# rabmo -- optimal multi-dimensional quadrature formulas

## Synopsis

• Usage:
rabmo(kk)
• 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 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).

 i1 : rabmo(QQ) 2 2 o1 = {x + x + x + 2x - 1, x x + x x + 2x x + 2x x + 2x x - -, x x + 1 3 5 7 1 2 3 4 5 6 7 8 7 9 3 1 2 ------------------------------------------------------------------------ 2 2 2 2 2 3 3 3 3 3 x x + 2x x + 2x x + 2x x - -, x x + x x + 2x x + 2x x + 2x x - 3 4 5 6 7 8 7 9 5 1 2 3 4 5 6 7 8 7 9 ------------------------------------------------------------------------ 2 4 4 4 4 4 2 2 1 4 -, x x + x x + 2x x + 2x x + 2x x - -, x x + 2x x x - -, x x + 7 1 2 3 4 5 6 7 8 7 9 9 5 6 7 8 9 9 5 6 ------------------------------------------------------------------------ 2 2 1 3 2 2 1 4 3 3 1 2x x x - --, x x + x x x + x x x - --, x x + x x x + x x x - --} 7 8 9 25 5 6 7 8 9 7 8 9 15 5 6 7 8 9 7 8 9 21 o1 : List