next | previous | forward | backward | up | top | index | toc | Macaulay2 website
ExampleSystems :: rbpl24s

rbpl24s -- parallel robot with 24 real solutions, after variable scaling

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 40 solutions found in 3.740 seconds (with a Bezout bound of 576).

Reference: generated by Fabrice Rouillier, as a deformation of a system found in Innocenti.

See also: http://homepages.math.uic.edu/~jan/Demo/rbpl24s.html.

i1 : rbpl24s(RR_53)

              2           2          2                    2           2  
o1 = {.902353x  + .506753y  + 1.1541z  - 1.89489, .547653x  + .401593y  +
              1           1          1                    2           2  
     ------------------------------------------------------------------------
             2                              2           2           2
     .914601z  - 1.374x  - 3.61818, 1.26481x  + .299954y  + 1.20376z  +
             2         2                    3           3           3  
     ------------------------------------------------------------------------
     .346368x  - 3.03447y  - 2.08335, 1.01543x x  + .651627y y  + 1.48404z z 
             3           3                    1 2           1 2           1 2
     ------------------------------------------------------------------------
     - 1.3475x  + .75575, 1.4913x x  + .544239y y  + 1.64533z z  + .1979x  -
              2                  1 3           1 3           1 3         3  
     ------------------------------------------------------------------------
     1.73377y  - 2.1825, 3.63357x x  + 1.51527y y  + 4.58093z z  - 4.97527x 
             3                   2 3           2 3           2 3           2
     ------------------------------------------------------------------------
     + .45581x  - 3.99328y  - .00437819, 1.74298x y z  - .991213x y z  -
              3           3                      3 2 1           2 3 1  
     ------------------------------------------------------------------------
     1.74298x y z  + 1.13265x y z  + 1.31579x y z  - 1.50355x y z  -
             3 1 2           1 3 2           2 1 3           1 2 3  
     ------------------------------------------------------------------------
     3.35742x y  + 3.07591x y  + 3.83651x y  - 3.71822x y  - 1.99884x y  +
             2 1           3 1           1 2           3 2           1 3  
     ------------------------------------------------------------------------
     2.11451x y  - .0493297x z  + .0451934x z  - 1.2983y z  + .67642y z  +
             2 3            2 1            3 1          2 1          3 1  
     ------------------------------------------------------------------------
     .0563687x z  - .0546307x z  + 1.2983y z  - .817669y z  - .0389852x z  +
              1 2            3 2          1 2           3 2            1 3  
     ------------------------------------------------------------------------
     .0412412x z  - .897916y z  + 1.08542y z  - 9.85984x  + 1.09273x  +
              2 3           1 3           2 3           1           2  
     ------------------------------------------------------------------------
     7.70206x  + .240411y  + .0363213y  - 10.5808y  - 37.2647z  - 5.62995z  +
             3           1            2           3           1           2  
     ------------------------------------------------------------------------
     21.2116z  - .695579, - .981142x y z  + .557965x y z  + .981142x y z  -
             3                      3 2 1           2 3 1           3 1 2  
     ------------------------------------------------------------------------
     .637583x y z  - .740673x y z  + .846363x y z  - 1.88369x y  +
             1 3 2           2 1 3           1 2 3           2 1  
     ------------------------------------------------------------------------
     1.72575x y  + 2.15249x y  - 2.08612x y  - 1.12146x y  + 1.18635x y  -
             3 1           1 2           3 2           1 3           2 3  
     ------------------------------------------------------------------------
     2.14929x z  + 1.96908x z  - 1.39179y z  + .725132y z  + 2.45598x z  -
             2 1           3 1           2 1           3 1           1 2  
     ------------------------------------------------------------------------
     2.38026x z  + 1.39179y z  - .876553y z  - 1.69859x z  + 1.79688x z  -
             3 2           1 2           3 2           1 3           2 3  
     ------------------------------------------------------------------------
     .962579y z  + 1.16358y z  + .527434x  + .943204x  + .344042x  -
             1 3           2 3           1           2           3  
     ------------------------------------------------------------------------
     .522684y  - .543486y  + .0767906y  + 1.04328z  + 1.0848z  + .649757z  +
             1           2            3           1          2           3  
     ------------------------------------------------------------------------
     .838949, 1.4167x  + .705867}
                     2

o1 : List

Ways to use rbpl24s :

For the programmer

The object rbpl24s is a method function.