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).

See also: http://homepages.math.uic.edu/~jan/Demo/rabmo.html.

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

Ways to use rabmo :

rabmo(Ring)

For the programmer

The object rabmo is a method function.