https://github.com/janverschelde/PHCpack
Tip revision: 1b7c69d37cd919359b5166b1c97d94c065360905 authored by Jan Verschelde on 17 November 2021, 01:50:30 UTC
loaded multipliers for the normalization of complex vectors in octo double precision into local variables
loaded multipliers for the normalization of complex vectors in octo double precision into local variables
Tip revision: 1b7c69d
extcyc6
6
z0 + z1 + z2 + z3 + z4 + z5 - 1;
z0*z1 + z1*z2 + z2*z3 + z3*z4 + z4*z5 + z5*z0 - 1;
z0*z1*z2 + z1*z2*z3 + z2*z3*z4 + z3*z4*z5 + z4*z5*z0 + z5*z0*z1 - 1;
z0*z1*z2*z3 + z1*z2*z3*z4 + z2*z3*z4*z5 + z3*z4*z5*z0 + z4*z5*z0*z1
+ z5*z0*z1*z2 - 1;
z0*z1*z2*z3*z4 + z1*z2*z3*z4*z5 + z2*z3*z4*z5*z0 + z3*z4*z5*z0*z1
+ z4*z5*z0*z1*z2 + z5*z0*z1*z2*z3 - 1 ;
z0*z1*z2*z3*z4*z5 - 1;
TITLE : extended cyclic 6-roots problem, to exploit the symmetry
ROOT COUNTS :
total degree : 6! = 720
mixed volume : 156
REFERENCES :
This is the Arnborg's system or Davenport's problem,
extended with the constant term to exploit symmetry.
For the original problem :
G\"oran Bj\"ork and Ralf Fr\"oberg:
`A faster way to count the solutions of inhomogeneous systems
of algebraic equations, with applications to cyclic n-roots',
J. Symbolic Computation (1991) 12, pp 329--336.
THE SOLUTIONS :
13 6
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : -1.09145911498337E-01 -2.82051661977533E-01
z1 : -1.19329529302722E+00 -3.08367868303911E+00
z2 : 6.84847142039119E-01 1.11902672009036E+00
z3 : 6.68044546894126E-01 8.74453630967107E-01
z4 : 5.51668586068374E-01 7.22120404126932E-01
z5 : 3.97880929523935E-01 6.50129589832241E-01
== err : 3.150E-15 = rco : 2.299E-02 = res : 1.404E-15 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : -3.53129181444054E-01 -4.55887812930893E-01
z1 : -1.06193432801704E+00 -1.37095132239199E+00
z2 : -2.50000000000000E-01 -9.68245836551854E-01
z3 : 1.34883344892200E-01 1.74133649482747E-01
z4 : 2.78018016456890E+00 3.58919715894384E+00
z5 : -2.50000000000000E-01 -9.68245836551854E-01
== err : 5.300E-15 = rco : 2.085E-02 = res : 1.256E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 3.21007829191040E-01 -2.54057382351715E+00
z1 : 3.21007829191040E-01 2.54057382351715E+00
z2 : 1.30039852922610E-01 9.91508767813914E-01
z3 : 4.89523178863507E-02 3.87426617400472E-01
z4 : 4.89523178863507E-02 -3.87426617400472E-01
z5 : 1.30039852922610E-01 -9.91508767813914E-01
== err : 4.347E-16 = rco : 6.306E-02 = res : 9.155E-16 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 2.66839454551322E-01 -9.63740995026544E-01
z1 : 7.89153930342621E-01 6.14195469068922E-01
z2 : -4.44985611119495E-01 8.95537718857564E-01
z3 : 7.44236290740844E-01 -6.67916419579807E-01
z4 : -4.96471667324206E-01 -8.68052926695327E-01
z5 : 1.41227602808914E-01 9.89977153375192E-01
== err : 8.917E-16 = rco : 1.092E-01 = res : 7.109E-16 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 7.44236290740845E-01 6.67916419579807E-01
z1 : -4.96471667324207E-01 8.68052926695327E-01
z2 : 1.41227602808914E-01 -9.89977153375192E-01
z3 : 2.66839454551322E-01 9.63740995026544E-01
z4 : 7.89153930342621E-01 -6.14195469068922E-01
z5 : -4.44985611119495E-01 -8.95537718857564E-01
