#G24.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.  This is the discriminant of the uiniversal eliminant.   It has
# three factors.  The first is harmless, The second not so bad, but the
# third is really interesting.  It is a square of a polynomial of degree 72
# in the parameters s, t, and u, with 595 terms.

interface(quiet=true):

Disc1:=
t^10*s^10*u^10*4024637071982973454846218628439512288164081610375433228909\
96932983398437500000000000000000000000000000000000000000000000000000000000000:
                                    

Disc2:=
25*t^8+220*t^6*u^2+220*t^6*s^2+220*t^2*u^6+220*t^2*s^6+25*s^8+220*s^6*u^2+220*u
^6*s^2+25*u^8+534*u^4*s^4+534*t^4*u^4+1188*t^2*u^2*s^4+1188*t^4*u^2*s^2+1188*t^
2*u^4*s^2+534*s^4*t^4:


Disc3:=
(1711664452050*u^44*s^28+423762700025*u^48*s^24+136549494000*u^50*s^22+
101356782915977070*t^40*s^20*u^12+39216117600*u^20*s^52+136549494000*u^22*s^50+
423762700025*u^24*s^48-2710713600*u^18*s^54+911980194900*u^26*s^46+
144336184933004196*t^40*s^18*u^14+911980194900*u^46*s^26-41104826331676604*t^40
*u^10*s^22+186624000*t^2*u^14*s^56-15007161600*t^2*u^16*s^54+39216117600*u^52*s
^20+2629819744100*u^42*s^30+3638456745975*t^40*u^32-2710713600*u^54*s^18-\
32903946295080*t^2*u^26*s^44+41990400*u^56*s^16-347669650800*t^2*u^20*s^50+
767200049117746*t^40*u^28*s^4-100787648679300*t^40*u^30*s^2-145362827235780*t^2
*u^38*s^32-100787648679300*t^2*s^40*u^30+308447979840*t^2*u^18*s^52-\
3874381575420*t^2*u^22*s^48-15368977105980*t^2*u^24*s^46-145362827235780*t^2*s^
38*u^32-161189693088480*t^2*s^36*u^34-161189693088480*t^2*s^34*u^36+
4312755955800*u^38*s^34-32903946295080*t^2*s^26*u^44-6075760763732520*t^40*u^24
*s^8+3638456745975*u^40*s^32-15368977105980*t^2*u^46*s^24-3874381575420*t^2*s^
22*u^48-71294295671880*t^2*s^28*u^42-71294295671880*t^2*s^42*u^28-\
20795427417774*t^48*u^20*s^4+423762700025*t^48*u^24-71294295671880*t^28*s^42*u^
2+308447979840*t^2*s^18*u^52-100787648679300*t^2*s^30*u^40+7923746097705762864*
t^16*u^30*s^26-17145039101520*t^16*s^50*u^6-15007161600*t^16*u^54*s^2-\
1168463735467386*t^16*u^44*s^12+173690123435565346*t^16*u^40*s^16-\
2320676852053356708*t^34*u^24*s^14-17177529302715192*t^34*u^28*s^10+
856732173392126856*t^34*u^12*s^26+3647157068239732944*t^34*u^18*s^20+
2304866195822546444*t^34*u^22*s^16+3647157068239732944*t^34*u^20*s^18+41990400*
t^16*u^56+2304866195822546444*t^34*u^16*s^22-2320676852053356708*t^34*u^14*s^24
-1462838836223460*t^34*s^32*u^6-17177529302715192*t^34*u^10*s^28+4622603130300*
u^36*s^36-16874540543413596*t^34*s^30*u^8-3874381575420*t^48*u^22*s^2-\
4105358485257*t^48*u^16*s^8+41990400*t^16*s^56-15007161600*t^16*s^54*u^2+
856732173392126856*t^34*u^26*s^12-4105358485257*t^48*u^8*s^16+71127059547516*t^
48*u^12*s^12+1073285010400*t^16*u^52*s^4-17145039101520*t^16*u^50*s^6+
127615229291451564*t^16*s^38*u^18-47766169088415204*t^16*u^42*s^14-\
9788297759350437504*t^26*u^28*s^18+13760642858083483944*t^16*u^28*s^28+
1711664452050*t^28*s^44+68173482310152*t^48*u^10*s^14-45032536553740*t^48*u^6*s
^18-32903946295080*t^26*u^44*s^2+911980194900*t^26*u^46-71244286446736368*t^26*
u^36*s^10-11704246449559292*t^26*u^38*s^8+1664717314077084*t^26*u^40*s^6+
