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ExampleSystems :: lumped

lumped -- lumped parameter chemically reacting system

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

For the programmer

The object lumped is a method function.