x0: F, x1: F, accuracy: F, iterations: usize) -> F { - let mut x0 = x0; - let mut x1 = x1; - let mut y0 = f(x0); - let mut y1 = f(x1); - let mut count = 0; - - println!("f({}) =\t{}", x1, y1); - while (y1 - target).abs() >= accuracy && count < iterations { - let new_x = x0 - (y0 - target) * (x1 - x0) / (y1 - y0); - x0 = x1; - x1 = new_x; - y0 = y1; - y1 = f(x1); - println!("f({}) =\t{}", x1, y1); - count += 1; - } - x0 -} - -fn power_method( - vec: nalgebra::DVector, - mat: nalgebra::DMatrix, - iterations: usize, - tolerance: f64, -) -> f64 { - let mut previous_entry = vec[0]; - let mut previous_val = 0f64; - let mut current = mat.clone() * vec; - let mut current_val = current[0] / previous_entry; - let mut count = 0; - while count < iterations && (current_val - previous_val).abs() > tolerance { - previous_val = current_val; - previous_entry = current[0]; - current = mat.clone() * current; - current_val = current[0] / previous_entry; - count += 1; - } - - println!("found eigenvalue {} in {} iterations", current_val, count); - current_val -} - -fn test(x: f64) -> f64 { - x.cos() - x -} - -fn lambda(q: f64) -> f64 { - let lq = fancy_l(q); - let mut phi0 = nalgebra::DVector::zeros(NC2); - phi0[0] = 1.0; - power_method(phi0, lq, 50, std::f64::EPSILON) -} - -fn main() { - // secant_method(lambda, 1.0, 1.3, 1.31, f64::EPSILON, 100); - // secant_method(test, 0.0, 0.0, 1.0, f64::EPSILON, 100); - println!("{}", normal_m(5, 1.3, 3, 3)); -} diff --git a/fractal_dimension/fractal_dimension.nb b/fractal_dimension/fractal_dimension.nb index a2b8e02..c094feb 100644 --- a/fractal_dimension/fractal_dimension.nb +++ b/fractal_dimension/fractal_dimension.nb @@ -10,14 +10,35 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 356704, 8682] -NotebookOptionsPosition[ 352872, 8631] -NotebookOutlinePosition[ 353362, 8649] -CellTagsIndexPosition[ 353319, 8646] +NotebookDataLength[ 359067, 8756] +NotebookOptionsPosition[ 353340, 8675] +NotebookOutlinePosition[ 353830, 8693] +CellTagsIndexPosition[ 353787, 8690] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ + +Cell[CellGroupData[{ +Cell["Handy functions", "Section", + CellChangeTimes->{{3.8646830510411797`*^9, + 3.864683053091597*^9}},ExpressionUUID->"d9d62207-947e-4a55-994c-\ +be968ba39c8b"], + +Cell[CellGroupData[{ + +Cell["Quadratic forms and linear relations", "Subsection", + CellChangeTimes->{{3.8646832235938597`*^9, + 3.864683227491637*^9}},ExpressionUUID->"ffcc14d7-54b2-406a-8618-\ +9531332769aa"], + +Cell["\<\ +Gets a list of indices of the pivots of a matrix in reduced echelon form.\ +\>", "Text", + CellChangeTimes->{{3.8646834675398283`*^9, 3.864683486796194*^9}, + 3.864683635933962*^9},ExpressionUUID->"ac72a206-5663-4fb8-9a75-\ +6d188f4c76e1"], + Cell[BoxData[ RowBox[{ RowBox[{"pivots", "[", "A_", "]"}], ":=", @@ -29,6 +50,30 @@ Cell[BoxData[ 3.831194930347896*^9, 3.831194932848599*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"e1bc883b-2413-4a7d-abe0-4a19eb3f78fd"], +Cell[TextData[{ + "Constructs the matrix we\[CloseCurlyQuote]ve been calling ", + Cell[BoxData[ + FormBox[ + TemplateBox[<|"boxes" -> FormBox[ + StyleBox["P", "TI"], TraditionalForm], "errors" -> {}, "input" -> "P", + "state" -> "Boxes"|>, + "TeXAssistantTemplate"], TraditionalForm]],ExpressionUUID-> + "b6d67594-7399-484f-ab24-507fe2e7cb7d"], + " of any dimension. The most useful one by far is the ", + Cell[BoxData[ + FormBox[ + TemplateBox[<|"boxes" -> FormBox[ + RowBox[{"4", "\[Cross]", "4"}], TraditionalForm], "errors" -> {}, + "input" -> "4\\times 4", "state" -> "Boxes"|>, + "TeXAssistantTemplate"], TraditionalForm]],ExpressionUUID-> + "a290e079-0f52-414c-9475-c308d5277d84"], + " one." +}], "Text", + CellChangeTimes->{{3.864683498626568*^9, 3.864683509251071*^9}, { + 3.864683595451868*^9, 3.864683668047246*^9}, {3.864731506766433*^9, + 3.86473166070006*^9}},ExpressionUUID->"87b40a25-ff96-4305-b802-\ +220d3c3714ee"], + Cell[BoxData[ RowBox[{ RowBox[{"pMatrix", "[", "n_", "]"}], ":=", @@ -56,7 +101,15 @@ Cell[BoxData[ CellChangeTimes->{{3.831107414093502*^9, 3.83110748040809*^9}, { 3.831107557920609*^9, 3.8311075805621977`*^9}, {3.8311076270925627`*^9, 3.831107722019619*^9}, {3.83468833600141*^9, 3.8346883410498962`*^9}}, - CellLabel->"In[2]:=",ExpressionUUID->"025b5df5-f2a6-4cee-a294-e76ee16e74d4"], + CellLabel->"In[9]:=",ExpressionUUID->"025b5df5-f2a6-4cee-a294-e76ee16e74d4"], + +Cell["\<\ +Computes the gram matrix given a matrix whose columns are circles in a tuple \ +in abbc coordinates.\ +\>", "Text", + CellChangeTimes->{{3.86468368363731*^9, + 3.8646837180951366`*^9}},ExpressionUUID->"03438c1b-508d-4333-9054-\ +9967574ef3d3"], Cell[BoxData[ RowBox[{ @@ -71,6 +124,15 @@ Cell[BoxData[ 3.831110193792735*^9}}, CellLabel->"In[3]:=",ExpressionUUID->"54cc4a6c-be37-4091-ac21-3dfd11eb53ea"], +Cell["\<\ +Computes the linear relations matrix given the gram matrix. This matrix maps \ +vectors of just four curvatures into the full tuple.\ +\>", "Text", + CellChangeTimes->{{3.864683730604188*^9, 3.864683747937598*^9}, { + 3.8646837997502403`*^9, + 3.8646838957084618`*^9}},ExpressionUUID->"b44fae9e-11fd-4fea-9594-\ +87a6c311bec8"], + Cell[BoxData[ RowBox[{ RowBox[{"linearRelationsMatrix", "[", "G_", "]"}], ":=", @@ -82,7 +144,14 @@ Cell[BoxData[ RowBox[{"MatrixRank", "[", "G", "]"}]}], "]"}], "]"}], "//", "Transpose"}]}]], "Input", CellChangeTimes->{{3.831109396818718*^9, 3.831109426888632*^9}}, - CellLabel->"In[4]:=",ExpressionUUID->"d3298122-6e10-4115-8e61-a949acba4e08"], + CellLabel->"In[3]:=",ExpressionUUID->"d3298122-6e10-4115-8e61-a949acba4e08"], + +Cell["\<\ +Converts the linear relations matrix into more human-readable equations.\ +\>", "Text", + CellChangeTimes->{{3.8646839148506317`*^9, + 3.86468394900528*^9}},ExpressionUUID->"551afa7d-856b-46fe-8670-\ +51fd64eff7cc"], Cell[BoxData[ RowBox[{ @@ -118,7 +187,12 @@ Cell[BoxData[ 3.831194680087949*^9, 3.831194680680228*^9}, {3.831194956352386*^9, 3.831195002875142*^9}, {3.831205178380069*^9, 3.831205187846324*^9}, 3.834688343633176*^9}, - CellLabel->"In[5]:=",ExpressionUUID->"4e2a5664-aeb5-4dfb-88fb-7e7839ba2141"], + CellLabel->"In[11]:=",ExpressionUUID->"4e2a5664-aeb5-4dfb-88fb-7e7839ba2141"], + +Cell["Same