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
gaukwa4
8
w1 + w2 + w3 + w4
+ ( 4.88303340950105E-01 - 8.72673963870222E-01*i);
w1*x1 + w2*x2 + w3*x3 + w4*x4
+ ( 5.18782365203204E-01 - 8.54906344317417E-01*i);
w1*x1**2 + w2*x2**2 + w3*x3**2 + w4*x4**2
+ ( -9.00683429228647E-01 - 4.34475960569656E-01*i);
w1*x1**3 + w2*x2**3 + w3*x3**3 + w4*x4**3
+ ( -9.48682692199895E-01 - 3.16229583562890E-01*i);
w1*x1**4 + w2*x2**4 + w3*x3**4 + w4*x4**4
+ ( 4.63259783551860E-01 + 8.86222530148881E-01*i);
w1*x1**5 + w2*x2**5 + w3*x3**5 + w4*x4**5
+ (-7.89936368499146E-01 + 6.13188823872697E-01*i);
w1*x1**6 + w2*x2**6 + w3*x3**6 + w4*x4**6
+ ( 9.79201808025014E-01 + 2.02888686625312E-01*i);
w1*x1**7 + w2*x2**7 + w3*x3**7 + w4*x4**7
+ (-2.74557888517134E-01 - 9.61570572476619E-01*i);
TITLE : Gaussian quadrature formula with 4 knots and 4 weights
ROOT COUNTS :
total degree : 8! = 40320
2-homogeneous Bezout bound : 6769.
with partition : {w1 w2 w3 w4 }{x1 x2 x3 x4 }
mixed volume : 729
NOTE :
The moments are randomly complex chosen coefficients.
By a particular symmetric choice of the subdivision,
only one solution path needs to be traced.
THE GENERATING SOLUTIONS :
1 8
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 24
the solution for t :
w1 : -8.96692094492292E-01 6.38170292403620E-01
w2 : 2.80402306915529E-01 1.15138545346693E-01
w3 : -8.51835305232690E-03 1.45273304678796E-02
w4 : 1.36504799678985E-01 1.04837795652029E-01
x1 : 5.59984862188214E-01 -6.79436139074726E-01
x2 : -9.59291346545661E-01 7.19343084013266E-01
x3 : -2.93171086615633E-01 1.81847906572470E+00
x4 : -9.91696113366362E-01 -5.80505222592590E-01
== err : 1.837E-15 = rco : 4.215E-04 = res : 6.713E-16 ==