#G24.half.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 is a
# polynomial in s^2, t^2, and u^2.  Taking square roots of the variables, we
# obtain a simpler polynomial, with t 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 36 in the parameters s, t, and u, with 595 terms.

interface(quiet=true):

Disc1:=
402463707198297345484621862843951228816408161037543322890996932983398437500000000000000000000000000000000000000000000000000000000000000*t^5*s^5*u^5:

Disc2:=
25*t^4+220*t^3*u+220*t^3*s+220*t*u^3+220*t*s^3+25*s^4+220*s^3*u+220*u^3*s+25*u^4+534*u^2*s^2+534*t^2*u^2+1188*t*u*s^2+1188*t^2*u*s+1188*t*u^2*s+534*s^2*t^2:

Disc3:=
(41990400*t^8*s^28+1711664452050*t^14*s^22+423762700025*t^24*s^12+39216117600*t
^26*s^10+911980194900*t^13*s^23+911980194900*t^23*s^13+4312755955800*t^19*s^17+
136549494000*t^25*s^11+1711664452050*t^22*s^14+4312755955800*t^17*s^19+41990400
*t^28*s^8-2710713600*t^9*s^27+3638456745975*t^16*s^20+136549494000*t^11*s^25+
423762700025*t^12*s^24+2629819744100*t^21*s^15+39216117600*t^10*s^26+
4622603130300*t^18*s^18-2710713600*t^27*s^9+3638456745975*t^20*s^16+
2629819744100*t^15*s^21+1711664452050*u^22*s^14+423762700025*u^24*s^12+
136549494000*u^25*s^11+39216117600*u^10*s^26+136549494000*u^11*s^25+
423762700025*u^12*s^24-2710713600*u^9*s^27+911980194900*u^13*s^23+911980194900*
u^23*s^13+39216117600*u^26*s^10+2629819744100*u^21*s^15-2710713600*u^27*s^9+
41990400*u^28*s^8+4312755955800*u^19*s^17+3638456745975*u^20*s^16+4622603130300
*u^18*s^18+4312755955800*u^17*s^19+3638456745975*u^16*s^20+41990400*u^8*s^28+
1711664452050*u^14*s^22+2629819744100*u^15*s^21+3638456745975*t^20*u^16+
423762700025*t^24*u^12+41990400*t^8*u^28+911980194900*t^13*u^23+4312755955800*t
^17*u^19+136549494000*t^11*u^25+4312755955800*t^19*u^17+41990400*t^28*u^8+
911980194900*t^23*u^13+1711664452050*t^22*u^14-2710713600*t^9*u^27+
3638456745975*t^16*u^20-2710713600*t^27*u^9+4622603130300*t^18*u^18+
423762700025*t^12*u^24+2629819744100*t^15*u^21+136549494000*t^25*u^11+
39216117600*t^10*u^26+2629819744100*t^21*u^15+39216117600*t^26*u^10+
1711664452050*t^14*u^22-1820310088719392*t^7*u^7*s^22+794034833865252*t^12*u^21
*s^3-15368977105980*t*u^23*s^12-47766169088415204*t^21*u^7*s^8-145362827235780*
t*s^19*u^16-71294295671880*t^14*s^21*u+767200049117746*t^20*u^14*s^2-\
6075760763732520*t^20*u^12*s^4-32903946295080*t*u^13*s^22-15368977105980*t*u^12
*s^23-19963189455326900928*t^10*s^15*u^11-20795427417774*t^24*u^10*s^2-\
71294295671880*t*s^14*u^21+7923746097705762864*t^8*u^15*s^13-\
1727954189973246474*t^8*u^18*s^10+186624000*t*u^7*s^28-100787648679300*t*s^15*u
^20-41104826331676604*t^20*u^5*s^11-17145039101520*t^8*s^25*u^3-3874381575420*t
*u^11*s^24-15007161600*t*u^8*s^27+1628536296992576*t^2*u^17*s^17-\
145362827235780*t*u^19*s^16+9598124661392952288*t^12*s^13*u^11-95632627200*t^5*
s^27*u^4+101356782915977070*t^20*s^10*u^6-32903946295080*t*s^13*u^22-\
3874381575420*t*s^11*u^24-6075760763732520*t^20*s^12*u^4-4910039300686975200*t^
14*u^15*s^7-2320676852053356708*t^7*u^12*s^17+308447979840*t*u^9*s^26+650188800
