# quadgrid -- interpolating quadrature formula for function defined on a grid

## Synopsis

• Usage:
• Inputs:
• kk, a ring, the coefficient ring
• Outputs:
• a list, of polynomials in the system

## Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U 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.

 i1 : quadgrid(RR_53) o1 = {w + w + w + w - 1, w b + w b + w b + w b + .5w + w + 1.5w - 0 1 2 3 0 1 2 3 1 2 3 ------------------------------------------------------------------------ 2 2 2 2 .633975, w b + w b + w b + w b + w b + 2w b + 3w b + .25w + w + 0 1 2 3 1 2 3 1 2 ------------------------------------------------------------------------ 3 3 3 3 2 2 2 4.5w - .401924, w b + w b + w b + w b + 1.5w b + 3w b + 4.5w b + 3 0 1 2 3 1 2 3 ------------------------------------------------------------------------ 4 4 .75w b + 3w b + 6.75w b + .125w + w + 3.375w - .131092, w b + w b + 1 2 3 1 2 3 0 1 ------------------------------------------------------------------------ 4 4 3 3 3 2 2 2 w b + w b + 2w b + 4w b + 6w b + 1.5w b + 6w b + 13.5w b + .5w b 2 3 1 2 3 1 2 3 1 ------------------------------------------------------------------------ + 4w b + 13.5w b + .0625w + w + 5.0625w + .302193} 2 3 1 2 3 o1 : List