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Example 4.2: a K5 and pentagon glued along an edge -- example 4.2 in arXiv 2312.16069

The first example is a pentagon. The second example is K5 with a 5-cycle glued along an edge.

i1 : needsPackage "Oscillators";
i2 : printingPrecision = 3;
i3 : Pent = graph{{0,1},{1,2},{2,3},{3,4},{4,0}}

o3 = Graph{0 => {1, 4}}
           1 => {0, 2}
           2 => {1, 3}
           3 => {2, 4}
           4 => {0, 3}

o3 : Graph
i4 : K5C5 = graph{{0,1},{0,2},{0,3},{0,4},{1,2},{1,3},{1,4},
         {2,3},{2,4},{3,4},{0,5},{5,6},{6,7},{1,7}}

o4 = Graph{0 => {1, 2, 3, 4, 5}}
           1 => {0, 2, 3, 4, 7}
           2 => {0, 1, 3, 4}
           3 => {0, 1, 2, 4}
           4 => {0, 1, 2, 3}
           5 => {0, 6}
           6 => {5, 7}
           7 => {1, 6}

o4 : Graph
i5 : stablesolsK5C5 = {{1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
         {.92, .98, .98, .98, .101, -.98, -.298, -.393, -.201, -.201, -.201, .995, .201, -.954},
         {.92, .98, .98, .98, .101, -.98, -.298, .393, .201, .201, .201, -.995, -.201, .954}}

o5 = {{1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {.92, .98, .98, .98, .101,
     ------------------------------------------------------------------------
     -.98, -.298, -.393, -.201, -.201, -.201, .995, .201, -.954}, {.92, .98,
     ------------------------------------------------------------------------
     .98, .98, .101, -.98, -.298, .393, .201, .201, .201, -.995, -.201,
     ------------------------------------------------------------------------
     .954}}

o5 : List
i6 : elapsedTime stablesolsPent = showExoticSolutions Pent
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)
 -- .428s elapsed
 -- .473s elapsed
-- found extra exotic solutions for graph Graph{0 => {1, 4}} --
                                                1 => {0, 2}
                                                2 => {1, 3}
                                                3 => {2, 4}
                                                4 => {0, 3}
+----+-----+-----+----+-----+-----+-----+-----+
|.309|-.809|-.809|.309|.951 |.588 |-.588|-.951|
+----+-----+-----+----+-----+-----+-----+-----+
|.309|-.809|-.809|.309|-.951|-.588|.588 |.951 |
+----+-----+-----+----+-----+-----+-----+-----+
|1   |1    |1    |1   |0    |0    |0    |0    |
+----+-----+-----+----+-----+-----+-----+-----+
-- angles (in degrees), first angle is zero and omitted --
+---+---+---+---+
|72 |144|216|288|
+---+---+---+---+
|288|216|144|72 |
+---+---+---+---+
|0  |0  |0  |0  |
+---+---+---+---+

o6 = {{.309, -.809, -.809, .309, .951, .588, -.588, -.951}, {.309, -.809,
     ------------------------------------------------------------------------
     -.809, .309, -.951, -.588, .588, .951}, {1, 1, 1, 1, 0, 0, 0, 0}}

o6 : List

Computing the (linearly) stable solutions for K5C5 takes a minute or two:

elapsedTime stablesolsK5C5 = showExoticSolutions K5C5

See also


The source of this document is in Oscillators/Documentation.m2:868:0.