== err : 6.069E-16 = rco : 1.043E-01 = res : 8.951E-16 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : -1.30493744993987E+00 1.10325388562335E+00
z1 : 2.47735189059043E+00 -1.20477380171330E+00
z2 : 8.86709471424394E-01 -4.62327063112546E-01
z3 : 3.26450487727244E-01 -1.58757823894198E-01
z4 : -4.46891660260174E-01 3.77822676985343E-01
z5 : -9.38682739542032E-01 3.44782126111355E-01
== err : 6.011E-15 = rco : 6.878E-02 = res : 7.216E-16 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : -3.81966011250105E-01 6.04048609987806E-92
z1 : 6.85410196624969E+00 8.43750439348047E-91
z2 : 1.45898033750315E-01 -4.45845402610047E-92
z3 : -2.61803398874990E+00 -5.44602556306467E-91
z4 : -3.81966011250105E-01 6.61577049034264E-92
z5 : -2.61803398874990E+00 -3.83522926976385E-91
== err : 4.788E-15 = rco : 1.766E-03 = res : 8.882E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 5.00000000000000E-01 -8.66025403784439E-01
z1 : -9.57427107756338E-01 -2.88675134594813E-01
z2 : -9.57427107756338E-01 2.88675134594813E-01
z3 : 5.00000000000000E-01 8.66025403784439E-01
z4 : 9.57427107756338E-01 2.88675134594813E-01
z5 : 9.57427107756338E-01 -2.88675134594813E-01
== err : 4.711E-16 = rco : 1.213E-01 = res : 7.109E-16 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 3.26450487727244E-01 1.58757823894198E-01
z1 : 8.86709471424394E-01 4.62327063112546E-01
z2 : 2.47735189059043E+00 1.20477380171330E+00
z3 : -1.30493744993987E+00 -1.10325388562335E+00
z4 : -9.38682739542032E-01 -3.44782126111355E-01
z5 : -4.46891660260174E-01 -3.77822676985343E-01
== err : 5.690E-15 = rco : 5.844E-02 = res : 6.713E-16 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 1.00000000000000E+00 3.41829996175611E-86
z1 : 1.00000000000000E+00 -3.01614702507892E-86
z2 : 1.00000000000000E+00 3.61937643009471E-86
z3 : 1.00000000000000E+00 -2.61399408840173E-86
z4 : -3.81966011250105E-01 -3.21722349341752E-86
z5 : -2.61803398874990E+00 4.12206760094120E-86
== err : 4.720E-15 = rco : 3.715E-02 = res : 2.220E-16 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 5.51668586068374E-01 -7.22120404126932E-01
z1 : 3.97880929523935E-01 -6.50129589832240E-01
z2 : -1.09145911498336E-01 2.82051661977533E-01
z3 : -1.19329529302722E+00 3.08367868303911E+00
z4 : 6.84847142039118E-01 -1.11902672009036E+00
z5 : 6.68044546894127E-01 -8.74453630967107E-01
== err : 3.182E-15 = rco : 2.489E-02 = res : 1.201E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : -6.04864265798915E-01 -7.96328587933109E-01
z1 : 1.15709953428924E-01 9.93283044593774E-01
z2 : 9.89154312369991E-01 -1.46880040576826E-01
z3 : -6.04864265798915E-01 7.96328587933109E-01
z4 : 1.15709953428924E-01 -9.93283044593774E-01
z5 : 9.89154312369991E-01 1.46880040576826E-01
== err : 6.660E-16 = rco : 1.458E-01 = res : 8.006E-16 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 12
the solution for t :
z0 : 1.34883344892200E-01 -1.74133649482747E-01
z1 : -2.50000000000000E-01 9.68245836551854E-01
z2 : -1.06193432801704E+00 1.37095132239199E+00
z3 : -3.53129181444054E-01 4.55887812930893E-01
z4 : -2.50000000000000E-01 9.68245836551854E-01
z5 : 2.78018016456890E+00 -3.58919715894384E+00
== err : 5.011E-15 = rco : 1.055E-02 = res : 9.155E-16 ==