heart -- an 8-dimensional economics problem

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 2 solutions found in 3.356 seconds (with a Bezout bound of 1458).

Reference: "Determination of magnitudes, directions, and locations of two independent dipoles in a circular conducting region from boundary potential measurements" by C.V. Nelson and B.C. Hodgkin (pages 817-823), "Coefficient-Parameter Polynomial Continuation" by A.P. Morgan and A.J. Sommese (pages 123-160), "Mathematical reduction of a heart dipole model" by A.P. Morgan and A. Sommese and L.T. Watson (pages 407-410).

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

i1 : heart(RR_53)

o1 = {a + b - .63254, c + d + 1.34534, a*t + b*u - c*v - d*w + .836535, c*t +
     ------------------------------------------------------------------------
     d*u + a*v + b*w - 1.73453, | -2ctv-2duw+2at+2bu-2av-2bw-1.35235 |, |
     ------------------------------------------------------------------------
     2atv+2buw+2ct+2du-2cv-2dw+.843453 |, |
     ------------------------------------------------------------------------
     -6atv-6ctv-6buw-6duw+3at+3bu+3cv+3dw+.956345 |, |
     ------------------------------------------------------------------------
     6atv-6ctv+6buw-6duw+3ct+3du-3av-3bw-1.23425 |}

o1 : List