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# dipole2 -- Dipole2 system

- Usage:
    `dipole2(kk)`
- Inputs:
  - kk, a ring, the coefficient ring
- Outputs:
  - a list, of the polynomials in the system

## Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-8250U CPU at 1.60GHz.

There were 4 solutions found in 22.0781 seconds (with a Bezout bound of 576).

Reference: COCONUT, modified by COPRIN.

See also: http://www-sop.inria.fr/coprin/logiciels/ALIAS/Benches/node1.html#SECTION000114000000000000000

    i1 : dipole2(RR_53)

    o1 = {a + b - .63254, c + d + 1.34534, a*t + b*u - c*v - d*w + .836535, c*t +
         ------------------------------------------------------------------------
                                       2      2               2               2
         d*u + a*v + b*w - 1.73453, a*t  + b*u  - 2c*t*v - a*v  - 2d*u*w - b*w  -
         ------------------------------------------------------------------------
                     2      2               2               2               3
         1.35235, c*t  + d*u  + 2a*t*v - c*v  + 2b*u*w - d*w  + .843453, a*t  +
         ------------------------------------------------------------------------
            3       2          2      3       2          2      3               3
         b*u  - 3c*t v - 3a*t*v  + c*v  - 3d*u w - 3b*u*w  + d*w  + .956345, c*t
         ------------------------------------------------------------------------
              3       2          2      3       2          2      3
         + d*u  + 3a*t v - 3c*t*v  - a*v  + 3b*u w - 3d*u*w  - b*w  - 1.23425}

    o1 : List

## Ways to use dipole2:

- `dipole2(Ring)`

## For the programmer

The object dipole2 is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ExampleSystems/dipole2.m2:47:0.