but from a tuple.", "Text", + CellChangeTimes->{{3.86468395374198*^9, + 3.864683987995091*^9}},ExpressionUUID->"7914b40a-8924-4161-b52d-\ +1ca82c95c0c4"], Cell[BoxData[ RowBox[{ @@ -130,6 +204,15 @@ Cell[BoxData[ 3.831206070230084*^9}, CellLabel->"In[6]:=",ExpressionUUID->"c9a1b25a-8cb3-40d1-ac83-1d2405398934"], +Cell["\<\ +A left inverse for the linear relations matrix (i.e. sends a full tuple to \ +just the four \[OpenCurlyDoubleQuote]special\[CloseCurlyDoubleQuote] linearly \ +independent curvatures).\ +\>", "Text", + CellChangeTimes->{{3.864684056842209*^9, + 3.864684121412198*^9}},ExpressionUUID->"777e5618-fae9-4bb5-b529-\ +4f4902364898"], + Cell[BoxData[ RowBox[{ RowBox[{"inverseLinearRelations", "[", "G_", "]"}], ":=", @@ -163,7 +246,24 @@ Cell[BoxData[ "]"}]}], ")"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.831194278291965*^9, 3.831194298458626*^9}, 3.831195204231324*^9}, - CellLabel->"In[7]:=",ExpressionUUID->"30b57c08-a123-4e7d-9b0a-b512fcfecee8"], + CellLabel->"In[13]:=",ExpressionUUID->"30b57c08-a123-4e7d-9b0a-b512fcfecee8"], + +Cell[TextData[{ + "Various functions to construct a quadratic form associated with a packing \ +from the root tuple, ", + Cell[BoxData[ + FormBox[ + TemplateBox[<|"boxes" -> FormBox[ + StyleBox["G", "TI"], TraditionalForm], "errors" -> {}, "input" -> "G", + "state" -> "Boxes"|>, + "TeXAssistantTemplate"], TraditionalForm]],ExpressionUUID-> + "b2c98825-e401-425d-b550-e32292e83fe4"], + ", etc." +}], "Text", + CellChangeTimes->{{3.864684144417095*^9, 3.864684183254436*^9}, { + 3.8647314865256433`*^9, + 3.86473148733366*^9}},ExpressionUUID->"c96de117-3c03-4391-9112-\ +59dc2aa87e38"], Cell[BoxData[ RowBox[{ @@ -243,7 +343,22 @@ Cell[BoxData[ RowBox[{"G", ",", "L"}], "]"}], ",", "L"}], "]"}]}], "]"}]}]], "Input",\ CellChangeTimes->{{3.8312049925958433`*^9, 3.8312050200596113`*^9}}, - CellLabel->"In[11]:=",ExpressionUUID->"810323e6-91cb-44f2-ad55-323fbec422eb"], + CellLabel->"In[11]:=",ExpressionUUID->"810323e6-91cb-44f2-ad55-323fbec422eb"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Graph utilities", "Subsection", + CellChangeTimes->{{3.86468325145858*^9, + 3.864683253669279*^9}},ExpressionUUID->"30f99b83-ea38-48b2-b913-\ +e9a970532db2"], + +Cell["\<\ +Given G, returns a planar Mathematica graph representing the tangencies\ +\>", "Text", + CellChangeTimes->{{3.864684194015627*^9, + 3.864684215161499*^9}},ExpressionUUID->"4192620c-85de-4442-8b77-\ +a4f0439b11b4"], Cell[BoxData[ RowBox[{ @@ -266,6 +381,24 @@ Cell[BoxData[ 3.831584545556731*^9, 3.831584563248426*^9}}, CellLabel->"In[12]:=",ExpressionUUID->"948959db-c926-4458-9e45-ef7f3fb99ba5"], +Cell[TextData[{ + "A series of functions stolen from StackOverflow that find the faces of a \ +planar graph (which are unique in our case, since the graph is always the \ +vertex graph of a polyhedron). Usefully, the indices are guaranteed to line \ +up with ", + Cell[BoxData[ + FormBox[ + TemplateBox[<|"boxes" -> FormBox[ + StyleBox["G", "TI"], TraditionalForm], "errors" -> {}, "input" -> "G", + "state" -> "Boxes"|>, + "TeXAssistantTemplate"], TraditionalForm]],ExpressionUUID-> + "6d8e0958-42ce-4301-a0a0-b98a052dbdf6"] +}], "Text", + CellChangeTimes->{{3.8646842229863787`*^9, 3.864684357501741*^9}, { + 3.864731477969768*^9, + 3.864731478614419*^9}},ExpressionUUID->"652feb5a-94e0-4b51-96b7-\ +66625315f8ef"], + Cell[BoxData[ RowBox[{ RowBox[{ @@ -312,7 +445,7 @@ Cell[BoxData[{ "\[IndentingNewLine]", RowBox[{"FindFace", "[", RowBox[{"g", ",", "emb"}], "]"}]}]}], "]"}]}], ";"}], - "\[IndentingNewLine]"}], "\n", + "\n"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FindFace", "[", RowBox[{ @@ -403,7 +536,26 @@ Cell[BoxData[{ CellChangeTimes->{{3.8312108953940573`*^9, 3.831210895411563*^9}, 3.8312119634327393`*^9, 3.831542420732052*^9, {3.834688353349917*^9, 3.8346883534550037`*^9}}, - CellLabel->"In[14]:=",ExpressionUUID->"5cb4f612-3c02-42ac-ad57-4fb2daf3366b"], + CellLabel->"In[14]:=",ExpressionUUID->"5cb4f612-3c02-42ac-ad57-4fb2daf3366b"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Algebraic and Geometric Generators", "Subsection", + CellChangeTimes->{{3.864683268299602*^9, 3.864683270300555*^9}, { + 3.8646833152616262`*^9, + 3.8646833208091173`*^9}},ExpressionUUID->"a54eae0a-eac8-4408-bb48-\ +69eb10a7147f"], + +Cell["\<\ +These three functions find the generators of the algebraic Apollonian group \ +of a polyhedral packing. These yield different matrices from the process \ +discussed in our first paper, but they still work.\ +\>", "Text", + CellChangeTimes->{{3.864684365608055*^9, 3.864684397908317*^9}, { + 3.8646844317958393`*^9, + 3.864684510105069*^9}},ExpressionUUID->"6773c37a-4ed3-4315-9304-\ +64d7ebb905b7"], Cell[BoxData[ RowBox[{ @@ -845,6 +997,16 @@ Cell[BoxData[ 3.833982029038528*^9}, CellLabel->"In[18]:=",ExpressionUUID->"bd52b017-bd99-4bdf-9126-b7c62804c9f2"], +Cell["\<\ +abbctoxyr is a very convenient function for converting between abbc \ +coordinates and xyr (x,y coordinates of center and radius) coordinates. 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This is a very old algorithm that is extremely slow \ +and has serious issues. 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+NotebookOutlinePosition[ 33321, 879] +CellTagsIndexPosition[ 33278, 876] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ +Cell["Early Attempt at Finding Gram Matrices", "Title", + CellChangeTimes->{{3.864735481164455*^9, + 3.864735489248959*^9}},ExpressionUUID->"c51c1c8b-2540-4a63-92f6-\ +4e7d3d5f9d76"], + +Cell["\<\ +The goal here was to use a formula found by Dylan to construct a massive \ +system of equations and attempt to chuck it into \ +Mathematica\[CloseCurlyQuote]s Solve function in hopes of getting the gram \ +matrix out the other end, but this code at least didn\[CloseCurlyQuote]t end \ +up working particularly well. There is no guarantee that these equations are \ +solvable, which is unfortunate, and I think there are some mistakes or \ +something in this implementation, because it should work with some polyhedra.