# comb3000s -- a combustion chemistry example for a temperature of 3000 degrees

## Synopsis

• Usage:
comb3000s(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) i5-4258U CPU at 2.40GHz.

There were 16 solutions found in 0.707914 seconds (with a Bezout bound of 96).

Reference: A.P. Morgan. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems', Prentice-Hall, Englewood Cliffs, N.J., 1987. Chapter 9.

 i1 : comb3000s(RR_53) o1 = {.101815x + .98961x + 1.34637x + 3.4697x - 2.12454, .57674x + 2 6 9 10 3 ------------------------------------------------------------------------ .78995x - 2.19493, .087316x + .895129x + 1.37722x + 2.45208x + 8 1 3 5 8 ------------------------------------------------------------------------ .719622x + .927261x - 5.67773, .0025003x + 19.9988x - 19.9988, - 9 10 4 7 ------------------------------------------------------------------------ 2 2 2 1.37722x + .726099x , - .98961x + 1.0105x , - 19.9988x + .050003x , - 1 5 2 6 4 7 ------------------------------------------------------------------------ 2 1.93702x x + .516256x , - .968878x x + 1.03212x , - 3.21732x x + 1 3 8 1 2 9 1 2 ------------------------------------------------------------------------ .310818x } 10 o1 : List