2304866195822546444*t^16*s^34*u^22+127615229291451564*t^16*u^38*s^18+
247563706268304*t^26*u^42*s^4+423762700025*t^48*s^24-161189693088480*t^34*s^36*
u^2+7923746097705762864*t^16*u^26*s^30+173690123435565346*t^16*u^16*s^40-\
3874381575420*t^48*u^2*s^22+186624000*t^2*u^56*s^14+9598124661392952288*t^26*u^
24*s^22+2304866195822546444*t^16*u^34*s^22+4312755955800*u^34*s^38-\
20795427417774*t^48*u^4*s^20-3866072340031538692*t^26*u^32*s^14+39216117600*t^
52*s^20+2391855333120*t^52*u^6*s^14-161189693088480*t^34*u^36*s^2+
9598124661392952288*t^26*u^22*s^24-11704246449559292*t^26*s^38*u^8-15007161600*
t^2*u^54*s^16-9788297759350437504*t^26*u^18*s^28+3630473254080*t^52*u^8*s^12-\
4031900857165138304*t^26*u^20*s^26+856732173392126856*t^26*u^12*s^34+
3638456745975*u^32*s^40-3866072340031538692*t^26*u^14*s^32+1664717314077084*t^
26*s^40*u^6-1168463735467386*t^16*s^44*u^12-4105358485257*t^16*s^48*u^8+
1073285010400*t^52*u^4*s^16-4105358485257*t^16*u^48*s^8-71244286446736368*t^26*
s^36*u^10+1249099104510540*t^16*u^46*s^10+119219413790646*t^44*s^24*u^4+
1055164415961360*t^44*s^22*u^6+4376177697854227968*t^22*u^18*s^32-\
19963189455326900928*t^22*u^20*s^30-1820310088719392*t^14*u^44*s^14-\
1469335879988888376*t^14*u^36*s^22+4312755955800*t^34*u^38+144336184933004196*t
^14*s^40*u^18-347669650800*t^2*s^20*u^50+106255660654347816*t^14*s^38*u^20-\
47766169088415204*t^14*u^42*s^16+144336184933004196*t^14*u^40*s^18+
2391855333120*t^14*s^52*u^6+1585546337955216*t^14*u^12*s^46+7923746097705762864
*t^26*u^30*s^16+911980194900*t^26*s^46+3630473254080*t^52*u^12*s^8-\
41104826331676604*t^22*s^40*u^10-1469335879988888376*t^22*u^36*s^14+
2391855333120*t^52*u^14*s^6+1055164415961360*t^22*s^44*u^6-3593194854258468*t^
22*s^42*u^8-1469335879988888376*t^22*u^14*s^36-19749140661416*t^22*s^46*u^4-\
19749140661416*t^22*u^46*s^4+1073285010400*t^52*u^16*s^4+398365848805584912*t^
22*u^12*s^38-16874540543413596*t^34*u^30*s^8+1628536296992576*t^34*u^34*s^4+
1055164415961360*t^22*u^44*s^6-19963189455326900928*t^22*s^20*u^30-\
3593194854258468*t^22*u^42*s^8+4376177697854227968*t^22*s^18*u^32-3874381575420
*t^22*u^48*s^2+136549494000*t^22*u^50+889791527035164*t^46*u^18*s^8+
101356782915977070*t^40*u^20*s^12+4073711955840*t^52*u^10*s^10-1462838836223460
*t^34*u^32*s^6+1249099104510540*t^46*u^16*s^10+889791527035164*t^46*s^18*u^8+
1585546337955216*t^46*s^14*u^12+1249099104510540*t^46*s^16*u^10-15368977105980*
t^46*s^24*u^2+794034833865252*t^6*u^42*s^24+911980194900*t^46*s^26-\
1462838836223460*t^6*u^34*s^32+340391829046944*t^6*u^28*s^38-609463902381256*t^
6*u^30*s^36+1055164415961360*t^6*u^22*s^44+1664717314077084*t^6*u^26*s^40+
794034833865252*t^6*u^24*s^42-45032536553740*t^6*u^18*s^48-74461824000*t^6*s^54
*u^12-19749140661416*t^46*u^22*s^4+174028218149784*t^46*u^20*s^6-15368977105980
*t^46*u^24*s^2+174028218149784*t^46*s^20*u^6+174028218149784*t^6*u^46*s^20+
1055164415961360*t^6*u^44*s^22+340391829046944*t^6*u^38*s^28+1664717314077084*t
^6*u^40*s^26-1462838836223460*t^6*u^32*s^34+340391829046944*t^38*u^6*s^28-\
11704246449559292*t^38*u^8*s^26-74461824000*t^6*u^54*s^12+4312755955800*t^38*s^
34+650188800*t^6*u^56*s^10-45032536553740*t^6*u^48*s^18+2391855333120*t^6*u^52*