*t^5*u^28*s^3-1168463735467386*t^8*u^22*s^6-100787648679300*t*s^20*u^15-\
161189693088480*t*s^17*u^18-15007161600*t^8*u^27*s+1249099104510540*t^8*s^23*u^
5-234432097211352*t^22*u^5*s^9+1585546337955216*t^23*s^6*u^7+144336184933004196
*t^20*s^9*u^7-347669650800*t*u^10*s^25-17177529302715192*t^5*u^17*s^14-\
3874381575420*t^11*s^24*u-100787648679300*t^20*u^15*s-45032536553740*t^24*u^9*s
^3+9598124661392952288*t^11*u^13*s^12-71294295671880*t*s^21*u^14+308447979840*t
*s^9*u^26-161189693088480*t*s^18*u^17+173690123435565346*t^8*u^20*s^8-\
2320676852053356708*t^17*u^12*s^7-17177529302715192*t^17*u^14*s^5+
856732173392126856*t^17*u^6*s^13+3647157068239732944*t^17*u^9*s^10+
2304866195822546444*t^17*u^11*s^8+3647157068239732944*t^17*u^10*s^9+
2304866195822546444*t^17*u^8*s^11-2320676852053356708*t^17*u^7*s^12-\
1462838836223460*t^17*s^16*u^3-17177529302715192*t^17*u^5*s^14-\
16874540543413596*t^17*s^15*u^4-3874381575420*t^24*u^11*s-4105358485257*t^24*u^
8*s^4+6741239065543148535*t^12*u^16*s^8+9598124661392952288*t^12*s^11*u^13-\
15007161600*t^8*s^27*u+856732173392126856*t^17*u^13*s^6-4105358485257*t^24*u^4*
s^8+71127059547516*t^24*u^6*s^6-71244286446736368*t^5*u^13*s^18+1073285010400*t
^8*u^26*s^2-17145039101520*t^8*u^25*s^3+127615229291451564*t^8*s^19*u^9-\
47766169088415204*t^8*u^21*s^7-9788297759350437504*t^13*u^14*s^9+
13760642858083483944*t^8*u^14*s^14-37195369527200*t^25*u^4*s^7+68173482310152*t
^24*u^5*s^7-45032536553740*t^24*u^3*s^9-32903946295080*t^13*u^22*s-\
71244286446736368*t^13*u^18*s^5-11704246449559292*t^13*u^19*s^4+
1664717314077084*t^13*u^20*s^3+2304866195822546444*t^8*s^17*u^11+
127615229291451564*t^8*u^19*s^9+247563706268304*t^13*u^21*s^2-161189693088480*t
^17*s^18*u+7923746097705762864*t^8*u^13*s^15+173690123435565346*t^8*u^8*s^20-\
3874381575420*t^24*u*s^11+186624000*t*u^28*s^7+9598124661392952288*t^13*u^12*s^
11+2304866195822546444*t^8*u^17*s^11-20795427417774*t^24*u^2*s^10-\
3866072340031538692*t^13*u^16*s^7+2391855333120*t^26*u^3*s^7-161189693088480*t^
17*u^18*s+9598124661392952288*t^13*u^11*s^12-11704246449559292*t^13*s^19*u^4-\
15007161600*t*u^27*s^8-9788297759350437504*t^13*u^9*s^14+3630473254080*t^26*u^4
*s^6-4031900857165138304*t^13*u^10*s^13+856732173392126856*t^13*u^6*s^17-\
3866072340031538692*t^13*u^7*s^16+1664717314077084*t^13*s^20*u^3-\
1168463735467386*t^8*s^22*u^6-4105358485257*t^8*s^24*u^4+1073285010400*t^26*u^2
*s^8-4105358485257*t^8*u^24*s^4-2320676852053356708*t^7*u^17*s^12-\
71244286446736368*t^13*s^18*u^5+119219413790646*t^12*s^22*u^2+1249099104510540*
t^8*u^23*s^5+119219413790646*t^22*s^12*u^2-4910039300686975200*t^7*s^15*u^14+
1055164415961360*t^22*s^11*u^3+4376177697854227968*t^11*u^9*s^16-\
19963189455326900928*t^11*u^10*s^15-1820310088719392*t^7*u^22*s^7-\
1469335879988888376*t^7*u^18*s^11+144336184933004196*t^7*s^20*u^9-347669650800*
t*s^10*u^25+106255660654347816*t^7*s^19*u^10-47766169088415204*t^7*u^21*s^8+
144336184933004196*t^7*u^20*s^9+2391855333120*t^7*s^26*u^3+1585546337955216*t^7
*u^6*s^23+7923746097705762864*t^13*u^15*s^8+3630473254080*t^26*u^6*s^4-\
12301839364672265568*t^15*u^9*s^12-41104826331676604*t^11*s^20*u^5-\
