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 |