s^14+174028218149784*t^6*u^20*s^46+144336184933004196*t^40*u^18*s^14+41990400*u
^16*s^56+127615229291451564*t^38*u^16*s^18-41196672000*t^14*s^54*u^4+
2391855333120*t^14*u^52*s^6+186624000*t^14*u^56*s^2-37195369527200*t^14*u^50*s^
8+1664717314077084*t^40*u^26*s^6+4312755955800*t^38*u^34-145362827235780*t^38*u
^32*s^2-29925344661169092*t^38*u^24*s^10+340391829046944*t^38*u^28*s^6-\
11704246449559292*t^38*u^26*s^8+127615229291451564*t^38*u^18*s^16+
398365848805584912*t^38*u^22*s^12+106255660654347816*t^38*u^20*s^14-\
2320676852053356708*t^14*u^24*s^34-4910039300686975200*t^14*s^30*u^28-\
1820310088719392*t^14*u^14*s^44+2304866195822546444*t^22*u^34*s^16+
9598124661392952288*t^22*u^24*s^26-41196672000*t^14*u^54*s^4-\
1469335879988888376*t^14*s^36*u^22-1168463735467386*t^12*u^44*s^16+
1049026187971928406*t^12*u^28*s^32+1711664452050*u^28*s^44+71127059547516*t^12*
s^48*u^12+470884360072570490*t^12*u^24*s^36+1585546337955216*t^12*s^46*u^14+
186624000*t^14*s^56*u^2-49236628364640*t^12*s^50*u^10-19963189455326900928*t^20
*u^30*s^22-17177529302715192*t^28*u^34*s^10+136549494000*t^50*s^22-\
47766169088415204*t^14*u^16*s^42-3866072340031538692*t^14*u^32*s^26+
2629819744100*u^30*s^42-2320676852053356708*t^14*u^34*s^24-3866072340031538692*
t^14*s^32*u^26+429235200*t^56*u^4*s^12+429235200*t^12*u^56*s^4+1073285010400*t^
16*s^52*u^4+101356782915977070*t^12*u^40*s^20+1249099104510540*t^16*s^46*u^10+
3630473254080*t^12*u^52*s^8+398365848805584912*t^12*u^38*s^22-34861095386989864
*t^12*u^42*s^18-34861095386989864*t^12*s^42*u^18+1711664452050*t^44*s^28-\
32903946295080*t^44*s^26*u^2+650188800*t^56*u^10*s^6-1727954189973246474*t^16*u
^36*s^20-1727954189973246474*t^16*s^36*u^20-4031900857165138304*t^26*u^26*s^20+
186624000*t^56*u^14*s^2+41990400*t^56*u^16+429235200*t^56*u^12*s^4+650188800*t^
56*u^6*s^10+1628536296992576*t^34*s^34*u^4+4312755955800*t^34*s^38+739366400*t^
56*u^8*s^8-45032536553740*t^48*u^18*s^6+68173482310152*t^48*u^14*s^10+
6741239065543148535*t^16*u^24*s^32+41990400*t^56*s^16+186624000*t^56*u^2*s^14+
911980194900*t^46*u^26+650188800*t^6*u^10*s^56+1585546337955216*t^46*s^12*u^14+
308447979840*t^18*u^52*s^2-19749140661416*t^46*s^22*u^4+55671559343344672896*t^
22*s^22*u^28+9598124661392952288*t^22*u^26*s^24-3874381575420*t^22*s^48*u^2-\
41104826331676604*t^22*u^40*s^10-4534944586800*t^18*u^50*s^4+398365848805584912
*t^22*u^38*s^12-234432097211352*t^18*u^44*s^10-45032536553740*t^18*u^48*s^6+
55671559343344672896*t^22*u^22*s^28-37195369527200*t^14*s^50*u^8-32903946295080
*t^26*s^44*u^2+247563706268304*t^26*s^42*u^4+106255660654347816*t^14*u^38*s^20-\
95632627200*t^8*s^54*u^10+889791527035164*t^18*u^46*s^8+1055164415961360*t^44*u
^22*s^6+856732173392126856*t^26*u^34*s^12+68173482310152*t^14*u^48*s^10+
1585546337955216*t^14*u^46*s^12+7923746097705762864*t^26*u^16*s^30+
1711664452050*t^44*u^28-1820310088719392*t^44*u^14*s^14-1168463735467386*t^44*u
^16*s^12-47766169088415204*t^16*s^42*u^14-234432097211352*t^44*u^18*s^10+
2891677089922034*t^44*u^20*s^8+2891677089922034*t^44*u^8*s^20-234432097211352*t
^44*u^10*s^18-1168463735467386*t^44*u^12*s^16+398365848805584912*t^12*u^22*s^38
+101356782915977070*t^12*u^20*s^40+889791527035164*t^18*s^46*u^8-\