1469335879988888376*t^11*u^18*s^7+2391855333120*t^26*u^7*s^3+1055164415961360*t
^11*s^22*u^3-3593194854258468*t^11*s^21*u^4-1469335879988888376*t^11*u^7*s^18-\
19749140661416*t^11*s^23*u^2-19749140661416*t^11*u^23*s^2+1073285010400*t^26*u^
8*s^2+398365848805584912*t^11*u^6*s^19-16874540543413596*t^17*u^15*s^4+
1628536296992576*t^17*u^17*s^2+1055164415961360*t^11*u^22*s^3-\
19963189455326900928*t^11*s^10*u^15-3593194854258468*t^11*u^21*s^4+
4376177697854227968*t^11*s^9*u^16-3874381575420*t^11*u^24*s+889791527035164*t^
23*u^9*s^4+4547084859146612880*t^14*u^12*s^10+101356782915977070*t^20*u^10*s^6+
4073711955840*t^26*u^5*s^5-1462838836223460*t^17*u^16*s^3+1249099104510540*t^23
*u^8*s^5+889791527035164*t^23*s^9*u^4+794034833865252*t^21*u^12*s^3+
1585546337955216*t^23*s^7*u^6+308447979840*t^26*u^9*s+1249099104510540*t^23*s^8
*u^5-15368977105980*t^23*s^12*u+794034833865252*t^3*u^21*s^12-1462838836223460*
t^3*u^17*s^16+340391829046944*t^3*u^14*s^19-609463902381256*t^3*u^15*s^18-\
37195369527200*t^25*u^7*s^4+1055164415961360*t^3*u^11*s^22+1664717314077084*t^3
*u^13*s^20+794034833865252*t^3*u^12*s^21-45032536553740*t^3*u^9*s^24-\
74461824000*t^3*s^27*u^6-19749140661416*t^23*u^11*s^2+174028218149784*t^23*u^10
*s^3-15368977105980*t^23*u^12*s+174028218149784*t^23*s^10*u^3+174028218149784*t
^3*u^23*s^10+1055164415961360*t^3*u^22*s^11+340391829046944*t^3*u^19*s^14+
1664717314077084*t^3*u^20*s^13-1462838836223460*t^3*u^16*s^17+340391829046944*t
^19*u^3*s^14-11704246449559292*t^19*u^4*s^13-74461824000*t^3*u^27*s^6+650188800
*t^3*u^28*s^5-45032536553740*t^3*u^24*s^9+2391855333120*t^3*u^26*s^7+
174028218149784*t^3*u^10*s^23-12301839364672265568*t^12*u^9*s^15+
144336184933004196*t^20*u^9*s^7+127615229291451564*t^19*u^8*s^9-41196672000*t^7
*s^27*u^2+2391855333120*t^7*u^26*s^3+186624000*t^7*u^28*s-37195369527200*t^7*u^
25*s^4+1664717314077084*t^20*u^13*s^3-145362827235780*t^19*u^16*s-\
29925344661169092*t^19*u^12*s^5+340391829046944*t^19*u^14*s^3-11704246449559292
*t^19*u^13*s^4+127615229291451564*t^19*u^9*s^8+398365848805584912*t^19*u^11*s^6
-17145039101520*t^25*u^8*s^3+106255660654347816*t^19*u^10*s^7+
2304866195822546444*t^11*u^17*s^8+9598124661392952288*t^11*u^12*s^13-\
19963189455326900928*t^10*u^15*s^11-41196672000*t^7*u^27*s^2-\
1469335879988888376*t^7*s^18*u^11-1168463735467386*t^6*u^22*s^8+
1049026187971928406*t^6*u^14*s^16+71127059547516*t^6*s^24*u^6+
470884360072570490*t^6*u^12*s^18+1585546337955216*t^6*s^23*u^7+186624000*t^7*s^
28*u-49236628364640*t^6*s^25*u^5-17177529302715192*t^14*u^17*s^5-\
47766169088415204*t^7*u^8*s^21-3866072340031538692*t^7*u^16*s^13-\
3866072340031538692*t^7*s^16*u^13+429235200*t^28*u^2*s^6+429235200*t^6*u^28*s^2
-16874540543413596*t^4*u^15*s^17+1073285010400*t^8*s^26*u^2+101356782915977070*
t^6*u^20*s^10+3630473254080*t^6*u^26*s^4+398365848805584912*t^6*u^19*s^11-\
34861095386989864*t^6*u^21*s^9-34861095386989864*t^6*s^21*u^9-32903946295080*t^
22*s^13*u+650188800*t^28*u^5*s^3-1727954189973246474*t^8*s^18*u^10-\
4031900857165138304*t^13*u^13*s^10+186624000*t^28*u^7*s+429235200*t^28*u^6*s^2+
