X-Received: by 2002:ad4:498e:0:b0:670:f16d:193b with SMTP id u14-20020ad4498e000000b00670f16d193bmr459411qvx.6.1701194786876;
        Tue, 28 Nov 2023 10:06:26 -0800 (PST)
X-Received: by 2002:a05:690c:2f0d:b0:5cb:e3c9:ca22 with SMTP id
 ev13-20020a05690c2f0d00b005cbe3c9ca22mr434206ywb.7.1701194786429; Tue, 28 Nov
 2023 10:06:26 -0800 (PST)
Path: ...!news.nobody.at!newsreader4.netcologne.de!news.netcologne.de!peer01.ams1!peer.ams1.xlned.com!news.xlned.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: fr.sci.maths
Date: Tue, 28 Nov 2023 10:06:26 -0800 (PST)
In-Reply-To: <6565bd77$0$7445$426a34cc@news.free.fr>
Injection-Info: google-groups.googlegroups.com; posting-host=37.174.253.203; posting-account=1qbAGAkAAADcUtlizzXUEb5jUjfAdE2y
NNTP-Posting-Host: 37.174.253.203
References: <5fe4bff6-0e96-42e6-b2a1-6d03d27820ban@googlegroups.com>
 <6565abee$0$6454$426a74cc@news.free.fr> <uk4bl4$7eca$1@dont-email.me> <6565bd77$0$7445$426a34cc@news.free.fr>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <0b78f563-349d-44a3-b5f7-8527315ba7dfn@googlegroups.com>
Subject: =?UTF-8?Q?Re=3A_Equation_de_g=C3=A9om=C3=A9trie_impossible_pour_Maxima_e?=
	=?UTF-8?Q?t_d=27autres?=
From: Yanick Toutain <yanicktoutain@gmail.com>
Injection-Date: Tue, 28 Nov 2023 18:06:26 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 12709
Bytes: 12860
Lines: 180

Le mardi 28 novembre 2023 =C3=A0 11:14:17 UTC+1, Michel Talon a =C3=A9crit=
=C2=A0:
> Le 28/11/2023 =C3=A0 10:24, efji a =C3=A9crit :=20
> > L'=C3=A9quation me semble du type=20
> >=20
> > a*sqrt(P(x)) + b*sqrt(Q(x)) + c =3D 0=20
> >=20
> > avec P et Q des polyn=C3=B4mes de degr=C3=A9 2.=20
> > On ne peut pas s'en sortir analytiquement pour =C3=A9liminer les racine=
s (il=20
> > me semble),
> Si on peut, maxima:=20
> (%i1) eq1:a*sqrt(P(x))=3Dc-b*sqrt(Q(x));=20
> (%o1) a*sqrt(P(x)) =3D c-b*sqrt(Q(x))=20
> (%i2) expand(eq1^2);=20
> (%o2) a^2*P(x) =3D b^2*Q(x)-2*b*c*sqrt(Q(x))+c^2=20
> (%i3) eq2:b^2*Q(x)+c^2-a^2*P(x)=3D2*b*c*sqrt(Q(x));=20
> (%o3) b^2*Q(x)-a^2*P(x)+c^2 =3D 2*b*c*sqrt(Q(x))=20
> (%i4) expand(eq2^2);=20
> (%o4)=20
> b^4*Q(x)^2-2*a^2*b^2*P(x)*Q(x)+2*b^2*c^2*Q(x)+a^4*P(x)^2-2*a^2*c^2*P(x)=
=20
> +c ^4 =3D 4*b^2*c^2*Q(x)=20
>=20
> qui est de degr=C3=A9 4 en x via Q^2 et P*Q donc soluble explicitement da=
ns=20
> maxima.=20
> Cela =C3=A9tant avec une formule monstrueuse.=20
>=20
> --=20
> Michel Talon
Merci de la r=C3=A9ponse
J'y ai pens=C3=A9 apr=C3=A8s avoir post=C3=A9 mais Maxima me donne des solu=
tions qui sont fausses sur le tableur
Je divise par a pour passer de aX^4 =C3=A0 X^4=20
et  avoir directement les cases libre office remplies
en posant
A1 B1 C1  D1 et E1
je calcule
F1=3DB1/A1
G1 =3D C1/A1
H1 =3D D1/A1
I1=3D E1/A1
je demande =C3=A0 Maxima les 4 racines

