-- An example of zero dimensional Non-Homogeneous Solving using the classical linear homotopy.
-- We want to find isolated solutions of the following system.
Use QQ[x[1..3]];
P := [
x[1]x[2]x[3] - x[1]x[2]-15,
3x[1]x[2]-x[1]+5,
7x[1]x[3] - x[1],
24x[1]x[2]+x[3] - 3x[1]x[3] - 1,
x[1]^2 - x[1]
];
HomTyp:=1;
-- Then we compute the solution with
Hom.SRSolve(P,HomTyp);
-- Now you have to interact with ApCoCoAServer
-- Enter 1 for the polyhedral homotopy and 2 for the classical linear homotopy.
-- Since we want to use the classical linear homotopy therefore we enter 2.
-- The all finite solutions are:
----------------------------------------
[
[[-2902316230611307/1250000000000000, -27857718907640603/10000000000000000],
[-5674959881126967/500000000000000000, -8937804463608219/25000000000000000],
[46724750476097837/100000000000000000, -38716232173770071/100000000000000000]],
[[65920011696250427/1000000000000000, -1372011739419221/12500000000000],
[84785163919836641/10000000000000000, -10345947531705213/25000000000000000],
[12838340038652873/1000000000000000, 1179955721096759/156250000000000]],
[[-11200479653149161/50000000000000000000, -1847541166671739/4000000000000000000],
[-398464307671313/250000000000, -83690324485203917/100000000000000],
[27034776057405041/100000000000000000, -16633293038412589/1000000000000000]],
[[1283479859536169/400000000000000, 226533750215299/80000000000000],
[-739601189373527/40000000000000000, 10474383104189437/50000000000000000],
[-4621056904224851/25000000000000000, 6394233590549897/25000000000000000]],
[[4510213996339667/12500000000000000000, 551766683622709/4000000000000000000],
[-26177318181795687/50000000000000, -3490003097264787/2000000000000],
[31612616513119707/10000000000000000, 21347082990880249/1000000000000000]]
]
-- The smallest list represents a complex number.
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