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export{"rabmo"}
rabmo = method()
rabmo (Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_9];
{ x_1 + x_3 + x_5 + 2*x_7 - 1,
x_1*x_2 + x_3*x_4 + 2*x_5*x_6 + 2*x_7*x_8 + 2*x_7*x_9 - 2/3,
x_1*x_2^2 + x_3*x_4^2 + 2*x_5*x_6^2 + 2*x_7*x_8^2 + 2*x_7*x_9^2 - 2/5,
x_1*x_2^3 + x_3*x_4^3 + 2*x_5*x_6^3 + 2*x_7*x_8^3 + 2*x_7*x_9^3 - 2/7,
x_1*x_2^4 + x_3*x_4^4 + 2*x_5*x_6^4 + 2*x_7*x_8^4 + 2*x_7*x_9^4 - 2/9,
x_5*x_6^2 + 2*x_7*x_8*x_9 - 1/9,
x_5*x_6^4 + 2*x_7*x_8^2*x_9^2 - 1/25,
x_5*x_6^3 + x_7*x_8*x_9^2 + x_7*x_8^2*x_9 - 1/15,
x_5*x_6^4 + x_7*x_8*x_9^3 + x_7*x_8^3*x_9 - 1/21 }
)
beginDocumentation()
doc ///
Key
rabmo
(rabmo,Ring)
Headline
optimal multi-dimensional quadrature formulas
Usage
rabmo(kk)
Inputs
kk:Ring
the coefficient ring
Outputs
:List
of 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) i5-5250U CPU at 1.60GHz.
There were 58 solutions found in 1642.07 seconds (with a Bezout bound of 36000).
Reference: "Methods and applications of interval analysis" by Ramon E. Moore (p. 64).
See also: http://homepages.math.uic.edu/~jan/Demo/rabmo.html.
Example
rabmo(QQ)
///
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