\ +\ +\>", "Text", + CellChangeTimes->{{3.864735500116888*^9, + 3.8647356437317877`*^9}},ExpressionUUID->"c3406f07-a0d8-4f8a-a2e4-\ +1d424c3c89ef"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Get", "[", "\"\False]], "Print", CellChangeTimes->{3.8321516294929905`*^9, 3.8321792446538467`*^9, - 3.8321888483607073`*^9, 3.83223375355267*^9}, + 3.8321888483607073`*^9, 3.83223375355267*^9, 3.864734398606039*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"fa2b838b-e3df-4e8d-9350-d8f470c0acc1"], +In[1]:=",ExpressionUUID->"9a0f644e-76e7-49b2-bf2e-a5a0439d2bff"], Cell[BoxData[ TemplateBox[{ @@ -50,13 +71,13 @@ with the same version number \ (\\!\\(\\*RowBox[{\\\"\\\\\\\"0.5.1\\\\\\\"\\\"}]\\)) is already installed. \ Use PacletUninstall to remove the existing version first, or call \ PacletInstall with ForceVersionInstall -> True.\"", 2, 1, 1, - 26206157531447520602, "Local"}, + 18949302130080748064, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.83217924731254*^9, 3.832188855090274*^9, - 3.832233757585519*^9}, + 3.832233757585519*^9, 3.864734407033389*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"7cedf722-9dff-466e-8c29-7474221bbcff"], +In[1]:=",ExpressionUUID->"1c5f7cf6-0738-487e-8e29-494d036393b4"], Cell[BoxData[ InterpretationBox[ @@ -70,10 +91,10 @@ Cell[BoxData[ Hyperlink["https://github.com/szhorvat/IGraphM#installation"]], Editable->False]], "Print", CellChangeTimes->{3.8321516294929905`*^9, 3.8321792446538467`*^9, - 3.8321888483607073`*^9, 3.832233757594738*^9}, + 3.8321888483607073`*^9, 3.83223375355267*^9, 3.864734407044916*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"bc4bba27-1aaf-4b2a-b377-2ee419fb494f"] +In[1]:=",ExpressionUUID->"f93216f6-8658-427f-a66d-a212aa30c39f"] }, Open ]], Cell[CellGroupData[{ @@ -94,8 +115,8 @@ Cell[BoxData[ GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"]], "Output", CellChangeTimes->{3.8321516533863616`*^9, 3.832179248194338*^9, - 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CellLabel->"In[5]:=",ExpressionUUID->"64960a86-3c40-410a-a0bf-67dc0dda7253"], + CellLabel->"In[4]:=",ExpressionUUID->"64960a86-3c40-410a-a0bf-67dc0dda7253"], Cell["Takes adjacency matrix and spits out dual adjacency matrix", "Text", CellChangeTimes->{{3.832168708906446*^9, @@ -150,7 +171,7 @@ Cell[BoxData[ RowBox[{"dgraph", "[", "adjmat", "]"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.8321574651675024`*^9, 3.8321575207418165`*^9}, { 3.832157919355533*^9, 3.832157942375414*^9}}, - CellLabel->"In[6]:=",ExpressionUUID->"2df0273a-68b0-4420-a181-5533de3142ef"], + CellLabel->"In[5]:=",ExpressionUUID->"2df0273a-68b0-4420-a181-5533de3142ef"], Cell["\<\ Takes adjacency matrix, graph, dual adjacency matrix, and dual graph and \ @@ -280,7 +301,7 @@ Cell[BoxData[ CellChangeTimes->{{3.8321575269876523`*^9, 3.8321576763644238`*^9}, { 3.832159927387419*^9, 3.8321599288063574`*^9}, {3.832178568505596*^9, 3.8321785886368113`*^9}}, - CellLabel->"In[7]:=",ExpressionUUID->"466eedf4-1501-4c34-b467-6afcd6ee9c2b"], + CellLabel->"In[6]:=",ExpressionUUID->"466eedf4-1501-4c34-b467-6afcd6ee9c2b"], Cell["\<\ Computes entire extended gram matrix just given adjacency graph\ @@ -299,15 +320,14 @@ Cell[BoxData[ RowBox[{"dgraph", "[", "adjmat", "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.832159893936446*^9, 3.832159919205484*^9}, 3.832159950380535*^9, {3.832168786146203*^9, 3.832168807346489*^9}}, - CellLabel->"In[8]:=",ExpressionUUID->"07904a6d-75de-42b6-bd6e-25258c9dfc13"], + CellLabel->"In[7]:=",ExpressionUUID->"07904a6d-75de-42b6-bd6e-25258c9dfc13"], Cell[TextData[{ "Dylan\[CloseCurlyQuote]s formula: computes ", Cell[BoxData[ FormBox[ SubscriptBox["\[Alpha]", - RowBox[{"i", ",", "j"}]], TraditionalForm]], - FormatType->TraditionalForm,ExpressionUUID-> + RowBox[{"i", ",", "j"}]], TraditionalForm]],ExpressionUUID-> "b3c7d5f4-d091-4a74-aebc-91ee5194a0e1"], " given all bilinear forms between two tangent circles, c1 and c2, and their \ shared dual circle d" @@ -383,7 +403,7 @@ Cell[BoxData[ CellChangeTimes->{{3.8321784141799994`*^9, 3.832178465721493*^9}, { 3.83217860325821*^9, 3.832178655554688*^9}, {3.83217875635993*^9, 3.832178873607215*^9}}, - CellLabel->"In[9]:=",ExpressionUUID->"bf8ef1f1-47be-4283-b703-c185b6f0b640"], + CellLabel->"In[8]:=",ExpressionUUID->"bf8ef1f1-47be-4283-b703-c185b6f0b640"], Cell["\<\ Uses Dylan\[CloseCurlyQuote]s formula and the extended gram matrix to create \ @@ -406,7 +426,7 @@ Cell[BoxData[ RowBox[{"i", ",", "j"}], "\[RightDoubleBracket]"}]}]}]], "Input", CellChangeTimes->{{3.832179077629673*^9, 3.832179079427682*^9}, { 3.8321791928839073`*^9, 3.832179236666037*^9}}, - CellLabel->"In[10]:=",ExpressionUUID->"420e0d3e-8926-42c8-bf5b-90e13c9517d3"], + CellLabel->"In[9]:=",ExpressionUUID->"420e0d3e-8926-42c8-bf5b-90e13c9517d3"], Cell["Creates a list of all relevant variables", "Text", CellChangeTimes->{{3.832188674746522*^9, @@ -431,7 +451,7 @@ Cell[BoxData[ RowBox[{"n", "+", "m"}]}], "}"}]}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.832180251879418*^9, 3.832180286404707*^9}, { 3.83218032560913*^9, 3.832180334849931*^9}}, - CellLabel->"In[11]:=",ExpressionUUID->"6be67f5a-9ae0-4ab1-a49b-076a5355b7fb"], + CellLabel->"In[10]:=",ExpressionUUID->"6be67f5a-9ae0-4ab1-a49b-076a5355b7fb"], Cell["\<\ Given the adjacency matrix and which three rows/columns to pick (I\ @@ -453,7 +473,8 @@ Cell[BoxData[ RowBox[{"{", RowBox[{ "Gext", ",", "c1s", ",", "c2s", ",", "ds", ",", "n", ",", "m", ",", - "rules", ",", "assumptions"}], "}"}], ",", "\[IndentingNewLine]", + "rules", ",", "assumptions", ",", "temp"}], "}"}], ",", + "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "=", RowBox[{"Length", "[", "adjmat", "]"}]}], ";", "\[IndentingNewLine]", @@ -517,12 +538,17 @@ Cell[BoxData[ RowBox[{"n", "+", "m"}]}], "}"}]}], "]"}], "]"}], "//", RowBox[{"DeleteCases", "[", RowBox[{"Indeterminate", "\[Equal]", "__"}], "]"}]}], "//", - 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FrontEnd`EvaluationNotebook[]]}]& , Evaluator -> None, Appearance -> + None, BaseStyle -> "Link"]], + Editable->False]], "Print", + CellChangeTimes->{3.832337217807197*^9, 3.832358883859474*^9, + 3.832368244249806*^9, 3.832669858541595*^9, 3.864732718158339*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"871ff450-762e-4ceb-b980-847aca12b375"] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -87,17 +465,25 @@ Cell[BoxData[ GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"]], "Output", CellChangeTimes->{3.832337477452114*^9, 3.832358888188767*^9, - 3.832368249132185*^9, 3.832669863650465*^9}, - CellLabel->"Out[2]=",ExpressionUUID->"a497a5ba-b350-4cd9-af35-0caa6485e9a9"] + 3.832368249132185*^9, 3.832669863650465*^9, 3.864732719426708*^9}, + CellLabel->"Out[2]=",ExpressionUUID->"a8376a7b-ede1-4b76-906c-5ba8a5545969"] +}, Open ]] }, Open ]], +Cell[CellGroupData[{ + +Cell["Import Polyhedra", "Section", + CellChangeTimes->{{3.86473218472358*^9, + 3.8647321903474703`*^9}},ExpressionUUID->"ebf114c1-39fc-40ae-b9dd-\ +3068b7a4fc97"], + Cell["\<\ Function to convert some representation of a graph to mathematica\ \[CloseCurlyQuote]s representation. You can give it the option \ -`format->graph6` if in graph6 format\ +`format->graph6` if in graph6 format.\ \>", "Text", - CellChangeTimes->{{3.832358495397357*^9, - 3.8323585393912582`*^9}},ExpressionUUID->"b79ac481-66e7-4669-b8f4-\ + CellChangeTimes->{{3.832358495397357*^9, 3.8323585393912582`*^9}, + 3.864732404686041*^9},ExpressionUUID->"b79ac481-66e7-4669-b8f4-\ 0cea700ed78c"], Cell[BoxData[{ @@ -145,16 +531,59 @@ Cell[BoxData[{ CellChangeTimes->{{3.832336494011004*^9, 3.832336534340336*^9}, { 3.8323517999289827`*^9, 3.832351947441263*^9}, {3.8323520237090063`*^9, 3.8323520406687717`*^9}, {3.8323532427822723`*^9, 3.832353249640938*^9}}, - CellLabel->"In[3]:=",ExpressionUUID->"0491d7dc-7152-49be-9137-070980e44ae7"], + CellLabel->"In[3]:=",ExpressionUUID->"0491d7dc-7152-49be-9137-070980e44ae7"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Polyhedra Decomposition", "Section", + CellChangeTimes->{{3.8647322788211317`*^9, + 3.86473228272716*^9}},ExpressionUUID->"2e5d31b9-09d1-455d-9b0f-\ +6af51112842a"], Cell["\<\ -Function to tell if a polyhedron is prime. About O(2^n) and not likely able \ -to improve. There are about O(2^n) cycles (it\[CloseCurlyQuote]s been \ -rigorously proven to be P-hard to count the number of cycles), and I don\ -\[CloseCurlyQuote]t see a way of getting around that.\ +Heads up: I think these functions are quite a bit buggy, but it\ +\[CloseCurlyQuote]s hard to tell for sure. It\[CloseCurlyQuote]s not super \ +useful anyway, since we can\[CloseCurlyQuote]t verify that the faces are \ +compatible just from the graph alone.\ \>", "Text", - CellChangeTimes->{{3.83235854587254*^9, - 3.832358618254396*^9}},ExpressionUUID->"83ebdaf9-e7b9-4912-83aa-\ + CellChangeTimes->{{3.864734244978354*^9, + 3.864734304257506*^9}},ExpressionUUID->"f4d61d60-fb66-403c-a5a7-\ +fc30fbb1ff48"], + +Cell[TextData[{ + "Function to tell if a polyhedron is prime, i.e. cannot be decomposed. About \ +", + Cell[BoxData[ + FormBox[ + TemplateBox[<|"boxes" -> FormBox[ + RowBox[{ + StyleBox["O", "TI"], "(", + SuperscriptBox["2", + StyleBox["n", "TI"]], ")"}], TraditionalForm], "errors" -> {}, + "input" -> "O(2^n)", "state" -> "Boxes"|>, + "TeXAssistantTemplate"], TraditionalForm]],ExpressionUUID-> + "6d317853-b9dc-4f40-a831-0339e5fd5a0d"], + " and