lumped -- lumped parameter chemically reacting system

Synopsis

Usage:

lumped(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 4 solutions found in 0.178 seconds (with a Bezout bound of 16).

Reference: "Solving deficient polynomial systems with homotopies which keep the subschemes at infinity invariant" by T.Y. Li and X. Wang (pages 693-710).

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

i1 : lumped(CC_53)

o1 = {(.767719 + .328203*ii)x x  + (.767719 + .328203*ii)x x  + (- 1.76772 -
                             1 3                          1 4               
     ------------------------------------------------------------------------
     .328203*ii)x  + (.548909 + .109395*ii)x  + .0479608 + .888687*ii, (.3301
                 1                          3                                
     ------------------------------------------------------------------------
     + .890584*ii)x x  + (.3301 + .890584*ii)x x  + (- 1.3301 - .890584*ii)x 
                   2 3                        2 4                           2
     ------------------------------------------------------------------------
     + (.111291 + .671775*ii)x  + .829152 + .669877*ii, (- .767719 -
                              4                                     
     ------------------------------------------------------------------------
     .328203*ii)x x  + (- .767719 - .328203*ii)x x  + (- .892482 -
                 1 3                            1 4               
     ------------------------------------------------------------------------
     .452966*ii)x x  + (.767719 + .328203*ii)x  + (- .548909 - .109395*ii)x ,
                 3 4                          1                            3 
     ------------------------------------------------------------------------
     (- .3301 - .890584*ii)x x  + (- .3301 - .890584*ii)x x  + (- .892482 -
                            2 3                          2 4               
     ------------------------------------------------------------------------
     .452966*ii)x x  + (.3301 + .890584*ii)x  + (- .111291 - .671775*ii)x }
                 3 4                        2                            4

o1 : List

Ways to use lumped :

lumped(Ring)

For the programmer

The object lumped is a method function.