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showExoticSolutions -- Display exotic solutions: linearly stable solutions which are not all-in-phase solution

Description

This function first calls getLinearlyStableSolutions, and then displays any exotic solutions that exist. A stable solution is exotic if it is not the all-in-phase solution (all the angles are the same), and returns all of the stable solutions found.

Note: The methods getExoticSolutions and showExoticSolutions are the same, for historical reasons.

The warning that there are non-regular solutions generally means that it has come across a positive dimensional solution set while looking for solutions. No such solutions can be linearly stable, so the warning is generally not relevant.

i1 : G = graph {{0,1},{1,2},{2,3},{3,4},{4,0}}

o1 = Graph{0 => {1, 4}}
           1 => {0, 2}
           2 => {1, 3}
           3 => {2, 4}
           4 => {0, 3}

o1 : Graph
i2 : showExoticSolutions G
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)
 -- .420703s elapsed
-- found extra exotic solutions for graph Graph{0 => {1, 4}} --
                                                1 => {0, 2}
                                                2 => {1, 3}
                                                3 => {2, 4}
                                                4 => {0, 3}
+-------+--------+--------+-------+--------+--------+--------+--------+
|.309017|-.809017|-.809017|.309017|.951057 |.587785 |-.587785|-.951057|
+-------+--------+--------+-------+--------+--------+--------+--------+
|.309017|-.809017|-.809017|.309017|-.951057|-.587785|.587785 |.951057 |
+-------+--------+--------+-------+--------+--------+--------+--------+
|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  |
+---+---+---+---+

o2 = {{.309017, -.809017, -.809017, .309017, .951057, .587785, -.587785,
     ------------------------------------------------------------------------
     -.951057}, {.309017, -.809017, -.809017, .309017, -.951057, -.587785,
     ------------------------------------------------------------------------
     .587785, .951057}, {1, 1, 1, 1, 0, 0, 0, 0}}

o2 : List

Note that if there are exotic solutions, all linearly stable solutions are displayed, and if there are no exotic solutions, nothing is displayed (other than possibly warnings and timings).

i3 : G = graph {{0,1},{1,2},{2,3},{3,4},{4,2},{4,0}}

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

o3 : Graph
i4 : showExoticSolutions G
 -- .550633s elapsed

o4 = {{1, 1, 1, 1, 0, 0, 0, 0}}

o4 : List

See also

Ways to use showExoticSolutions:

  • showExoticSolutions(Graph)

For the programmer

The object showExoticSolutions is a method function.


The source of this document is in Oscillators/Documentation.m2:612:0.