650188800*t^28*u^3*s^5+1628536296992576*t^17*s^17*u^2+739366400*t^28*u^4*s^4+
68173482310152*t^24*u^7*s^5+6741239065543148535*t^8*u^12*s^16+186624000*t^28*u*
s^7+650188800*t^3*u^5*s^28+308447979840*t^9*u^26*s-19749140661416*t^23*s^11*u^2
+55671559343344672896*t^11*s^11*u^14-41104826331676604*t^11*u^20*s^5-\
4534944586800*t^9*u^25*s^2+398365848805584912*t^11*u^19*s^6-234432097211352*t^9
*u^22*s^5-45032536553740*t^9*u^24*s^3+55671559343344672896*t^11*u^11*s^14-\
37195369527200*t^7*s^25*u^4-32903946295080*t^13*s^22*u+247563706268304*t^13*s^
21*u^2+106255660654347816*t^7*u^19*s^10-95632627200*t^4*s^27*u^5+
889791527035164*t^9*u^23*s^4+1055164415961360*t^22*u^11*s^3+856732173392126856*
t^13*u^17*s^6+68173482310152*t^7*u^24*s^5+1585546337955216*t^7*u^23*s^6+
7923746097705762864*t^13*u^8*s^15-1820310088719392*t^22*u^7*s^7-\
1168463735467386*t^22*u^8*s^6-41104826331676604*t^5*u^20*s^11-47766169088415204
*t^8*s^21*u^7-234432097211352*t^22*u^9*s^5+2891677089922034*t^22*u^10*s^4+
2891677089922034*t^22*u^4*s^10-1168463735467386*t^22*u^6*s^8+398365848805584912
*t^6*u^11*s^19+101356782915977070*t^6*u^10*s^20+889791527035164*t^9*s^23*u^4-\
1168463735467386*t^6*s^22*u^8-4910039300686975200*t^7*s^14*u^15+68173482310152*
t^7*s^24*u^5+1077889930449576*t^19*u^15*s^2-34861095386989864*t^9*s^21*u^6-\
4534944586800*t^9*s^25*u^2+308447979840*t^9*s^26*u+398365848805584912*t^19*u^6*
s^11+106255660654347816*t^19*u^7*s^10-29925344661169092*t^19*u^5*s^12-\
17145039101520*t^3*u^25*s^8-609463902381256*t^3*u^18*s^15+144336184933004196*t^
9*s^20*u^7+119219413790646*t^22*u^12*s^2-32903946295080*t^22*u^13*s+
127615229291451564*t^9*u^19*s^8-9788297759350437504*t^9*u^14*s^13+
856732173392126856*t^6*u^17*s^13+1049026187971928406*t^6*u^16*s^14+
3647157068239732944*t^9*u^10*s^17-12301839364672265568*t^9*u^12*s^15-\
12301839364672265568*t^9*u^15*s^12+856732173392126856*t^6*u^13*s^17+
127615229291451564*t^9*u^8*s^19-1649777846472319584*t^9*u^9*s^18+
4376177697854227968*t^9*u^11*s^16+3630473254080*t^6*s^26*u^4+
4547084859146612880*t^14*u^10*s^12-45032536553740*t^9*s^24*u^3-234432097211352*
t^9*s^22*u^5+144336184933004196*t^9*u^20*s^7-3866072340031538692*t^16*u^13*s^7+
4376177697854227968*t^16*s^11*u^9-2425984759505937048*t^16*u^10*s^10+
1049026187971928406*t^16*s^14*u^6+6741239065543148535*t^16*u^8*s^12-\
3866072340031538692*t^16*s^13*u^7-1462838836223460*t^16*s^17*u^3-\
43872201311247444*t^16*s^15*u^5+767200049117746*t^20*s^14*u^2-27506078114557150
*t^16*s^16*u^4+3647157068239732944*t^9*u^17*s^10+4376177697854227968*t^9*u^16*s
^11-1469335879988888376*t^18*u^11*s^7-1649777846472319584*t^9*u^18*s^9-\
9788297759350437504*t^9*u^13*s^14-609463902381256*t^18*u^15*s^3+
470884360072570490*t^18*u^12*s^6-100787648679300*t^20*s^15*u+1565384303740134*t
^2*u^16*s^18-71244286446736368*t^18*u^13*s^5-1727954189973246474*t^18*u^10*s^8+
470884360072570490*t^18*u^6*s^12-1727954189973246474*t^18*u^8*s^10-\
1649777846472319584*t^18*u^9*s^9-1469335879988888376*t^18*u^7*s^11+
2304866195822546444*t^11*u^8*s^17+1565384303740134*t^16*u^18*s^2-\
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