#G24.simple.disc
#
#   Here, we compute the universal eliminant for Shapiro's conjecture when
# m=4 and p=2,  AND the flags osculate the rational normal
# curve at points  s,t,u,-s,-t,-u. The universal eliminant is a polynomial
# in x12^2, here, we have substituted x12^(1/2) for x12.  This is the
# discriminant of that new polynomial.   It has three factors.
# The first is harmless, The second is a square, and the third is interesting.
# These are both polynomials in s^2, t^2, and u^2.

Disc1:=
2589928271845565177500247955322265625000000000000000000000000*u^4*t^4*s^4:


Disc2:=
(80*u^12-273870*t^4*s^4*u^4+28938*t^4*s^6*u^2+28938*t^6*s^4*u^2+28938*t^6*s^2*u
^4+41334*u^8*s^2*t^2+41334*s^8*u^2*t^2+28938*u^6*s^4*t^2+41334*t^8*s^2*u^2+
28938*t^4*s^2*u^6+28938*u^4*s^6*t^2-2760*s^10*t^2+1605*s^8*t^4-5690*s^6*t^6+
1605*s^4*t^8-2760*u^10*t^2+1605*u^8*t^4+1605*u^4*t^8-5690*u^6*t^6-2760*u^2*t^10
-2760*s^2*t^10+1605*u^8*s^4-2760*u^10*s^2-2760*s^10*u^2-5690*u^6*s^6+1605*u^4*s
^8+80*s^12+80*t^12)^2:

