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18 changes: 9 additions & 9 deletions docs/examples/boshernitzan_conjecture.html
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Expand Up @@ -594,7 +594,7 @@ <h5>Flowing from the Large Edge to Construct an Interval Exchange Transformation
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[a: (-5*c^9 + 95/2*c^7 - 155*c^5 + 200*c^3 - 165/2*c ~ 0.65529062)] [b: (5/2*c^9 - 45/2*c^7 + 70*c^5 - 90*c^3 + 85/2*c ~ 0.63925068)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [d: (-5*c^9 + 50*c^7 - 355/2*c^5 + 525/2*c^3 - 265/2*c ~ 0.34915894)] [e: (5*c^9 - 50*c^7 + 175*c^5 - 495/2*c^3 + 225/2*c ~ 0.42025316)] [f: (5/2*c^9 - 45/2*c^7 + 70*c^5 - 90*c^3 + 85/2*c ~ 0.63925068)] [g: (-5/2*c^7 + 20*c^5 - 95/2*c^3 + 30*c ~ 1.0755438)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [i: (-5/2*c^3 + 10*c ~ 0.40094723)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[a: (-c^9 + 19/2*c^7 - 31*c^5 + 40*c^3 - 33/2*c ~ 0.13105812)] [b: (1/2*c^9 - 9/2*c^7 + 14*c^5 - 18*c^3 + 17/2*c ~ 0.12785014)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [d: (-c^9 + 10*c^7 - 71/2*c^5 + 105/2*c^3 - 53/2*c ~ 0.069831789)] [e: (c^9 - 10*c^7 + 35*c^5 - 99/2*c^3 + 45/2*c ~ 0.084050632)] [f: (1/2*c^9 - 9/2*c^7 + 14*c^5 - 18*c^3 + 17/2*c ~ 0.12785014)] [g: (-1/2*c^7 + 4*c^5 - 19/2*c^3 + 6*c ~ 0.21510876)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [i: (-1/2*c^3 + 2*c ~ 0.080189447)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
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Expand All @@ -614,7 +614,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[b: (5/2*c^9 - 45/2*c^7 + 70*c^5 - 90*c^3 + 85/2*c ~ 0.63925068)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [d: (-5*c^9 + 50*c^7 - 355/2*c^5 + 525/2*c^3 - 265/2*c ~ 0.34915894)] [e: (5*c^9 - 50*c^7 + 175*c^5 - 495/2*c^3 + 225/2*c ~ 0.42025316)] [f: (5/2*c^9 - 45/2*c^7 + 70*c^5 - 90*c^3 + 85/2*c ~ 0.63925068)] [a: (-5*c^9 + 95/2*c^7 - 155*c^5 + 200*c^3 - 165/2*c ~ 0.65529062)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 495/2*c^3 + 225/2*c ~ 0.42025316)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [i: (-5/2*c^3 + 10*c ~ 0.40094723)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[b: (1/2*c^9 - 9/2*c^7 + 14*c^5 - 18*c^3 + 17/2*c ~ 0.12785014)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [d: (-c^9 + 10*c^7 - 71/2*c^5 + 105/2*c^3 - 53/2*c ~ 0.069831789)] [e: (c^9 - 10*c^7 + 35*c^5 - 99/2*c^3 + 45/2*c ~ 0.084050632)] [f: (1/2*c^9 - 9/2*c^7 + 14*c^5 - 18*c^3 + 17/2*c ~ 0.12785014)] [a: (-c^9 + 19/2*c^7 - 31*c^5 + 40*c^3 - 33/2*c ~ 0.13105812)] [g: (c^9 - 10*c^7 + 35*c^5 - 99/2*c^3 + 45/2*c ~ 0.084050632)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [i: (-1/2*c^3 + 2*c ~ 0.080189447)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
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Expand All @@ -628,7 +628,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[b: (-5/2*c^9 + 55/2*c^7 - 105*c^5 + 315/2*c^3 - 70*c ~ 0.21899752)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [d: (-5*c^9 + 50*c^7 - 355/2*c^5 + 525/2*c^3 - 265/2*c ~ 0.34915894)] [e: (5*c^9 - 50*c^7 + 175*c^5 - 495/2*c^3 + 225/2*c ~ 0.42025316)] [f: (5/2*c^9 - 45/2*c^7 + 70*c^5 - 90*c^3 + 85/2*c ~ 0.63925068)] [a: (-5*c^9 + 95/2*c^7 - 155*c^5 + 200*c^3 - 165/2*c ~ 0.65529062)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 495/2*c^3 + 225/2*c ~ 0.42025316)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [i: (-5/2*c^3 + 10*c ~ 0.40094723)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[b: (-1/2*c^9 + 11/2*c^7 - 21*c^5 + 63/2*c^3 - 14*c ~ 0.043799504)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [d: (-c^9 + 10*c^7 - 71/2*c^5 + 105/2*c^3 - 53/2*c ~ 0.069831789)] [e: (c^9 - 10*c^7 + 35*c^5 - 99/2*c^3 + 45/2*c ~ 0.084050632)] [f: (1/2*c^9 - 9/2*c^7 + 14*c^5 - 18*c^3 + 17/2*c ~ 0.12785014)] [a: (-c^9 + 19/2*c^7 - 31*c^5 + 40*c^3 - 33/2*c ~ 0.13105812)] [g: (c^9 - 10*c^7 + 35*c^5 - 99/2*c^3 + 45/2*c ~ 0.084050632)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [i: (-1/2*c^3 + 2*c ~ 0.080189447)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