1168463735467386*t^12*s^44*u^16-4910039300686975200*t^14*s^28*u^30+
68173482310152*t^14*s^48*u^10+1077889930449576*t^38*u^30*s^4-34861095386989864*
t^18*s^42*u^12-4534944586800*t^18*s^50*u^4-2710713600*t^18*s^54+308447979840*t^
18*s^52*u^2+398365848805584912*t^38*u^12*s^22+106255660654347816*t^38*u^14*s^20
-29925344661169092*t^38*u^10*s^24-17145039101520*t^6*u^50*s^16-609463902381256*
t^6*u^36*s^30+144336184933004196*t^18*s^40*u^14+119219413790646*t^44*u^24*s^4-\
32903946295080*t^44*u^26*s^2+127615229291451564*t^18*u^38*s^16-\
9788297759350437504*t^18*u^28*s^26+856732173392126856*t^12*u^34*s^26+
1049026187971928406*t^12*u^32*s^28+3647157068239732944*t^18*u^20*s^34-\
12301839364672265568*t^18*u^24*s^30-12301839364672265568*t^18*u^30*s^24+
856732173392126856*t^12*u^26*s^34+127615229291451564*t^18*u^16*s^38-\
1649777846472319584*t^18*u^18*s^36+4376177697854227968*t^18*u^22*s^32+
3630473254080*t^12*s^52*u^8-45032536553740*t^18*s^48*u^6-234432097211352*t^18*s
^44*u^10+144336184933004196*t^18*u^40*s^14-3866072340031538692*t^32*u^26*s^14+
4376177697854227968*t^32*s^22*u^18-2425984759505937048*t^32*u^20*s^20+
1049026187971928406*t^32*s^28*u^12+6741239065543148535*t^32*u^16*s^24-\
3866072340031538692*t^32*s^26*u^14-1462838836223460*t^32*s^34*u^6-\
43872201311247444*t^32*s^30*u^10-27506078114557150*t^32*s^32*u^8+
3647157068239732944*t^18*u^34*s^20+3638456745975*t^32*s^40+4376177697854227968*
t^18*u^32*s^22-2710713600*t^18*u^54-1469335879988888376*t^36*u^22*s^14-\
1649777846472319584*t^18*u^36*s^18-9788297759350437504*t^18*u^26*s^28-\
609463902381256*t^36*u^30*s^6+470884360072570490*t^36*u^24*s^12+
1565384303740134*t^4*u^32*s^36-71244286446736368*t^36*u^26*s^10-\
1727954189973246474*t^36*u^20*s^16+470884360072570490*t^36*u^12*s^24-\
1727954189973246474*t^36*u^16*s^20-1649777846472319584*t^36*u^18*s^18-\
1469335879988888376*t^36*u^14*s^22+2304866195822546444*t^22*u^16*s^34+
136549494000*t^22*s^50+1565384303740134*t^32*u^36*s^4+3638456745975*t^32*u^40-\
145362827235780*t^32*u^38*s^2-43872201311247444*t^32*u^30*s^10+
6741239065543148535*t^32*u^24*s^16+1049026187971928406*t^32*u^28*s^12+
4376177697854227968*t^32*u^22*s^18-1462838836223460*t^32*u^34*s^6-\
27506078114557150*t^32*u^32*s^8+767200049117746*t^4*s^40*u^28+1077889930449576*
t^4*u^30*s^38-20795427417774*t^4*s^48*u^20-15007161600*t^54*u^16*s^2-2710713600
*t^54*u^18+4622603130300*t^36*u^36-19749140661416*t^4*s^46*u^22+119219413790646
*t^4*s^44*u^24+1073285010400*t^4*s^52*u^16-4534944586800*t^4*s^50*u^18-\
161189693088480*t^36*u^34*s^2+1565384303740134*t^36*u^32*s^4-34861095386989864*
t^18*u^42*s^12-41196672000*t^4*u^14*s^54+429235200*t^4*u^12*s^56-\
22665475234742034*t^36*u^28*s^8+7923746097705762864*t^30*u^16*s^26-\
609463902381256*t^30*s^36*u^6-43872201311247444*t^30*u^10*s^32-\
16874540543413596*t^30*u^8*s^34+1628536296992576*t^4*u^34*s^34+1565384303740134
*t^4*u^36*s^32-41196672000*t^4*u^54*s^14+429235200*t^4*u^56*s^12-19749140661416
*t^4*u^46*s^22-20795427417774*t^4*u^48*s^20-4534944586800*t^4*u^50*s^18+
1077889930449576*t^4*u^38*s^30+247563706268304*t^4*u^42*s^26+1073285010400*t^4*
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