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export {"comb3000s"}
comb3000s = method();
comb3000s(Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_10];
{ 1.01815483301669e-1*x_2+ 9.89610100506422e-1*x_6+ 1.34637048100730*x_9 + 3.46970317210432*x_10-2.12454115933396,
5.76739795357135e-1*x_3+ 7.89949754301577e-1*x_8-2.19492968782850,
7.19621954936988e-1*x_9+ 9.27261335190857e-1*x_10+ 8.95128807036246e-1*x_3+ 2.45208250541714*x_8+ 8.73159766974099e-2*x_1+ 1.37722259176202*x_5-5.67773314994310,
2.50030218520604e-3*x_4+ 19.9987913687438*x_7-19.9987913687440,
-1.37722259176203*x_1^2+ 7.26099038733160e-1*x_5,
-9.89610100506425e-1*x_2^2+ 1.01049898287039*x_6,
-19.9987913687438*x_4^2+ 5.00030217607503e-2*x_7,
-1.93702197268146*x_3*x_1+ 5.16256404988361e-1*x_8,
-9.68877757611935e-1*x_2*x_1+ 1.03212194948595*x_9,
-3.21732159608141*x_2^2*x_1+ 3.10817545009477e-1*x_10
}
)
beginDocumentation()
doc ///
Key
comb3000s
(comb3000s,Ring)
Headline
a combustion chemistry example for a temperature of 3000 degrees
Usage
comb3000s(kk)
Inputs
kk:Ring
the coefficient ring
Outputs
:List
of the polynomials in the system
Description
Text
This system was solved in May 2020, using @TO 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.
See also: http://homepages.math.uic.edu/~jan/Demo/comb3000s.html
Example
comb3000s(RR_53)
///
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