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Expand All @@ -644,7 +644,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-5*c^9 + 50*c^7 - 355/2*c^5 + 525/2*c^3 - 265/2*c ~ 0.34915894)] [e: (5*c^9 - 50*c^7 + 175*c^5 - 495/2*c^3 + 225/2*c ~ 0.42025316)] [f: (5/2*c^9 - 45/2*c^7 + 70*c^5 - 90*c^3 + 85/2*c ~ 0.63925068)] [a: (-5*c^9 + 95/2*c^7 - 155*c^5 + 200*c^3 - 165/2*c ~ 0.65529062)] [b: (-5/2*c^9 + 55/2*c^7 - 105*c^5 + 315/2*c^3 - 70*c ~ 0.21899752)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [i: (-5/2*c^3 + 10*c ~ 0.40094723)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-c^9 + 10*c^7 - 71/2*c^5 + 105/2*c^3 - 53/2*c ~ 0.069831789)] [e: (c^9 - 10*c^7 + 35*c^5 - 99/2*c^3 + 45/2*c ~ 0.084050632)] [f: (1/2*c^9 - 9/2*c^7 + 14*c^5 - 18*c^3 + 17/2*c ~ 0.12785014)] [a: (-c^9 + 19/2*c^7 - 31*c^5 + 40*c^3 - 33/2*c ~ 0.13105812)] [b: (-1/2*c^9 + 11/2*c^7 - 21*c^5 + 63/2*c^3 - 14*c ~ 0.043799504)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [g: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [i: (-1/2*c^3 + 2*c ~ 0.080189447)] / [g] [b] [d] [i] [e] [a] [c] [h] [f]
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Expand All @@ -666,7 +666,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[f: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [a: (-5*c^9 + 95/2*c^7 - 155*c^5 + 200*c^3 - 165/2*c ~ 0.65529062)] [d: (-25/2*c^9 + 245/2*c^7 - 845/2*c^5 + 595*c^3 - 535/2*c ~ 0.091549570)] [b: (10*c^9 - 95*c^7 + 635/2*c^5 - 875/2*c^3 + 395/2*c ~ 0.12744795)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [e: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [i: (-5/2*c^9 + 55/2*c^7 - 105*c^5 + 315/2*c^3 - 70*c ~ 0.21899752)] / [e] [a] [c] [h] [i] [b] [g] [d] [f]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[f: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [a: (-c^9 + 19/2*c^7 - 31*c^5 + 40*c^3 - 33/2*c ~ 0.13105812)] [d: (-5/2*c^9 + 49/2*c^7 - 169/2*c^5 + 119*c^3 - 107/2*c ~ 0.018309914)] [b: (2*c^9 - 19*c^7 + 127/2*c^5 - 175/2*c^3 + 79/2*c ~ 0.025489590)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [g: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [e: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [i: (-1/2*c^9 + 11/2*c^7 - 21*c^5 + 63/2*c^3 - 14*c ~ 0.043799504)] / [e] [a] [c] [h] [i] [b] [g] [d] [f]
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Expand All @@ -680,7 +680,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[a: (-5*c^9 + 95/2*c^7 - 155*c^5 + 200*c^3 - 165/2*c ~ 0.65529062)] [d: (-25/2*c^9 + 245/2*c^7 - 845/2*c^5 + 595*c^3 - 535/2*c ~ 0.091549570)] [b: (10*c^9 - 95*c^7 + 635/2*c^5 - 875/2*c^3 + 395/2*c ~ 0.12744795)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [e: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [i: (-5/2*c^9 + 55/2*c^7 - 105*c^5 + 315/2*c^3 - 70*c ~ 0.21899752)] / [a] [c] [h] [i] [b] [g] [d] [e]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[a: (-c^9 + 19/2*c^7 - 31*c^5 + 40*c^3 - 33/2*c ~ 0.13105812)] [d: (-5/2*c^9 + 49/2*c^7 - 169/2*c^5 + 119*c^3 - 107/2*c ~ 0.018309914)] [b: (2*c^9 - 19*c^7 + 127/2*c^5 - 175/2*c^3 + 79/2*c ~ 0.025489590)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [g: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [e: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [i: (-1/2*c^9 + 11/2*c^7 - 21*c^5 + 63/2*c^3 - 14*c ~ 0.043799504)] / [a] [c] [h] [i] [b] [g] [d] [e]