not likely able to improve. There are about ", + Cell[BoxData[ + FormBox[ + TemplateBox[<|"boxes" -> FormBox[ + RowBox[{ + StyleBox["O", "TI"], "(", + SuperscriptBox["2", + StyleBox["n", "TI"]], ")"}], TraditionalForm], "errors" -> {}, + "input" -> "O(2^n)", "state" -> "Boxes"|>, + "TeXAssistantTemplate"], TraditionalForm]],ExpressionUUID-> + "42af4f74-334b-4f07-bd7d-d82a896ebb50"], + " possible cycles (it\[CloseCurlyQuote]s been rigorously proven to be P-hard \ +to count the number of cycles), and I don\[CloseCurlyQuote]t see a way of \ +getting around that. This algorithm basically works by checking if any cycle \ +splits the polyhedron into two polyhedra (i.e. 3-connected planar graphs). If \ +so, it is not prime." +}], "Text", + CellChangeTimes->{{3.83235854587254*^9, 3.832358618254396*^9}, { + 3.8647322851060266`*^9, 3.864732374153657*^9}, {3.8647324102931347`*^9, + 3.864732413182369*^9}},ExpressionUUID->"83ebdaf9-e7b9-4912-83aa-\ 66018e3b4210"], Cell[BoxData[ @@ -284,14 +713,21 @@ Cell[BoxData[ Cell["\<\ Function to find the possible decompositions of a graph. Returns a list where \ the first element of the list is the number of possible face decompositions \ -and the second is the number of possible vertex decompositions. Should be \ -easy to modify to actually return the decompositions. I wonder if we could \ -extend this recursively to \[OpenCurlyDoubleQuote]prime factorize\ -\[CloseCurlyDoubleQuote] polyhedra?\ +and the second is the number of possible vertex decompositions. This \ +corresponds to face gluing (the kind of gluing we\[CloseCurlyQuote]ve been \ +working with) and vertex gluing (like in Kontorovich\[CloseCurlyQuote]s \ +students\[CloseCurlyQuote] paper). Should be easy to modify to actually \ +return the decompositions. I wonder if we could extend this recursively to \ +\[OpenCurlyDoubleQuote]prime factorize\[CloseCurlyDoubleQuote] polyhedra? \ +Such a \[OpenCurlyDoubleQuote]factorization\[CloseCurlyDoubleQuote] clearly \ +won\[CloseCurlyQuote]t be unique, however. Note that these decompositions \ +might not actually work for the purposes of glue.nb, as the faces might not \ +be \[OpenCurlyDoubleQuote]compatible,\[CloseCurlyDoubleQuote] e.g. a square \ +face glued onto a rhombus.\ \>", "Text", - CellChangeTimes->{{3.832358623451818*^9, - 3.832358720650798*^9}},ExpressionUUID->"a601bc96-4656-4520-9aeb-\ -158895d9368a"], + CellChangeTimes->{{3.832358623451818*^9, 3.832358720650798*^9}, { + 3.8647324570755157`*^9, 3.864732470920993*^9}, {3.864732526429549*^9, + 3.8647325948108*^9}},ExpressionUUID->"a601bc96-4656-4520-9aeb-158895d9368a"], Cell[BoxData[ RowBox[{ @@ -419,7 +855,199 @@ Cell[BoxData[ 3.832341105249135*^9}, {3.832341215107959*^9, 3.832341309459516*^9}, { 3.83234151306717*^9, 3.8323415312540283`*^9}, {3.832669981679708*^9, 3.832669985443377*^9}}, - CellLabel->"In[11]:=",ExpressionUUID->"58712807-a428-4b89-8b30-be4ce33480f8"], + CellLabel->"In[7]:=",ExpressionUUID->"58712807-a428-4b89-8b30-be4ce33480f8"], + +Cell["\<\ +Slight modification 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