6 s1**2+g1**2 - 1; s2**2+g2**2 - 1; C1*g1**3+C2*g2**3 - 1.2; C1*s1**3+C2*s2**3 - 1.2; C1*g1**2*s1+C2*g2**2*s2 - 0.7; C1*g1*s1**2+C2*g2*s2**2 - 0.7; TITLE : neurofysiology, posted by Sjirk Boon ROOT COUNTS : total degree : 1024 3-homogeneous Bezout number : 344 with partition : {s1 s2 }{g1 g2 }{C1 C2 } generalized Bezout number : 216 based on the set structure : {s1 g1 }{s1 g1 } {s2 g2 }{s2 g2 } {g1 g2 }{g1 g2 }{g1 g2 }{C1 C2 } {s1 s2 }{s1 s2 }{s1 s2 }{C1 C2 } {s1 s2 }{g1 g2 }{g1 g2 }{C1 C2 } {s1 s2 }{s1 s2 }{g1 g2 }{C1 C2 } mixed volume : 20 NOTE : There are only 8 finite solutions for general values of the constant terms. It can be proved that it is equivalent to a quadrature formula problem, so that there is only one solution upon symmetry. REFERENCES : The system has been posted to the newsgroup sci.math.num-analysis by Sjirk Boon. P. Van Hentenryck, D. McAllester and D. Kapur: `Solving Polynomial Systems Using a Branch and Prune Approach' SIAM J. Numerical Analysis, Vol. 34, No. 2, pp 797-827, 1997. SYMMETRY GROUP : g2 s2 g1 s1 C2 C1 g1 s1 g2 s2 C1 C2 s2 g2 s1 g1 C2 C1 s1 g1 s2 g2 C1 C2 -s1 s2 -g1 g2 -C1 C2 s1 -s2 g1 -g2 C1 -C2 THE GENERATING SOLUTIONS : 1 6 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 8 the solution for t : s1 : -4.02451939639181E-01 -6.67657107123736E-67 g1 : -9.15441115681758E-01 3.52374584315305E-67 s2 : 9.15441115681758E-01 4.26558707329054E-67 g2 : 4.02451939639181E-01 -7.41841230137484E-67 C1 : -1.44169513021472E+00 -1.24258406048029E-66 C2 : 1.44169513021472E+00 -1.07566978369935E-66 == err : 3.255E-15 = rco : 1.566E-02 = res : 2.220E-16 ==