-- 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.LRSolve(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:
----------------------------------------
[
[[9455327382203569/5000000000000000, -25208009777282481/10000000000000000],
[13172347071045859/1000000000000000000, 780259255441451/10000000000000000],
[50662103933981573/100000000000000000, 24894084616179979/50000000000000000]],
[[94045825811783779/10000000000000000000, -18561325122258089/500000000000000000],
[-11252856171103929/500000000000000, 53756347909614881/10000000000000000],
[43866568184785617/10000000000000000, -970984718484509/40000000000000]],
[[23564339009933287/1000000000000000000, 37422202697036111/1000000000000000000],
[-20929334925895049/1000000000000000, -24991129623196171/2500000000000000],
[26847721395327557/10000000000000000, 20456859352398073/1000000000000000]],
[[-5340666810400797/10000000000000000, 7138058708108771/2500000000000000],
[157412137424673/4000000000000000, -15131835631465503/250000000000000000],
[45533206002984217/1000000000000000000, -67237130550938307/100000000000000000]],
[[2223557602823067/10000000000000, -19326230622413977/250000000000000],
[-15392736087963673/2000000000000000, 18511778667155307/200000000000000000],
[-25906948948013323/1000000000000000, 3338667600178357/50000000000000]]
]
-- The smallest list represents a complex number.
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