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ExampleSystems :: ipp

ipp -- six-revolute-joint problem of mechanics

Synopsis

Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.

There were 48 solutions found in 1.708 seconds (with a Bezout bound of 256).

Reference: "Computing all solutions to polynomial systems using homotopy continuation" by A. Morgan and A. Sommese (pages 115-138).

See also: http://homepages.math.uic.edu/~jan/Demo/ipp.html.

i1 : ipp(RR_53)

       2    2       2    2       2    2       2    2
o1 = {x  + x  - 1, x  + x  - 1, x  + x  - 1, x  + x  - 1, - .249151x x  +
       1    2       3    4       5    6       7    8                1 3  
     ------------------------------------------------------------------------
     .279423x x  + 1.60914x x  + 1.4348x x  - .800528x x  + .400264x x  +
             2 3           1 4          2 4           6 7           5 8  
     ------------------------------------------------------------------------
     .0740524x  - .08305x  - .38616x  - .755266x  + .504202x  - 1.09163x  +
              1          2          3           4           5           6  
     ------------------------------------------------------------------------
     .400264x  + .0492073, .125016x x  - .119228x x  - .686607x x  -
             8                     1 3           2 3           1 4  
     ------------------------------------------------------------------------
     .71994x x  - .432419x x  - .864839x x  - .0371573x  + .0354369x  +
            2 4           5 7           6 8            1            2  
     ------------------------------------------------------------------------
     .0853835x  - .039252x  - .432419x  + .013873, - .63555x x  - .666404x x 
              3           5           7                     1 3           2 3
     ------------------------------------------------------------------------
     - .11572x x  + .110362x x  + .290702x x  - .629388x x  + 1.25878x x  +
              1 4           2 4           5 7           6 7           5 8  
     ------------------------------------------------------------------------
     .581404x x  + .195947x  - 1.22803x  - .0790342x  + .0263879x  -
             6 8           1           2            4            5  
     ------------------------------------------------------------------------
     .0571314x  - 1.16281x  + 1.25878x  + 2.16257, 1.48948x x  + 1.32811x x 
              6           7           8                    1 3           2 3
     ------------------------------------------------------------------------
     + .230623x x  - .258645x x  + 1.16517x x  + .53817x x  - .269085x x  +
               1 4           2 4           5 7          6 7           5 8  
     ------------------------------------------------------------------------
     .582586x x  - .20817x  + 2.68683x  - .699103x  + .357444x  + 1.24991x  +
             6 8          1           2           3           4           5  
     ------------------------------------------------------------------------
     1.46774x  + 1.16517x  + 1.10763x  - .696868}
             6           7           8

o1 : List

Ways to use ipp :

For the programmer

The object ipp is a method function.