Disc3:=
115526*s^24*u^24+101592*s^22*u^26+101592*s^26*u^22+67068*s^28*u^20+67068*s^12*u
^32*t^4+67068*s^4*u^32*t^12-1359240*s^20*u^24*t^4+38544*s^8*u^30*t^10+39643968*
s^24*u^14*t^10-3787008*s^12*u^26*t^10-1359240*s^24*u^4*t^20+67068*s^32*u^12*t^4
-3787008*s^22*u^6*t^20-1359240*s^24*u^20*t^4-3787008*s^10*u^26*t^12-135791808*s
^20*u^18*t^10+2880*s^30*u^6*t^12-3787008*s^26*u^10*t^12+29160*u^18*t^30+67068*s
^20*u^28+6561*s^16*u^32+39643968*s^14*u^24*t^10-2544384*s^10*u^10*t^28-176756*s
^16*u^4*t^28+275468544*s^14*u^14*t^20+85818972*s^16*u^12*t^20+2880*s^26*u^2*t^
20+51794736*s^8*u^20*t^20+531248*s^26*u^8*t^14+275468544*s^14*u^20*t^14-\
135791808*s^14*u^22*t^12+39643968*s^10*u^14*t^24-176756*s^28*u^16*t^4+101592*s^
22*t^26+67068*u^20*t^28+67068*u^28*t^20+101592*s^26*t^22+67068*s^20*t^28+67068*
s^28*t^20+6561*s^16*t^32+101592*u^26*t^22+6561*u^32*t^16+6561*s^32*t^16+115526*
s^24*t^24+29160*s^30*t^18+2880*s^6*u^12*t^30+119880*s^2*u^16*t^30-131100136*s^
22*u^16*t^10-176756*s^16*u^28*t^4-2544384*s^10*u^28*t^10+119880*s^2*u^30*t^16+
2880*s^2*u^26*t^20-135791808*s^10*u^18*t^20-1359240*s^4*u^24*t^20+51794736*s^20
*u^8*t^20+67068*s^12*u^4*t^32-3787008*s^6*u^22*t^20+202752*s^14*u^4*t^30+38544*
s^10*u^8*t^30+29160*s^18*u^30+29160*s^30*u^18+115526*s^8*u^8*t^32+6561*s^32*u^
16+29160*u^30*t^18+6561*u^16*t^32+101592*u^22*t^26+115526*u^24*t^24+29160*s^18*
t^30+2880*s^20*u^2*t^26-3787008*s^10*u^12*t^26+531248*s^8*u^14*t^26+85818972*s^
12*u^16*t^20+38544*s^2*u^22*t^24-1918080*s^18*u^26*t^4+101592*s^6*u^10*t^32-\
2544384*s^22*u^22*t^4+202752*s^30*u^14*t^4-2544384*s^22*u^4*t^22+202752*s^2*u^
18*t^28+38544*s^22*u^2*t^24+531248*s^6*u^18*t^24+2880*s^20*u^26*t^2-1918080*s^6
*u^14*t^28-1359240*s^8*u^12*t^28-1918080*s^26*u^18*t^4+101592*s^32*u^10*t^6+
38544*s^24*u^2*t^22+202752*s^4*u^14*t^30+85818972*s^20*u^12*t^16+2880*s^26*u^20
*t^2+202752*s^14*u^30*t^4+29160*s^14*u^32*t^2+202752*s^18*u^2*t^28+202752*s^4*u
^30*t^14-135791808*s^22*u^12*t^14+67332072*s^18*u^16*t^14-135791808*s^18*u^20*t
^10+2880*s^6*u^30*t^12-7382472*s^6*u^26*t^16+531248*s^14*u^26*t^8+85818972*s^16
*u^20*t^12+29160*s^2*u^32*t^14-1918080*s^18*u^4*t^26+531248*s^14*u^8*t^26+2880*
s^2*u^20*t^26+39643968*s^24*u^10*t^14-135791808*s^12*u^22*t^14+275468544*s^20*u
^14*t^14+202752*s^30*u^4*t^14+29160*s^32*u^2*t^14-3787008*s^12*u^10*t^26+38544*
s^22*u^24*t^2-1359240*s^12*u^8*t^28-7382472*s^6*u^16*t^26-7382472*s^16*u^6*t^26
+531248*s^18*u^6*t^24+39643968*s^14*u^10*t^24-1918080*s^28*u^6*t^14+39643968*s^
10*u^24*t^14-1918080*s^6*u^28*t^14+67332072*s^16*u^18*t^14+531248*s^8*u^26*t^14
+51794736*s^20*u^20*t^8+44708778*s^16*u^24*t^8+115526*s^8*u^32*t^8-1078100838*s
^16*u^16*t^16+44708778*s^8*u^24*t^16+29160*u^14*s^2*t^32-176756*s^28*u^4*t^16+
202752*s^18*u^28*t^2+44708778*s^24*u^8*t^16+44708778*s^24*u^16*t^8+51794736*s^
24*u^12*t^12-1359240*s^28*u^12*t^8-1359240*s^12*u^28*t^8+115526*s^32*u^8*t^8-\
1359240*u^20*s^4*t^24+44708778*u^16*s^8*t^24+2880*s^12*u^30*t^6+101592*s^10*u^
32*t^6-1918080*s^14*u^28*t^6-3787008*s^20*u^22*t^6-176756*s^4*u^16*t^28-3787008
*s^20*u^6*t^22-2544384*s^4*u^22*t^22+29160*s^32*u^14*t^2+119880*s^30*u^16*t^2+
2880*s^30*u^12*t^6-7382472*s^26*u^16*t^6-135791808*s^12*u^14*t^22-135791808*s^
14*u^12*t^22-1918080*s^14*u^6*t^28-7382472*s^16*u^26*t^6+67068*s^4*u^12*t^32+
531248*s^18*u^24*t^6-135791808*s^18*u^10*t^20+531248*s^26*u^14*t^8-1918080*s^4*
u^26*t^18+85818972*s^12*u^20*t^16-135791808*s^10*u^20*t^18+202752*s^28*u^18*t^2
+119880*s^16*u^30*t^2-131100136*s^10*u^16*t^22+38544*s^2*u^24*t^22+39643968*s^8
*u^18*t^22-3787008*s^22*u^20*t^6+531248*s^24*u^18*t^6+38544*s^8*u^10*t^30+
39643968*s^18*u^8*t^22-135791808*s^22*u^14*t^12-131100136*s^16*u^10*t^22+
67332072*s^14*u^16*t^18+39643968*s^8*u^22*t^18+67332072*s^16*u^14*t^18-1918080*
s^4*u^18*t^26+29160*s^14*u^2*t^32+67332072*s^18*u^14*t^16+39643968*s^22*u^18*t^
8+38544*s^30*u^10*t^8+38544*s^24*u^22*t^2-3787008*s^6*u^20*t^22+39643968*s^22*u
^8*t^18+51794736*s^12*u^24*t^12-131100136*s^22*u^10*t^16+39643968*s^18*u^22*t^8
+38544*s^10*u^30*t^8+67068*s^32*u^4*t^12-1918080*s^26*u^4*t^18-1918080*s^28*u^
14*t^6-131100136*s^10*u^22*t^16+101592*s^6*u^32*t^10-131100136*s^16*u^22*t^10+
119880*s^16*u^2*t^30+2880*s^12*u^6*t^30-176756*u^28*s^4*t^16+67332072*s^14*u^18
*t^16-135791808*s^20*u^10*t^18-1359240*s^8*u^28*t^12+531248*s^24*u^6*t^18+
101592*s^10*u^6*t^32-1359240*s^28*u^8*t^12+101592*s^32*u^6*t^10+275468544*s^18*
u^18*t^12-3787008*s^26*u^12*t^10+202752*s^2*u^28*t^18+85818972*s^20*u^16*t^12+
38544*s^30*u^8*t^10+275468544*s^18*u^12*t^18-7382472*s^26*u^6*t^16+202752*s^28*
u^2*t^18+531248*s^6*u^24*t^18-2544384*s^28*u^10*t^10+44708778*u^8*s^16*t^24+
51794736*u^12*s^12*t^24-1359240*s^20*u^4*t^24+275468544*s^12*u^18*t^18+119880*s
^30*u^2*t^16:



nops(Disc3);