For details see: A.J. Sommese, J. Verschelde, and C.W. Wampler, "Introduction to numerical algebraic geometry", in "Solving polynomial equations" (2005), 301--338
i1 : R = CC[x,y,z]; |
i2 : T = {x^2+y^2-1, x*y^2, x^5+y*z+3}; |
i3 : totalDegreeStartSystem T 2 3 5 o3 = ({x - 1, y - 1, z - 1}, {{-1, -.5+.866025*ii, -.809017-.587785*ii}, {-1, -.5-.866025*ii, -.809017+.587785*ii}, {-1, ---------------------------------------------------------------------------------------------------------------------------- -.5-.866025*ii, 1}, {-1, 1, -.809017-.587785*ii}, {1, -.5-.866025*ii, -.809017-.587785*ii}, {-1, -.5+.866025*ii, ---------------------------------------------------------------------------------------------------------------------------- -.809017+.587785*ii}, {-1, -.5-.866025*ii, .309017-.951057*ii}, {-1, -.5+.866025*ii, 1}, {1, -.5+.866025*ii, ---------------------------------------------------------------------------------------------------------------------------- -.809017-.587785*ii}, {-1, 1, -.809017+.587785*ii}, {1, -.5-.866025*ii, -.809017+.587785*ii}, {-1, -.5+.866025*ii, ---------------------------------------------------------------------------------------------------------------------------- .309017-.951057*ii}, {-1, -.5-.866025*ii, .309017+.951057*ii}, {-1, 1, 1}, {1, -.5-.866025*ii, 1}, {1, 1, ---------------------------------------------------------------------------------------------------------------------------- -.809017-.587785*ii}, {1, -.5+.866025*ii, -.809017+.587785*ii}, {-1, 1, .309017-.951057*ii}, {1, -.5-.866025*ii, ---------------------------------------------------------------------------------------------------------------------------- .309017-.951057*ii}, {-1, -.5+.866025*ii, .309017+.951057*ii}, {1, -.5+.866025*ii, 1}, {1, 1, -.809017+.587785*ii}, {1, ---------------------------------------------------------------------------------------------------------------------------- -.5+.866025*ii, .309017-.951057*ii}, {-1, 1, .309017+.951057*ii}, {1, -.5-.866025*ii, .309017+.951057*ii}, {1, 1, 1}, {1, 1, ---------------------------------------------------------------------------------------------------------------------------- .309017-.951057*ii}, {1, -.5+.866025*ii, .309017+.951057*ii}, {-1, -.5-.866025*ii, -.809017-.587785*ii}, {1, 1, ---------------------------------------------------------------------------------------------------------------------------- .309017+.951057*ii}}) o3 : Sequence |