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Expand All @@ -695,7 +695,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-25/2*c^9 + 245/2*c^7 - 845/2*c^5 + 595*c^3 - 535/2*c ~ 0.091549570)] [b: (10*c^9 - 95*c^7 + 635/2*c^5 - 875/2*c^3 + 395/2*c ~ 0.12744795)] [c: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] [h: (-5/2*c^9 + 55/2*c^7 - 215/2*c^5 + 175*c^3 - 100*c ~ 0.58746239)] [e: (5/2*c^9 - 55/2*c^7 + 105*c^5 - 160*c^3 + 80*c ~ 0.18194971)] [i: (-5/2*c^9 + 55/2*c^7 - 105*c^5 + 315/2*c^3 - 70*c ~ 0.21899752)] / [c] [h] [i] [b] [g] [d] [e]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-5/2*c^9 + 49/2*c^7 - 169/2*c^5 + 119*c^3 - 107/2*c ~ 0.018309914)] [b: (2*c^9 - 19*c^7 + 127/2*c^5 - 175/2*c^3 + 79/2*c ~ 0.025489590)] [c: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [g: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] [h: (-1/2*c^9 + 11/2*c^7 - 43/2*c^5 + 35*c^3 - 20*c ~ 0.11749248)] [e: (1/2*c^9 - 11/2*c^7 + 21*c^5 - 32*c^3 + 16*c ~ 0.036389943)] [i: (-1/2*c^9 + 11/2*c^7 - 21*c^5 + 63/2*c^3 - 14*c ~ 0.043799504)] / [c] [h] [i] [b] [g] [d] [e]
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Expand All @@ -709,7 +709,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-10*c^9 + 105*c^7 - 385*c^5 + 1125/2*c^3 - 505/2*c ~ 0.017741877)] [h: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] [c: (10*c^9 - 100*c^7 + 705/2*c^5 - 510*c^3 + 245*c ~ 0.071094216)] [g: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] [b: (-5*c^9 + 55*c^7 - 210*c^5 + 635/2*c^3 - 150*c ~ 0.037047805)] [i: (-15/2*c^9 + 135/2*c^7 - 425/2*c^5 + 555/2*c^3 - 235/2*c ~ 0.054501765)] / [h] [d] [c] [b] [g] [i]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-2*c^9 + 21*c^7 - 77*c^5 + 225/2*c^3 - 101/2*c ~ 0.0035483753)] [h: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] [c: (2*c^9 - 20*c^7 + 141/2*c^5 - 102*c^3 + 49*c ~ 0.014218843)] [g: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] [b: (-c^9 + 11*c^7 - 42*c^5 + 127/2*c^3 - 30*c ~ 0.0074095609)] [i: (-3/2*c^9 + 27/2*c^7 - 85/2*c^5 + 111/2*c^3 - 47/2*c ~ 0.010900353)] / [h] [d] [c] [b] [g] [i]
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Expand All @@ -724,7 +724,7 @@ <h5>Zorich Induction on the Interval Exchange Transformation<a class="headerlink
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-10*c^9 + 105*c^7 - 385*c^5 + 1125/2*c^3 - 505/2*c ~ 0.017741877)] [h: (5*c^9 - 50*c^7 + 175*c^5 - 245*c^3 + 205/2*c ~ 0.019305928)] / [h] [d]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[d: (-2*c^9 + 21*c^7 - 77*c^5 + 225/2*c^3 - 101/2*c ~ 0.0035483753)] [h: (c^9 - 10*c^7 + 35*c^5 - 49*c^3 + 41/2*c ~ 0.0038611856)] / [h] [d]
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Expand Up @@ -759,7 +759,7 @@ <h2><span class="math notranslate nohighlight">\(SL_2(\mathbb{Z})\)</span> orbit
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.333996110314584]
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Expand Down Expand Up @@ -948,7 +948,7 @@ <h4>Some sample queries<a class="headerlink" href="#some-sample-queries" title="
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>{H_3(2, 1^2), H_3(1^4), H_3(2^2)}
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Expand All @@ -965,8 +965,8 @@ <h4>Some sample queries<a class="headerlink" href="#some-sample-queries" title="
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14,15,16)(17,18,19,20)
(1,3)(2,4,5,7,9,11)(6,8,10,13,17,15,19,12)(14,18,16,20)
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(1)(2,3,4,5)(6,7,8,9)(10)
(1,2)(3,6,10,8)(4,7,5,9)
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<p>We can work with <span class="math notranslate nohighlight">\(L^{\infty}\)</span>-Delaunay flat structures. These are also called <em>geometry</em> flat structures in <code class="docutils literal notranslate"><span class="pre">veerer</span></code>.</p>
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<p>We now explore the <span class="math notranslate nohighlight">\(L^\infty\)</span>-Delaunay of a given linear family.</p>
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