(%i1)	S^4+F1*S^3+G1*S^2+H1*S+I1;

Maxima me donne


S1=3D-racine(-(3*(-8*H1+4*F1*G1-F1^3))/(2*racine((36*(racine(-256*I1^3-(-19=
2*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G=
1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1=
^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^=
2))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*F1*H1-128*G1^2+=
144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+=
16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H=
1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1=
/3)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*=
G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4=
*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3=
^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)))-(ra=
cine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1=
^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*=
G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-=
I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)+((H1*F1-4*I1)/3+((-1)*G1^2)/9)/(rac=
ine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^=
2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G=
1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I=
1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)-(4*G1)/3+F1^2/2)/2-racine((36*(racin=
e(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)=
*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-=
4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*=
F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192=
*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1=
-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^=
2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2=
))/6+G1^3/27)^(1/3)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-12=
8*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1=
^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*=
G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3=
/27)^(1/3))/12+((-1)*F1)/4

S2=3Dracine(-(3*(-8*H1+4*F1*G1-F1^3))/(2*racine((36*(racine(-256*I1^3-(-192=
*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1=
-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^=
2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2=
))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*F1*H1-128*G1^2+1=
44*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+1=
6*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1=
^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/=
3)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G=
1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*=
F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^=
(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)))-(rac=
ine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^=
2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G=
1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I=
1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)+((H1*F1-4*I1)/3+((-1)*G1^2)/9)/(raci=
ne(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2=
)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1=
-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1=
*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)-(4*G1)/3+F1^2/2)/2-racine((36*(racine=
(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*=
H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4=
*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F=
1^2+4*I1*G1-H1^2))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*=
F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-=
80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2=
*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2)=
)/6+G1^3/27)^(1/3)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-128=
*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^=
2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G=
1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/=
27)^(1/3))/12+((-1)*F1)/4

S3=3D-racine((3*(-8*H1+4*F1*G1-F1^3))/(2*racine((36*(racine(-256*I1^3-(-192=
*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1=
-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^=
2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2=
))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*F1*H1-128*G1^2+1=
44*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+1=
6*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1=
^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/=
3)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G=
1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*=
F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^=
(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)))-(rac=
ine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^=
2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G=
1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I=
1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)+((H1*F1-4*I1)/3+((-1)*G1^2)/9)/(raci=
ne(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2=
)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1=
-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1=
*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)-(4*G1)/3+F1^2/2)/2+racine((36*(racine=
(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*=
H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4=
*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F=
1^2+4*I1*G1-H1^2))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*=
F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-=
80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2=
*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2)=
)/6+G1^3/27)^(1/3)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-128=
*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^=
2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G=
1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/=
27)^(1/3))/12+((-1)*F1)/4

S4=3Dracine((3*(-8*H1+4*F1*G1-F1^3))/(2*racine((36*(racine(-256*I1^3-(-192*=
F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-=
80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2=
*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2)=
)/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*F1*H1-128*G1^2+14=
4*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16=
*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^=
2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3=
)+48*I1-12*F1*H1+4*G1^2)/(racine(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1=
-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F=
1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(=
3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)))-(raci=
ne(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2=
)*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1=
-4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1=
*F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)+((H1*F1-4*I1)/3+((-1)*G1^2)/9)/(racin=
e(-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)=
*H1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-=
4*F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*=
F1^2+4*I1*G1-H1^2))/6+G1^3/27)^(1/3)-(4*G1)/3+F1^2/2)/2+racine((36*(racine(=
-256*I1^3-(-192*F1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H=
1^2+(18*F1^3*G1-80*F1*G1^2)*H1+16*G1^4-4*F1^2*G1^3)*I1+27*H1^4-(18*F1*G1-4*=
F1^3)*H1^3-(F1^2*G1^2-4*G1^3)*H1^2)/(2*3^(3/2))+(-G1*(H1*F1-4*I1)-3*(-I1*F1=
^2+4*I1*G1-H1^2))/6+G1^3/27)^(2/3)+(9*F1^2-24*G1)*(racine(-256*I1^3-(-192*F=
1*H1-128*G1^2+144*F1^2*G1-27*F1^4)*I1^2-((144*G1-6*F1^2)*H1^2+(18*F1^3*G1-8=
========== REMAINDER OF ARTICLE TRUNCATED ==========