proddeco -- system with a product-decomposition structure

Synopsis

Usage:

prodecco(kk)
Inputs:
- kk, a ring, the coefficient ring
Outputs:
- a list, of the polynomials in the system

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 68 solutions found in 7.236 seconds (with a Bezout bound of 256).

Reference: "A product-decomposition theorem for bounding Bezout numbers" by A.P. Morgan, A.J. Sommese, and C.W. Wampler (pages 1308-1325).

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

i1 : proddeco(RR_53)

              2 2                             2 2                  
o1 = {64.6329z z  - 129.266z z z z  + 64.6329z z  - 55.6619z z z  -
              2 3           1 2 3 4           1 4           1 2 3  
     ------------------------------------------------------------------------
            2               2           2                                   
     12.201z z  - 48.2115z z  + 55.6619z z  + 12.201z z z  + 48.2115z z z  -
            2 3           2 3           1 4          1 2 4           1 3 4  
     ------------------------------------------------------------------------
                             2                                            
     71.399z z z  + 71.399z z  + 50.7966z z  + 9.14137z z  + 62.3536z z  +
            2 3 4          1 4           1 3           2 3           1 4  
     ------------------------------------------------------------------------
                          2 2                             2 2                
     17.5403z z , 81.3704z z  - 162.741z z z z  + 81.3704z z  - 55.3638z z z 
             2 4          2 3           1 2 3 4           1 4           1 2 3
     ------------------------------------------------------------------------
               2               2           2                    
     - 25.0326z z  - 21.7819z z  + 55.3638z z  + 25.0326z z z  +
               2 3           2 3           1 4           1 2 4  
     ------------------------------------------------------------------------
                                               2                            
     21.7819z z z  - 55.0737z z z  + 55.0737z z  + 24.7967z z  + 9.562z z  +
             1 3 4           2 3 4           1 4           1 3         2 3  
     ------------------------------------------------------------------------
                                        2 2                             2 2  
     41.6882z z  + 20.9301z z , 35.2817z z  - 70.5634z z z z  + 35.2817z z  -
             1 4           2 4          2 3           1 2 3 4           1 4  
     ------------------------------------------------------------------------
                             2               2           2                  
     42.2584z z z  - 23.8847z z  - 8.07978z z  + 42.2584z z  + 23.8847z z z 
             1 2 3           2 3           2 3           1 4           1 2 4
     ------------------------------------------------------------------------
                                                 2                           
     + 8.07978z z z  - 23.1781z z z  + 23.1781z z  + 13.503z z  + 10.3468z z 
               1 3 4           2 3 4           1 4          1 3           2 3
     ------------------------------------------------------------------------
                                          2 2                             2 2
     + 37.0338z z  + 16.9465z z , 6.89936z z  - 13.7987z z z z  + 6.89936z z 
               1 4           2 4          2 3           1 2 3 4           1 4
     ------------------------------------------------------------------------
                               2               2           2    
     - 43.1035z z z  - 56.0575z z  - 2.37993z z  + 43.1035z z  +
               1 2 3           2 3           2 3           1 4  
     ------------------------------------------------------------------------
                                                               2
     56.0575z z z  + 2.37993z z z  - 6.40051z z z  + 6.40051z z  +
             1 2 4           1 3 4           2 3 4           1 4  
     ------------------------------------------------------------------------
     16.2879z z  + 22.5597z z  + 42.9769z z  + 55.4137z z }
             1 3           2 3           1 4           2 4

o1 : List

Ways to use proddeco :

proddeco(Ring)

For the programmer

The object proddeco is a method function.