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# 6-body

The problem is here to find the solutions of a set of 6 equations (eq1 to eq6). Two simplification procedures are used together with the 3B method. The HessianSolve procedure will allow to get exact results.

```
eq1:=3*(b-d)*(B-D)+B+D-6*F+4:
eq2:=3*(b-d)*(B+D-2*F)+5*(B-D):
eq3:=3*(b-d)^2-6*(b+d)+4*f+3:
eq4:=B^2*b^3-1:
eq5:=D^2*d^3-1:
eq6:=F^2*f^3-1:
with(ALIAS):
`ALIAS/lib`:="../Test/Lib":
`ALIAS/profil`:="../Profil":
`ALIAS/single_bisection`:=2:
`ALIAS/3B`:=0:
`ALIAS/Full3B`:=1:
`ALIAS/Full3B_Change`:=0.1:
`ALIAS/Delta3B`:=0.01:
`ALIAS/Max3B`:=10^16:
`ALIAS/Use_Simp_3B`:=0:
`ALIAS/debug`:=1:
`ALIAS/storage_mode`:=10:
`ALIAS/full_simplex`:=9:
`ALIAS/min_diam_simplex`:=1000:
`ALIAS/diam_simplex`:=0.1:
u:=[0,10^5]:
SimplexConsistency([eq1,eq2,eq3],[B,D,F,b,d,f],"Simp1");
HullConsistency([eq1,eq2,eq3,eq4,eq5,eq6],[B,D,F,b,d,f],"Simp2");
CatSimp("Simp","Simp1","Simp2",0.01);

HessianSolve([eq1,eq2,eq3,eq4,eq5,eq6],[B,D,F,b,d,f],
[u,u,u,u,u,u],"Simp");
```

Jean-Pierre Merlet 2012-12-20