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export{"quadgrid"}
quadgrid = method()
quadgrid (Ring) := kk -> (
(w,b) := (symbol w, symbol b);
R := kk[w_0..w_3,b];
{ w_0 + w_1 + w_2 + w_3 - 1,
w_0*b + w_1*b + w_2*b + w_3*b + 1/2*w_1 + w_2 + 3/2*w_3 - 0.63397459621556,
w_0*b^2 + w_1*b^2 + w_2*b^2 + w_3*b^2 + w_1*b + 2*w_2*b + 3*w_3*b + 1/4*w_1 + w_2 + 9/2*w_3 - 0.40192378864668,
w_0*b^3 + w_1*b^3 + w_2*b^3 + w_3*b^3 + 3/2*w_1*b^2 + 3*w_2*b^2 + 9/2 *w_3*b^2 + 3/4*w_1*b + 3*w_2*b + 27/4*w_3*b + 1/8*w_1 + w_2 + 27/8*w_3 - 0.13109155679036,
w_0*b^4 + w_1*b^4 + w_2*b^4 + w_3*b^4 + 2 * w_1*b^3 + 4*w_2*b^3 + 6 * w_3*b^3 + 3/2* w_1*b^2 + 6*w_2*b^2 + 27/2* w_3*b^2 + 1/2* w_1*b + 4*w_2*b + 27/2* w_3*b + 1/16*w_1 + w_2 + 81/16*w_3 + 0.30219332850656 }
)
beginDocumentation()
doc ///
Key
quadgrid
(quadgrid,Ring)
Headline
interpolating quadrature formula for function defined on a grid
Usage
quadgrid(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 5 solutions found in 1.653 seconds (with a Bezout bound of 120).
Note: This system is ill-conditioned. There are 4 complex and 1 real solution.
Reference: "The construction and application of wavelets in numerical analysis" by Wim Sweldens.
See also: http://homepages.math.uic.edu/~jan/Demo/quadgrid.html.
Example
quadgrid(RR_53)
///
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