Ptolemy 95
Geogebra sheet
Coq statement
Lemma Ptolemy95: forall O A B C D:point,
forall ab cd ad bc:R,
equaldistance O A O B ->
equaldistance O A O C ->
equaldistance O A O D ->
ab^2=(distance2 A B) ->
cd^2=(distance2 C D) ->
ad^2=(distance2 A D) ->
bc^2=(distance2 B C) ->
(distance2 A C)*(distance2 B D)=(ab*cd + ad*bc)^2
\/ (distance2 A C)*(distance2 B D)=(ab*cd - ad*bc)^2
\/ parallel A B C D.
Proof. geo_begin. tzR. Qed.
Algebraic version
p:= ((-1)) *a^4*b^4*f*i + (2) *a^2*b^2*c^2*d^2*f*i + ((-1)) *c^4*d^4*f*i + (2) *a^2*b^2*e^2*f*g^2*i + (2) *c^2*d^2*e^2*f*g^2*i + (2) *a^2*b^2*f^3*g^2*i + (2) *c^2*d^2*f^3*g^2*i + ((-1)) *e^4*f*g^4*i + ((-2)) *e^2*f^3*g^4*i + ((-1)) *f^5*g^4*i + (1) *a^4*b^4*h*i + ((-2)) *a^2*b^2*c^2*d^2*h*i + (1) *c^4*d^4*h*i + ((-2)) *a^2*b^2*e^2*g^2*h*i + ((-2)) *c^2*d^2*e^2*g^2*h*i + ((-2)) *a^2*b^2*f^2*g^2*h*i + ((-2)) *c^2*d^2*f^2*g^2*h*i + (1) *e^4*g^4*h*i + (2) *e^2*f^2*g^4*h*i + (1) *f^4*g^4*h*i + (2) *a^2*b^2*e^2*f*h^2*i + (2) *c^2*d^2*e^2*f*h^2*i + (2) *a^2*b^2*f^3*h^2*i + (2) *c^2*d^2*f^3*h^2*i + ((-2)) *e^4*f*g^2*h^2*i + ((-4)) *e^2*f^3*g^2*h^2*i + ((-2)) *f^5*g^2*h^2*i + ((-2)) *a^2*b^2*e^2*h^3*i + ((-2)) *c^2*d^2*e^2*h^3*i + ((-2)) *a^2*b^2*f^2*h^3*i + ((-2)) *c^2*d^2*f^2*h^3*i + (2) *e^4*g^2*h^3*i + (4) *e^2*f^2*g^2*h^3*i + (2) *f^4*g^2*h^3*i + ((-1)) *e^4*f*h^4*i + ((-2)) *e^2*f^3*h^4*i + ((-1)) *f^5*h^4*i + (1) *e^4*h^5*i + (2) *e^2*f^2*h^5*i + (1) *f^4*h^5*i + ((-4)) *a^2*b^2*e*f*g^2*i^2 + ((-4)) *c^2*d^2*e*f*g^2*i^2 + (4) *e^3*f*g^4*i^2 + (4) *e*f^3*g^4*i^2 + (4) *a^2*b^2*e*g^2*h*i^2 + (4) *c^2*d^2*e*g^2*h*i^2 + ((-4)) *e^3*g^4*h*i^2 + ((-4)) *e*f^2*g^4*h*i^2 + ((-4)) *a^2*b^2*e*f*h^2*i^2 + ((-4)) *c^2*d^2*e*f*h^2*i^2 + (8) *e^3*f*g^2*h^2*i^2 + (8) *e*f^3*g^2*h^2*i^2 + (4) *a^2*b^2*e*h^3*i^2 + (4) *c^2*d^2*e*h^3*i^2 + ((-8)) *e^3*g^2*h^3*i^2 + ((-8)) *e*f^2*g^2*h^3*i^2 + (4) *e^3*f*h^4*i^2 + (4) *e*f^3*h^4*i^2 + ((-4)) *e^3*h^5*i^2 + ((-4)) *e*f^2*h^5*i^2 + (2) *a^2*b^2*f*g^2*i^3 + (2) *c^2*d^2*f*g^2*i^3 + ((-6)) *e^2*f*g^4*i^3 + ((-2)) *f^3*g^4*i^3 + ((-2)) *a^2*b^2*g^2*h*i^3 + ((-2)) *c^2*d^2*g^2*h*i^3 + (6) *e^2*g^4*h*i^3 + (2) *f^2*g^4*h*i^3 + (2) *a^2*b^2*f*h^2*i^3 + (2) *c^2*d^2*f*h^2*i^3 + ((-12)) *e^2*f*g^2*h^2*i^3 + ((-4)) *f^3*g^2*h^2*i^3 + ((-2)) *a^2*b^2*h^3*i^3 + ((-2)) *c^2*d^2*h^3*i^3 + (12) *e^2*g^2*h^3*i^3 + (4) *f^2*g^2*h^3*i^3 + ((-6)) *e^2*f*h^4*i^3 + ((-2)) *f^3*h^4*i^3 + (6) *e^2*h^5*i^3 + (2) *f^2*h^5*i^3 + (4) *e*f*g^4*i^4 + ((-4)) *e*g^4*h*i^4 + (8) *e*f*g^2*h^2*i^4 + ((-8)) *e*g^2*h^3*i^4 + (4) *e*f*h^4*i^4 + ((-4)) *e*h^5*i^4 + ((-1)) *f*g^4*i^5 + (1) *g^4*h*i^5 + ((-2)) *f*g^2*h^2*i^5 + (2) *g^2*h^3*i^5 + ((-1)) *f*h^4*i^5 + (1) *h^5*i^5 + (1) *a^4*b^4*e*j + ((-2)) *a^2*b^2*c^2*d^2*e*j + (1) *c^4*d^4*e*j + ((-1)) *a^4*b^4*g*j + (2) *a^2*b^2*c^2*d^2*g*j + ((-1)) *c^4*d^4*g*j + ((-2)) *a^2*b^2*e^3*g^2*j + ((-2)) *c^2*d^2*e^3*g^2*j + ((-2)) *a^2*b^2*e*f^2*g^2*j + ((-2)) *c^2*d^2*e*f^2*g^2*j + (2) *a^2*b^2*e^2*g^3*j + (2) *c^2*d^2*e^2*g^3*j + (2) *a^2*b^2*f^2*g^3*j + (2) *c^2*d^2*f^2*g^3*j + (1) *e^5*g^4*j + (2) *e^3*f^2*g^4*j + (1) *e*f^4*g^4*j + ((-1)) *e^4*g^5*j + ((-2)) *e^2*f^2*g^5*j + ((-1)) *f^4*g^5*j + ((-2)) *a^2*b^2*e^3*h^2*j + ((-2)) *c^2*d^2*e^3*h^2*j + ((-2)) *a^2*b^2*e*f^2*h^2*j + ((-2)) *c^2*d^2*e*f^2*h^2*j + (2) *a^2*b^2*e^2*g*h^2*j + (2) *c^2*d^2*e^2*g*h^2*j + (2) *a^2*b^2*f^2*g*h^2*j + (2) *c^2*d^2*f^2*g*h^2*j + (2) *e^5*g^2*h^2*j + (4) *e^3*f^2*g^2*h^2*j + (2) *e*f^4*g^2*h^2*j + ((-2)) *e^4*g^3*h^2*j + ((-4)) *e^2*f^2*g^3*h^2*j + ((-2)) *f^4*g^3*h^2*j + (1) *e^5*h^4*j + (2) *e^3*f^2*h^4*j + (1) *e*f^4*h^4*j + ((-1)) *e^4*g*h^4*j + ((-2)) *e^2*f^2*g*h^4*j + ((-1)) *f^4*g*h^4*j + (4) *a^2*b^2*e^2*g^2*i*j + (4) *c^2*d^2*e^2*g^2*i*j + ((-4)) *a^2*b^2*f^2*g^2*i*j + ((-4)) *c^2*d^2*f^2*g^2*i*j + ((-4)) *a^2*b^2*e*g^3*i*j + ((-4)) *c^2*d^2*e*g^3*i*j + ((-4)) *e^4*g^4*i*j + (4) *f^4*g^4*i*j + (4) *e^3*g^5*i*j + (4) *e*f^2*g^5*i*j + (4) *a^2*b^2*f*g^2*h*i*j + (4) *c^2*d^2*f*g^2*h*i*j + ((-4)) *e^2*f*g^4*h*i*j + ((-4)) *f^3*g^4*h*i*j + (4) *a^2*b^2*e^2*h^2*i*j + (4) *c^2*d^2*e^2*h^2*i*j + ((-4)) *a^2*b^2*f^2*h^2*i*j + ((-4)) *c^2*d^2*f^2*h^2*i*j + ((-4)) *a^2*b^2*e*g*h^2*i*j + ((-4)) *c^2*d^2*e*g*h^2*i*j + ((-8)) *e^4*g^2*h^2*i*j + (8) *f^4*g^2*h^2*i*j + (8) *e^3*g^3*h^2*i*j + (8) *e*f^2*g^3*h^2*i*j + (4) *a^2*b^2*f*h^3*i*j + (4) *c^2*d^2*f*h^3*i*j + ((-8)) *e^2*f*g^2*h^3*i*j + ((-8)) *f^3*g^2*h^3*i*j + ((-4)) *e^4*h^4*i*j + (4) *f^4*h^4*i*j + (4) *e^3*g*h^4*i*j + (4) *e*f^2*g*h^4*i*j + ((-4)) *e^2*f*h^5*i*j + ((-4)) *f^3*h^5*i*j + ((-2)) *a^2*b^2*e*g^2*i^2*j + ((-2)) *c^2*d^2*e*g^2*i^2*j + (2) *a^2*b^2*g^3*i^2*j + (2) *c^2*d^2*g^3*i^2*j + (6) *e^3*g^4*i^2*j + ((-6)) *e*f^2*g^4*i^2*j + ((-6)) *e^2*g^5*i^2*j + ((-2)) *f^2*g^5*i^2*j + (8) *e*f*g^4*h*i^2*j + ((-2)) *a^2*b^2*e*h^2*i^2*j + ((-2)) *c^2*d^2*e*h^2*i^2*j + (2) *a^2*b^2*g*h^2*i^2*j + (2) *c^2*d^2*g*h^2*i^2*j + (12) *e^3*g^2*h^2*i^2*j + ((-12)) *e*f^2*g^2*h^2*i^2*j + ((-12)) *e^2*g^3*h^2*i^2*j + ((-4)) *f^2*g^3*h^2*i^2*j + (16) *e*f*g^2*h^3*i^2*j + (6) *e^3*h^4*i^2*j + ((-6)) *e*f^2*h^4*i^2*j + ((-6)) *e^2*g*h^4*i^2*j + ((-2)) *f^2*g*h^4*i^2*j + (8) *e*f*h^5*i^2*j + ((-4)) *e^2*g^4*i^3*j + (4) *f^2*g^4*i^3*j + (4) *e*g^5*i^3*j + ((-4)) *f*g^4*h*i^3*j + ((-8)) *e^2*g^2*h^2*i^3*j + (8) *f^2*g^2*h^2*i^3*j + (8) *e*g^3*h^2*i^3*j + ((-8)) *f*g^2*h^3*i^3*j + ((-4)) *e^2*h^4*i^3*j + (4) *f^2*h^4*i^3*j + (4) *e*g*h^4*i^3*j + ((-4)) *f*h^5*i^3*j + (1) *e*g^4*i^4*j + ((-1)) *g^5*i^4*j + (2) *e*g^2*h^2*i^4*j + ((-2)) *g^3*h^2*i^4*j + (1) *e*h^4*i^4*j + ((-1)) *g*h^4*i^4*j + (4) *a^2*b^2*e*f*g^2*j^2 + (4) *c^2*d^2*e*f*g^2*j^2 + ((-4)) *a^2*b^2*f*g^3*j^2 + ((-4)) *c^2*d^2*f*g^3*j^2 + ((-4)) *e^3*f*g^4*j^2 + ((-4)) *e*f^3*g^4*j^2 + (4) *e^2*f*g^5*j^2 + (4) *f^3*g^5*j^2 + (4) *a^2*b^2*e*f*h^2*j^2 + (4) *c^2*d^2*e*f*h^2*j^2 + ((-4)) *a^2*b^2*f*g*h^2*j^2 + ((-4)) *c^2*d^2*f*g*h^2*j^2 + ((-8)) *e^3*f*g^2*h^2*j^2 + ((-8)) *e*f^3*g^2*h^2*j^2 + (8) *e^2*f*g^3*h^2*j^2 + (8) *f^3*g^3*h^2*j^2 + ((-4)) *e^3*f*h^4*j^2 + ((-4)) *e*f^3*h^4*j^2 + (4) *e^2*f*g*h^4*j^2 + (4) *f^3*g*h^4*j^2 + (2) *a^2*b^2*f*g^2*i*j^2 + (2) *c^2*d^2*f*g^2*i*j^2 + (6) *e^2*f*g^4*i*j^2 + ((-6)) *f^3*g^4*i*j^2 + ((-8)) *e*f*g^5*i*j^2 + ((-2)) *a^2*b^2*g^2*h*i*j^2 + ((-2)) *c^2*d^2*g^2*h*i*j^2 + (2) *e^2*g^4*h*i*j^2 + (6) *f^2*g^4*h*i*j^2 + (2) *a^2*b^2*f*h^2*i*j^2 + (2) *c^2*d^2*f*h^2*i*j^2 + (12) *e^2*f*g^2*h^2*i*j^2 + ((-12)) *f^3*g^2*h^2*i*j^2 + ((-16)) *e*f*g^3*h^2*i*j^2 + ((-2)) *a^2*b^2*h^3*i*j^2 + ((-2)) *c^2*d^2*h^3*i*j^2 + (4) *e^2*g^2*h^3*i*j^2 + (12) *f^2*g^2*h^3*i*j^2 + (6) *e^2*f*h^4*i*j^2 + ((-6)) *f^3*h^4*i*j^2 + ((-8)) *e*f*g*h^4*i*j^2 + (2) *e^2*h^5*i*j^2 + (6) *f^2*h^5*i*j^2 + (4) *f*g^5*i^2*j^2 + ((-4)) *e*g^4*h*i^2*j^2 + (8) *f*g^3*h^2*i^2*j^2 + ((-8)) *e*g^2*h^3*i^2*j^2 + (4) *f*g*h^4*i^2*j^2 + ((-4)) *e*h^5*i^2*j^2 + ((-2)) *f*g^4*i^3*j^2 + (2) *g^4*h*i^3*j^2 + ((-4)) *f*g^2*h^2*i^3*j^2 + (4) *g^2*h^3*i^3*j^2 + ((-2)) *f*h^4*i^3*j^2 + (2) *h^5*i^3*j^2 + ((-2)) *a^2*b^2*e*g^2*j^3 + ((-2)) *c^2*d^2*e*g^2*j^3 + (2) *a^2*b^2*g^3*j^3 + (2) *c^2*d^2*g^3*j^3 + (2) *e^3*g^4*j^3 + (6) *e*f^2*g^4*j^3 + ((-2)) *e^2*g^5*j^3 + ((-6)) *f^2*g^5*j^3 + ((-2)) *a^2*b^2*e*h^2*j^3 + ((-2)) *c^2*d^2*e*h^2*j^3 + (2) *a^2*b^2*g*h^2*j^3 + (2) *c^2*d^2*g*h^2*j^3 + (4) *e^3*g^2*h^2*j^3 + (12) *e*f^2*g^2*h^2*j^3 + ((-4)) *e^2*g^3*h^2*j^3 + ((-12)) *f^2*g^3*h^2*j^3 + (2) *e^3*h^4*j^3 + (6) *e*f^2*h^4*j^3 + ((-2)) *e^2*g*h^4*j^3 + ((-6)) *f^2*g*h^4*j^3 + ((-4)) *e^2*g^4*i*j^3 + (4) *f^2*g^4*i*j^3 + (4) *e*g^5*i*j^3 + ((-4)) *f*g^4*h*i*j^3 + ((-8)) *e^2*g^2*h^2*i*j^3 + (8) *f^2*g^2*h^2*i*j^3 + (8) *e*g^3*h^2*i*j^3 + ((-8)) *f*g^2*h^3*i*j^3 + ((-4)) *e^2*h^4*i*j^3 + (4) *f^2*h^4*i*j^3 + (4) *e*g*h^4*i*j^3 + ((-4)) *f*h^5*i*j^3 + (2) *e*g^4*i^2*j^3 + ((-2)) *g^5*i^2*j^3 + (4) *e*g^2*h^2*i^2*j^3 + ((-4)) *g^3*h^2*i^2*j^3 + (2) *e*h^4*i^2*j^3 + ((-2)) *g*h^4*i^2*j^3 + ((-4)) *e*f*g^4*j^4 + (4) *f*g^5*j^4 + ((-8)) *e*f*g^2*h^2*j^4 + (8) *f*g^3*h^2*j^4 + ((-4)) *e*f*h^4*j^4 + (4) *f*g*h^4*j^4 + ((-1)) *f*g^4*i*j^4 + (1) *g^4*h*i*j^4 + ((-2)) *f*g^2*h^2*i*j^4 + (2) *g^2*h^3*i*j^4 + ((-1)) *f*h^4*i*j^4 + (1) *h^5*i*j^4 + (1) *e*g^4*j^5 + ((-1)) *g^5*j^5 + (2) *e*g^2*h^2*j^5 + ((-2)) *g^3*h^2*j^5 + (1) *e*h^4*j^5 + ((-1)) *g*h^4*j^5 + (1) *a^4*b^4*f*l + ((-2)) *a^2*b^2*c^2*d^2*f*l + (1) *c^4*d^4*f*l + ((-2)) *a^2*b^2*e^2*f*g^2*l + ((-2)) *c^2*d^2*e^2*f*g^2*l + ((-2)) *a^2*b^2*f^3*g^2*l + ((-2)) *c^2*d^2*f^3*g^2*l + (1) *e^4*f*g^4*l + (2) *e^2*f^3*g^4*l + (1) *f^5*g^4*l + ((-1)) *a^4*b^4*h*l + (2) *a^2*b^2*c^2*d^2*h*l + ((-1)) *c^4*d^4*h*l + (2) *a^2*b^2*e^2*g^2*h*l + (2) *c^2*d^2*e^2*g^2*h*l + (2) *a^2*b^2*f^2*g^2*h*l + (2) *c^2*d^2*f^2*g^2*h*l + ((-1)) *e^4*g^4*h*l + ((-2)) *e^2*f^2*g^4*h*l + ((-1)) *f^4*g^4*h*l + ((-2)) *a^2*b^2*e^2*f*h^2*l + ((-2)) *c^2*d^2*e^2*f*h^2*l + ((-2)) *a^2*b^2*f^3*h^2*l + ((-2)) *c^2*d^2*f^3*h^2*l + (2) *e^4*f*g^2*h^2*l + (4) *e^2*f^3*g^2*h^2*l + (2) *f^5*g^2*h^2*l + (2) *a^2*b^2*e^2*h^3*l + (2) *c^2*d^2*e^2*h^3*l + (2) *a^2*b^2*f^2*h^3*l + (2) *c^2*d^2*f^2*h^3*l + ((-2)) *e^4*g^2*h^3*l + ((-4)) *e^2*f^2*g^2*h^3*l + ((-2)) *f^4*g^2*h^3*l + (1) *e^4*f*h^4*l + (2) *e^2*f^3*h^4*l + (1) *f^5*h^4*l + ((-1)) *e^4*h^5*l + ((-2)) *e^2*f^2*h^5*l + ((-1)) *f^4*h^5*l + ((-4)) *a^2*b^2*e^2*f*g*i*l + ((-4)) *c^2*d^2*e^2*f*g*i*l + ((-4)) *a^2*b^2*f^3*g*i*l + ((-4)) *c^2*d^2*f^3*g*i*l + (4) *a^2*b^2*e*f*g^2*i*l + (4) *c^2*d^2*e*f*g^2*i*l + (4) *e^4*f*g^3*i*l + (8) *e^2*f^3*g^3*i*l + (4) *f^5*g^3*i*l + ((-4)) *e^3*f*g^4*i*l + ((-4)) 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*c^2*d^2*e*g*h*i*l^2 + (6) *e^4*g^2*h*i*l^2 + (12) *e^2*f^2*g^2*h*i*l^2 + (6) *f^4*g^2*h*i*l^2 + ((-16)) *e^3*g^3*h*i*l^2 + ((-16)) *e*f^2*g^3*h*i*l^2 + ((-2)) *e^4*f*h^2*i*l^2 + ((-4)) *e^2*f^3*h^2*i*l^2 + ((-2)) *f^5*h^2*i*l^2 + (16) *e^3*f*g*h^2*i*l^2 + (16) *e*f^3*g*h^2*i*l^2 + (2) *e^4*h^3*i*l^2 + (4) *e^2*f^2*h^3*i*l^2 + (2) *f^4*h^3*i*l^2 + ((-16)) *e^3*g*h^3*i*l^2 + ((-16)) *e*f^2*g*h^3*i*l^2 + ((-4)) *a^2*b^2*e*f*i^2*l^2 + ((-4)) *c^2*d^2*e*f*i^2*l^2 + (4) *a^2*b^2*f*g*i^2*l^2 + (4) *c^2*d^2*f*g*i^2*l^2 + (24) *e^3*f*g^2*i^2*l^2 + (24) *e*f^3*g^2*i^2*l^2 + ((-24)) *e^2*f*g^3*i^2*l^2 + ((-8)) *f^3*g^3*i^2*l^2 + (4) *a^2*b^2*e*h*i^2*l^2 + (4) *c^2*d^2*e*h*i^2*l^2 + ((-4)) *a^2*b^2*g*h*i^2*l^2 + ((-4)) *c^2*d^2*g*h*i^2*l^2 + ((-24)) *e^3*g^2*h*i^2*l^2 + ((-24)) *e*f^2*g^2*h*i^2*l^2 + (24) *e^2*g^3*h*i^2*l^2 + (8) *f^2*g^3*h*i^2*l^2 + (8) *e^3*f*h^2*i^2*l^2 + (8) *e*f^3*h^2*i^2*l^2 + ((-24)) *e^2*f*g*h^2*i^2*l^2 + ((-8)) *f^3*g*h^2*i^2*l^2 + ((-8)) *e^3*h^3*i^2*l^2 + ((-8)) *e*f^2*h^3*i^2*l^2 + (24) *e^2*g*h^3*i^2*l^2 + (8) *f^2*g*h^3*i^2*l^2 + (2) *a^2*b^2*f*i^3*l^2 + (2) *c^2*d^2*f*i^3*l^2 + ((-36)) *e^2*f*g^2*i^3*l^2 + ((-12)) *f^3*g^2*i^3*l^2 + (16) *e*f*g^3*i^3*l^2 + ((-2)) *a^2*b^2*h*i^3*l^2 + ((-2)) *c^2*d^2*h*i^3*l^2 + (36) *e^2*g^2*h*i^3*l^2 + (12) *f^2*g^2*h*i^3*l^2 + ((-16)) *e*g^3*h*i^3*l^2 + ((-12)) *e^2*f*h^2*i^3*l^2 + ((-4)) *f^3*h^2*i^3*l^2 + (16) *e*f*g*h^2*i^3*l^2 + (12) *e^2*h^3*i^3*l^2 + (4) *f^2*h^3*i^3*l^2 + ((-16)) *e*g*h^3*i^3*l^2 + (24) *e*f*g^2*i^4*l^2 + ((-4)) *f*g^3*i^4*l^2 + ((-24)) *e*g^2*h*i^4*l^2 + (4) *g^3*h*i^4*l^2 + (8) *e*f*h^2*i^4*l^2 + ((-4)) *f*g*h^2*i^4*l^2 + ((-8)) *e*h^3*i^4*l^2 + (4) *g*h^3*i^4*l^2 + ((-6)) *f*g^2*i^5*l^2 + (6) *g^2*h*i^5*l^2 + ((-2)) *f*h^2*i^5*l^2 + (2) *h^3*i^5*l^2 + ((-2)) *a^2*b^2*e^3*j*l^2 + ((-2)) *c^2*d^2*e^3*j*l^2 + ((-2)) *a^2*b^2*e*f^2*j*l^2 + ((-2)) *c^2*d^2*e*f^2*j*l^2 + (2) *a^2*b^2*e^2*g*j*l^2 + (2) *c^2*d^2*e^2*g*j*l^2 + ((-6)) *a^2*b^2*f^2*g*j*l^2 + ((-6)) *c^2*d^2*f^2*g*j*l^2 + (6) *e^5*g^2*j*l^2 + (12) *e^3*f^2*g^2*j*l^2 + (6) *e*f^4*g^2*j*l^2 + ((-6)) *e^4*g^3*j*l^2 + (4) *e^2*f^2*g^3*j*l^2 + (10) *f^4*g^3*j*l^2 + (8) *a^2*b^2*f*g*h*j*l^2 + (8) *c^2*d^2*f*g*h*j*l^2 + ((-16)) *e^2*f*g^3*h*j*l^2 + ((-16)) *f^3*g^3*h*j*l^2 + (2) *e^5*h^2*j*l^2 + (4) *e^3*f^2*h^2*j*l^2 + (2) *e*f^4*h^2*j*l^2 + ((-2)) *e^4*g*h^2*j*l^2 + (12) *e^2*f^2*g*h^2*j*l^2 + (14) *f^4*g*h^2*j*l^2 + ((-16)) *e^2*f*g*h^3*j*l^2 + ((-16)) *f^3*g*h^3*j*l^2 + (4) *a^2*b^2*e^2*i*j*l^2 + (4) *c^2*d^2*e^2*i*j*l^2 + ((-4)) *a^2*b^2*f^2*i*j*l^2 + ((-4)) *c^2*d^2*f^2*i*j*l^2 + ((-4)) *a^2*b^2*e*g*i*j*l^2 + ((-4)) *c^2*d^2*e*g*i*j*l^2 + ((-24)) *e^4*g^2*i*j*l^2 + (24) *f^4*g^2*i*j*l^2 + (24) *e^3*g^3*i*j*l^2 + ((-8)) *e*f^2*g^3*i*j*l^2 + (4) *a^2*b^2*f*h*i*j*l^2 + (4) *c^2*d^2*f*h*i*j*l^2 + ((-24)) *e^2*f*g^2*h*i*j*l^2 + ((-24)) *f^3*g^2*h*i*j*l^2 + (32) *e*f*g^3*h*i*j*l^2 + ((-8)) *e^4*h^2*i*j*l^2 + (8) *f^4*h^2*i*j*l^2 + (8) *e^3*g*h^2*i*j*l^2 + ((-24)) *e*f^2*g*h^2*i*j*l^2 + ((-8)) *e^2*f*h^3*i*j*l^2 + ((-8)) *f^3*h^3*i*j*l^2 + (32) *e*f*g*h^3*i*j*l^2 + ((-2)) *a^2*b^2*e*i^2*j*l^2 + ((-2)) *c^2*d^2*e*i^2*j*l^2 + (2) *a^2*b^2*g*i^2*j*l^2 + (2) *c^2*d^2*g*i^2*j*l^2 + (36) *e^3*g^2*i^2*j*l^2 + ((-36)) *e*f^2*g^2*i^2*j*l^2 + ((-36)) *e^2*g^3*i^2*j*l^2 + (4) *f^2*g^3*i^2*j*l^2 + (48) *e*f*g^2*h*i^2*j*l^2 + ((-16)) *f*g^3*h*i^2*j*l^2 + (12) *e^3*h^2*i^2*j*l^2 + ((-12)) *e*f^2*h^2*i^2*j*l^2 + ((-12)) *e^2*g*h^2*i^2*j*l^2 + (12) *f^2*g*h^2*i^2*j*l^2 + (16) *e*f*h^3*i^2*j*l^2 + ((-16)) *f*g*h^3*i^2*j*l^2 + ((-24)) *e^2*g^2*i^3*j*l^2 + (24) *f^2*g^2*i^3*j*l^2 + (24) *e*g^3*i^3*j*l^2 + ((-24)) *f*g^2*h*i^3*j*l^2 + ((-8)) *e^2*h^2*i^3*j*l^2 + (8) *f^2*h^2*i^3*j*l^2 + (8) *e*g*h^2*i^3*j*l^2 + ((-8)) *f*h^3*i^3*j*l^2 + (6) *e*g^2*i^4*j*l^2 + ((-6)) *g^3*i^4*j*l^2 + (2) *e*h^2*i^4*j*l^2 + ((-2)) *g*h^2*i^4*j*l^2 + (4) *a^2*b^2*e*f*j^2*l^2 + (4) *c^2*d^2*e*f*j^2*l^2 + ((-24)) *e^3*f*g^2*j^2*l^2 + ((-24)) *e*f^3*g^2*j^2*l^2 + (16) *e^2*f*g^3*j^2*l^2 + ((-4)) *a^2*b^2*g*h*j^2*l^2 + ((-4)) *c^2*d^2*g*h*j^2*l^2 + (8) *e^2*g^3*h*j^2*l^2 + (24) *f^2*g^3*h*j^2*l^2 + ((-8)) *e^3*f*h^2*j^2*l^2 + ((-8)) *e*f^3*h^2*j^2*l^2 + ((-16)) *f^3*g*h^2*j^2*l^2 + (8) *e^2*g*h^3*j^2*l^2 + (24) *f^2*g*h^3*j^2*l^2 + (2) *a^2*b^2*f*i*j^2*l^2 + (2) *c^2*d^2*f*i*j^2*l^2 + (36) *e^2*f*g^2*i*j^2*l^2 + ((-36)) *f^3*g^2*i*j^2*l^2 + ((-32)) *e*f*g^3*i*j^2*l^2 + ((-2)) *a^2*b^2*h*i*j^2*l^2 + ((-2)) *c^2*d^2*h*i*j^2*l^2 + (12) *e^2*g^2*h*i*j^2*l^2 + (36) *f^2*g^2*h*i*j^2*l^2 + ((-16)) *e*g^3*h*i*j^2*l^2 + (12) *e^2*f*h^2*i*j^2*l^2 + ((-12)) *f^3*h^2*i*j^2*l^2 + (4) *e^2*h^3*i*j^2*l^2 + (12) *f^2*h^3*i*j^2*l^2 + ((-16)) *e*g*h^3*i*j^2*l^2 + (16) *f*g^3*i^2*j^2*l^2 + ((-24)) *e*g^2*h*i^2*j^2*l^2 + (8) *g^3*h*i^2*j^2*l^2 + ((-8)) *e*h^3*i^2*j^2*l^2 + (8) *g*h^3*i^2*j^2*l^2 + ((-12)) *f*g^2*i^3*j^2*l^2 + (12) *g^2*h*i^3*j^2*l^2 + ((-4)) *f*h^2*i^3*j^2*l^2 + (4) *h^3*i^3*j^2*l^2 + ((-2)) *a^2*b^2*e*j^3*l^2 + ((-2)) *c^2*d^2*e*j^3*l^2 + (2) *a^2*b^2*g*j^3*l^2 + (2) *c^2*d^2*g*j^3*l^2 + (12) *e^3*g^2*j^3*l^2 + (36) *e*f^2*g^2*j^3*l^2 + ((-12)) *e^2*g^3*j^3*l^2 + ((-20)) *f^2*g^3*j^3*l^2 + ((-16)) *f*g^3*h*j^3*l^2 + (4) *e^3*h^2*j^3*l^2 + (12) *e*f^2*h^2*j^3*l^2 + ((-4)) *e^2*g*h^2*j^3*l^2 + (4) *f^2*g*h^2*j^3*l^2 + ((-16)) *f*g*h^3*j^3*l^2 + ((-24)) *e^2*g^2*i*j^3*l^2 + (24) *f^2*g^2*i*j^3*l^2 + (24) *e*g^3*i*j^3*l^2 + ((-24)) *f*g^2*h*i*j^3*l^2 + ((-8)) *e^2*h^2*i*j^3*l^2 + (8) *f^2*h^2*i*j^3*l^2 + (8) *e*g*h^2*i*j^3*l^2 + ((-8)) *f*h^3*i*j^3*l^2 + (12) *e*g^2*i^2*j^3*l^2 + ((-12)) *g^3*i^2*j^3*l^2 + (4) *e*h^2*i^2*j^3*l^2 + ((-4)) *g*h^2*i^2*j^3*l^2 + ((-24)) *e*f*g^2*j^4*l^2 + (20) *f*g^3*j^4*l^2 + (4) *g^3*h*j^4*l^2 + ((-8)) *e*f*h^2*j^4*l^2 + (4) *f*g*h^2*j^4*l^2 + (4) *g*h^3*j^4*l^2 + ((-6)) *f*g^2*i*j^4*l^2 + (6) *g^2*h*i*j^4*l^2 + ((-2)) *f*h^2*i*j^4*l^2 + (2) *h^3*i*j^4*l^2 + (6) *e*g^2*j^5*l^2 + ((-6)) *g^3*j^5*l^2 + (2) *e*h^2*j^5*l^2 + ((-2)) *g*h^2*j^5*l^2 + ((-2)) *a^2*b^2*e^2*f*l^3 + ((-2)) *c^2*d^2*e^2*f*l^3 + ((-2)) *a^2*b^2*f^3*l^3 + ((-2)) 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(2) *a^2*b^2*h*i^2*l^3 + (2) *c^2*d^2*h*i^2*l^3 + (16) *e^3*g*h*i^2*l^3 + (16) *e*f^2*g*h*i^2*l^3 + ((-36)) *e^2*g^2*h*i^2*l^3 + ((-12)) *f^2*g^2*h*i^2*l^3 + (12) *e^2*f*h^2*i^2*l^3 + (4) *f^3*h^2*i^2*l^3 + ((-12)) *e^2*h^3*i^2*l^3 + ((-4)) *f^2*h^3*i^2*l^3 + (24) *e^2*f*g*i^3*l^3 + (8) *f^3*g*i^3*l^3 + ((-24)) *e*f*g^2*i^3*l^3 + ((-24)) *e^2*g*h*i^3*l^3 + ((-8)) *f^2*g*h*i^3*l^3 + (24) *e*g^2*h*i^3*l^3 + ((-8)) *e*f*h^2*i^3*l^3 + (8) *e*h^3*i^3*l^3 + ((-16)) *e*f*g*i^4*l^3 + (6) *f*g^2*i^4*l^3 + (16) *e*g*h*i^4*l^3 + ((-6)) *g^2*h*i^4*l^3 + (2) *f*h^2*i^4*l^3 + ((-2)) *h^3*i^4*l^3 + (4) *f*g*i^5*l^3 + ((-4)) *g*h*i^5*l^3 + (4) *a^2*b^2*f^2*j*l^3 + (4) *c^2*d^2*f^2*j*l^3 + ((-4)) *e^5*g*j*l^3 + ((-8)) *e^3*f^2*g*j*l^3 + ((-4)) *e*f^4*g*j*l^3 + (4) *e^4*g^2*j*l^3 + ((-16)) *e^2*f^2*g^2*j*l^3 + ((-20)) *f^4*g^2*j*l^3 + ((-4)) *a^2*b^2*f*h*j*l^3 + ((-4)) *c^2*d^2*f*h*j*l^3 + (24) *e^2*f*g^2*h*j*l^3 + (24) *f^3*g^2*h*j*l^3 + ((-8)) *e^2*f^2*h^2*j*l^3 + ((-8)) *f^4*h^2*j*l^3 + (8) 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*f*h^2*i^5*n^2 + (6) *h^3*i^5*n^2 + ((-2)) *a^2*b^2*e^3*j*n^2 + ((-2)) *c^2*d^2*e^3*j*n^2 + ((-2)) *a^2*b^2*e*f^2*j*n^2 + ((-2)) *c^2*d^2*e*f^2*j*n^2 + (2) *a^2*b^2*e^2*g*j*n^2 + (2) *c^2*d^2*e^2*g*j*n^2 + (2) *a^2*b^2*f^2*g*j*n^2 + (2) *c^2*d^2*f^2*g*j*n^2 + (2) *e^5*g^2*j*n^2 + (4) *e^3*f^2*g^2*j*n^2 + (2) *e*f^4*g^2*j*n^2 + ((-2)) *e^4*g^3*j*n^2 + ((-4)) *e^2*f^2*g^3*j*n^2 + ((-2)) *f^4*g^3*j*n^2 + (8) *a^2*b^2*e*f*h*j*n^2 + (8) *c^2*d^2*e*f*h*j*n^2 + ((-8)) *a^2*b^2*f*g*h*j*n^2 + ((-8)) *c^2*d^2*f*g*h*j*n^2 + ((-16)) *e^3*f*g^2*h*j*n^2 + ((-16)) *e*f^3*g^2*h*j*n^2 + (16) *e^2*f*g^3*h*j*n^2 + (16) *f^3*g^3*h*j*n^2 + (6) *e^5*h^2*j*n^2 + (12) *e^3*f^2*h^2*j*n^2 + (6) *e*f^4*h^2*j*n^2 + ((-6)) *e^4*g*h^2*j*n^2 + ((-12)) *e^2*f^2*g*h^2*j*n^2 + ((-6)) *f^4*g*h^2*j*n^2 + ((-16)) *e^3*f*h^3*j*n^2 + ((-16)) *e*f^3*h^3*j*n^2 + (16) *e^2*f*g*h^3*j*n^2 + (16) *f^3*g*h^3*j*n^2 + (4) *a^2*b^2*e^2*i*j*n^2 + (4) *c^2*d^2*e^2*i*j*n^2 + ((-4)) *a^2*b^2*f^2*i*j*n^2 + ((-4)) *c^2*d^2*f^2*i*j*n^2 + ((-4)) *a^2*b^2*e*g*i*j*n^2 + ((-4)) *c^2*d^2*e*g*i*j*n^2 + ((-8)) *e^4*g^2*i*j*n^2 + (8) *f^4*g^2*i*j*n^2 + (8) *e^3*g^3*i*j*n^2 + (8) *e*f^2*g^3*i*j*n^2 + (4) *a^2*b^2*f*h*i*j*n^2 + (4) *c^2*d^2*f*h*i*j*n^2 + (24) *e^2*f*g^2*h*i*j*n^2 + ((-8)) *f^3*g^2*h*i*j*n^2 + ((-32)) *e*f*g^3*h*i*j*n^2 + ((-24)) *e^4*h^2*i*j*n^2 + (24) *f^4*h^2*i*j*n^2 + (24) *e^3*g*h^2*i*j*n^2 + (24) *e*f^2*g*h^2*i*j*n^2 + (8) *e^2*f*h^3*i*j*n^2 + ((-24)) *f^3*h^3*i*j*n^2 + ((-32)) *e*f*g*h^3*i*j*n^2 + ((-2)) *a^2*b^2*e*i^2*j*n^2 + ((-2)) *c^2*d^2*e*i^2*j*n^2 + (2) *a^2*b^2*g*i^2*j*n^2 + (2) *c^2*d^2*g*i^2*j*n^2 + (12) *e^3*g^2*i^2*j*n^2 + ((-12)) *e*f^2*g^2*i^2*j*n^2 + ((-12)) *e^2*g^3*i^2*j*n^2 + ((-4)) *f^2*g^3*i^2*j*n^2 + (16) *f*g^3*h*i^2*j*n^2 + (36) *e^3*h^2*i^2*j*n^2 + ((-36)) *e*f^2*h^2*i^2*j*n^2 + ((-36)) *e^2*g*h^2*i^2*j*n^2 + ((-12)) *f^2*g*h^2*i^2*j*n^2 + (32) *e*f*h^3*i^2*j*n^2 + (16) *f*g*h^3*i^2*j*n^2 + ((-8)) *e^2*g^2*i^3*j*n^2 + (8) *f^2*g^2*i^3*j*n^2 + (8) *e*g^3*i^3*j*n^2 + ((-8)) *f*g^2*h*i^3*j*n^2 + ((-24)) *e^2*h^2*i^3*j*n^2 + (24) *f^2*h^2*i^3*j*n^2 + (24) *e*g*h^2*i^3*j*n^2 + ((-24)) *f*h^3*i^3*j*n^2 + (2) *e*g^2*i^4*j*n^2 + ((-2)) *g^3*i^4*j*n^2 + (6) *e*h^2*i^4*j*n^2 + ((-6)) *g*h^2*i^4*j*n^2 + (4) *a^2*b^2*e*f*j^2*n^2 + (4) *c^2*d^2*e*f*j^2*n^2 + ((-4)) *a^2*b^2*f*g*j^2*n^2 + ((-4)) *c^2*d^2*f*g*j^2*n^2 + ((-8)) *e^3*f*g^2*j^2*n^2 + ((-8)) *e*f^3*g^2*j^2*n^2 + (8) *e^2*f*g^3*j^2*n^2 + (8) *f^3*g^3*j^2*n^2 + ((-4)) *a^2*b^2*e*h*j^2*n^2 + ((-4)) *c^2*d^2*e*h*j^2*n^2 + (4) *a^2*b^2*g*h*j^2*n^2 + (4) *c^2*d^2*g*h*j^2*n^2 + (8) *e^3*g^2*h*j^2*n^2 + (24) *e*f^2*g^2*h*j^2*n^2 + ((-8)) *e^2*g^3*h*j^2*n^2 + ((-24)) *f^2*g^3*h*j^2*n^2 + ((-24)) *e^3*f*h^2*j^2*n^2 + ((-24)) *e*f^3*h^2*j^2*n^2 + (24) *e^2*f*g*h^2*j^2*n^2 + (24) *f^3*g*h^2*j^2*n^2 + (8) *e^3*h^3*j^2*n^2 + (24) *e*f^2*h^3*j^2*n^2 + ((-8)) *e^2*g*h^3*j^2*n^2 + ((-24)) *f^2*g*h^3*j^2*n^2 + (2) *a^2*b^2*f*i*j^2*n^2 + (2) *c^2*d^2*f*i*j^2*n^2 + (12) *e^2*f*g^2*i*j^2*n^2 + ((-12)) *f^3*g^2*i*j^2*n^2 + ((-16)) *e*f*g^3*i*j^2*n^2 + ((-2)) *a^2*b^2*h*i*j^2*n^2 + ((-2)) *c^2*d^2*h*i*j^2*n^2 + ((-12)) *e^2*g^2*h*i*j^2*n^2 + (12) *f^2*g^2*h*i*j^2*n^2 + (16) *e*g^3*h*i*j^2*n^2 + (36) *e^2*f*h^2*i*j^2*n^2 + ((-36)) *f^3*h^2*i*j^2*n^2 + ((-48)) *e*f*g*h^2*i*j^2*n^2 + ((-4)) *e^2*h^3*i*j^2*n^2 + (36) *f^2*h^3*i*j^2*n^2 + (16) *e*g*h^3*i*j^2*n^2 + (8) *f*g^3*i^2*j^2*n^2 + ((-8)) *g^3*h*i^2*j^2*n^2 + (24) *f*g*h^2*i^2*j^2*n^2 + ((-16)) *e*h^3*i^2*j^2*n^2 + ((-8)) *g*h^3*i^2*j^2*n^2 + ((-4)) *f*g^2*i^3*j^2*n^2 + (4) *g^2*h*i^3*j^2*n^2 + ((-12)) *f*h^2*i^3*j^2*n^2 + (12) *h^3*i^3*j^2*n^2 + ((-2)) *a^2*b^2*e*j^3*n^2 + ((-2)) *c^2*d^2*e*j^3*n^2 + (2) *a^2*b^2*g*j^3*n^2 + (2) *c^2*d^2*g*j^3*n^2 + (4) *e^3*g^2*j^3*n^2 + (12) *e*f^2*g^2*j^3*n^2 + ((-4)) *e^2*g^3*j^3*n^2 + ((-12)) *f^2*g^3*j^3*n^2 + ((-16)) *e*f*g^2*h*j^3*n^2 + (16) *f*g^3*h*j^3*n^2 + (12) *e^3*h^2*j^3*n^2 + (36) *e*f^2*h^2*j^3*n^2 + ((-12)) *e^2*g*h^2*j^3*n^2 + ((-36)) *f^2*g*h^2*j^3*n^2 + ((-16)) *e*f*h^3*j^3*n^2 + (16) 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*f*h^2*j^4*l*n^2 + ((-6)) *h^3*j^4*l*n^2 + (4) *f*g*i*j^4*l*n^2 + ((-4)) *g*h*i*j^4*l*n^2 + ((-4)) *e*g*j^5*l*n^2 + (4) *g^2*j^5*l*n^2 + ((-4)) *e^4*f*g*l^2*n^2 + ((-8)) *e^2*f^3*g*l^2*n^2 + ((-4)) *f^5*g*l^2*n^2 + (4) *e^5*h*l^2*n^2 + (8) *e^3*f^2*h*l^2*n^2 + (4) *e*f^4*h*l^2*n^2 + ((-2)) *e^4*f*i*l^2*n^2 + ((-4)) *e^2*f^3*i*l^2*n^2 + ((-2)) *f^5*i*l^2*n^2 + (16) *e^3*f*g*i*l^2*n^2 + (16) *e*f^3*g*i*l^2*n^2 + ((-14)) *e^4*h*i*l^2*n^2 + ((-12)) *e^2*f^2*h*i*l^2*n^2 + (2) *f^4*h*i*l^2*n^2 + (8) *e^3*f*i^2*l^2*n^2 + (8) *e*f^3*i^2*l^2*n^2 + ((-24)) *e^2*f*g*i^2*l^2*n^2 + ((-8)) *f^3*g*i^2*l^2*n^2 + (16) *e^3*h*i^2*l^2*n^2 + ((-12)) *e^2*f*i^3*l^2*n^2 + ((-4)) *f^3*i^3*l^2*n^2 + (16) *e*f*g*i^3*l^2*n^2 + ((-4)) *e^2*h*i^3*l^2*n^2 + (4) *f^2*h*i^3*l^2*n^2 + (8) *e*f*i^4*l^2*n^2 + ((-4)) *f*g*i^4*l^2*n^2 + ((-4)) *e*h*i^4*l^2*n^2 + ((-2)) *f*i^5*l^2*n^2 + (2) *h*i^5*l^2*n^2 + (2) *e^5*j*l^2*n^2 + (4) *e^3*f^2*j*l^2*n^2 + (2) *e*f^4*j*l^2*n^2 + ((-2)) *e^4*g*j*l^2*n^2 + (12) 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*e*f*g*j^3*l*n^3 + (16) *f*g^2*j^3*l*n^3 + (16) *f^2*h*j^3*l*n^3 + ((-16)) *f*h^2*j^3*l*n^3 + (4) *e*g*j^4*l*n^3 + ((-4)) *g^2*j^4*l*n^3 + ((-4)) *f*h*j^4*l*n^3 + (4) *h^2*j^4*l*n^3 + ((-2)) *e^5*l^2*n^3 + ((-4)) *e^3*f^2*l^2*n^3 + ((-2)) *e*f^4*l^2*n^3 + (2) *e^4*g*l^2*n^3 + (4) *e^2*f^2*g*l^2*n^3 + (2) *f^4*g*l^2*n^3 + (8) *e^4*i*l^2*n^3 + (8) *e^2*f^2*i*l^2*n^3 + ((-8)) *e^3*g*i*l^2*n^3 + ((-8)) *e*f^2*g*i*l^2*n^3 + ((-12)) *e^3*i^2*l^2*n^3 + ((-4)) *e*f^2*i^2*l^2*n^3 + (12) *e^2*g*i^2*l^2*n^3 + (4) *f^2*g*i^2*l^2*n^3 + (8) *e^2*i^3*l^2*n^3 + ((-8)) *e*g*i^3*l^2*n^3 + ((-2)) *e*i^4*l^2*n^3 + (2) *g*i^4*l^2*n^3 + (8) *e^3*f*j*l^2*n^3 + (8) *e*f^3*j*l^2*n^3 + ((-8)) *e^2*f*g*j*l^2*n^3 + ((-8)) *f^3*g*j*l^2*n^3 + ((-16)) *e^2*f*i*j*l^2*n^3 + (16) *e*f*g*i*j*l^2*n^3 + (8) *e*f*i^2*j*l^2*n^3 + ((-8)) *f*g*i^2*j*l^2*n^3 + ((-4)) *e^3*j^2*l^2*n^3 + ((-12)) *e*f^2*j^2*l^2*n^3 + (4) *e^2*g*j^2*l^2*n^3 + (12) *f^2*g*j^2*l^2*n^3 + (8) *e^2*i*j^2*l^2*n^3 + ((-8)) *e*g*i*j^2*l^2*n^3 + ((-4)) *e*i^2*j^2*l^2*n^3 + (4) *g*i^2*j^2*l^2*n^3 + (8) *e*f*j^3*l^2*n^3 + ((-8)) *f*g*j^3*l^2*n^3 + ((-2)) *e*j^4*l^2*n^3 + (2) *g*j^4*l^2*n^3 + (4) *e^5*h*n^4 + (8) *e^3*f^2*h*n^4 + (4) *e*f^4*h*n^4 + ((-4)) *e^4*g*h*n^4 + ((-8)) *e^2*f^2*g*h*n^4 + ((-4)) *f^4*g*h*n^4 + ((-1)) *e^4*f*i*n^4 + ((-2)) *e^2*f^3*i*n^4 + ((-1)) *f^5*i*n^4 + ((-15)) *e^4*h*i*n^4 + ((-14)) *e^2*f^2*h*i*n^4 + (1) *f^4*h*i*n^4 + (16) *e^3*g*h*i*n^4 + (16) *e*f^2*g*h*i*n^4 + (4) *e^3*f*i^2*n^4 + (4) *e*f^3*i^2*n^4 + (20) *e^3*h*i^2*n^4 + (4) *e*f^2*h*i^2*n^4 + ((-24)) *e^2*g*h*i^2*n^4 + ((-8)) *f^2*g*h*i^2*n^4 + ((-6)) *e^2*f*i^3*n^4 + ((-2)) *f^3*i^3*n^4 + ((-10)) *e^2*h*i^3*n^4 + (2) *f^2*h*i^3*n^4 + (16) *e*g*h*i^3*n^4 + (4) *e*f*i^4*n^4 + ((-4)) *g*h*i^4*n^4 + ((-1)) *f*i^5*n^4 + (1) *h*i^5*n^4 + (1) *e^5*j*n^4 + (2) *e^3*f^2*j*n^4 + (1) *e*f^4*j*n^4 + ((-1)) *e^4*g*j*n^4 + ((-2)) *e^2*f^2*g*j*n^4 + ((-1)) *f^4*g*j*n^4 + ((-16)) *e^3*f*h*j*n^4 + ((-16)) *e*f^3*h*j*n^4 + (16) *e^2*f*g*h*j*n^4 + (16) *f^3*g*h*j*n^4 + ((-4)) *e^4*i*j*n^4 + (4) *f^4*i*j*n^4 + (4) *e^3*g*i*j*n^4 + (4) *e*f^2*g*i*j*n^4 + (28) *e^2*f*h*i*j*n^4 + ((-4)) *f^3*h*i*j*n^4 + ((-32)) *e*f*g*h*i*j*n^4 + (6) *e^3*i^2*j*n^4 + ((-6)) *e*f^2*i^2*j*n^4 + ((-6)) *e^2*g*i^2*j*n^4 + ((-2)) *f^2*g*i^2*j*n^4 + ((-8)) *e*f*h*i^2*j*n^4 + (16) *f*g*h*i^2*j*n^4 + ((-4)) *e^2*i^3*j*n^4 + (4) *f^2*i^3*j*n^4 + (4) *e*g*i^3*j*n^4 + ((-4)) *f*h*i^3*j*n^4 + (1) *e*i^4*j*n^4 + ((-1)) *g*i^4*j*n^4 + ((-4)) *e^3*f*j^2*n^4 + ((-4)) *e*f^3*j^2*n^4 + (4) *e^2*f*g*j^2*n^4 + (4) *f^3*g*j^2*n^4 + (8) *e^3*h*j^2*n^4 + (24) *e*f^2*h*j^2*n^4 + ((-8)) *e^2*g*h*j^2*n^4 + ((-24)) *f^2*g*h*j^2*n^4 + (6) *e^2*f*i*j^2*n^4 + ((-6)) *f^3*i*j^2*n^4 + ((-8)) *e*f*g*i*j^2*n^4 + ((-14)) *e^2*h*i*j^2*n^4 + (6) *f^2*h*i*j^2*n^4 + (16) *e*g*h*i*j^2*n^4 + (4) *f*g*i^2*j^2*n^4 + (4) *e*h*i^2*j^2*n^4 + ((-8)) *g*h*i^2*j^2*n^4 + ((-2)) *f*i^3*j^2*n^4 + (2) *h*i^3*j^2*n^4 + (2) *e^3*j^3*n^4 + (6) *e*f^2*j^3*n^4 + ((-2)) *e^2*g*j^3*n^4 + ((-6)) *f^2*g*j^3*n^4 + ((-16)) *e*f*h*j^3*n^4 + (16) *f*g*h*j^3*n^4 + ((-4)) *e^2*i*j^3*n^4 + (4) *f^2*i*j^3*n^4 + (4) *e*g*i*j^3*n^4 + ((-4)) *f*h*i*j^3*n^4 + (2) *e*i^2*j^3*n^4 + ((-2)) *g*i^2*j^3*n^4 + ((-4)) *e*f*j^4*n^4 + (4) *f*g*j^4*n^4 + (4) *e*h*j^4*n^4 + ((-4)) *g*h*j^4*n^4 + ((-1)) *f*i*j^4*n^4 + (1) *h*i*j^4*n^4 + (1) *e*j^5*n^4 + ((-1)) *g*j^5*n^4 + (1) *e^4*f*l*n^4 + (2) *e^2*f^3*l*n^4 + (1) *f^5*l*n^4 + ((-1)) *e^4*h*l*n^4 + ((-2)) *e^2*f^2*h*l*n^4 + ((-1)) *f^4*h*l*n^4 + ((-4)) *e^3*f*i*l*n^4 + ((-4)) *e*f^3*i*l*n^4 + (4) *e^3*h*i*l*n^4 + (4) *e*f^2*h*i*l*n^4 + (6) *e^2*f*i^2*l*n^4 + (2) *f^3*i^2*l*n^4 + ((-6)) *e^2*h*i^2*l*n^4 + ((-2)) *f^2*h*i^2*l*n^4 + ((-4)) *e*f*i^3*l*n^4 + (4) *e*h*i^3*l*n^4 + (1) *f*i^4*l*n^4 + ((-1)) *h*i^4*l*n^4 + ((-4)) *e^2*f^2*j*l*n^4 + ((-4)) *f^4*j*l*n^4 + (4) *e^2*f*h*j*l*n^4 + (4) *f^3*h*j*l*n^4 + (8) *e*f^2*i*j*l*n^4 + ((-8)) *e*f*h*i*j*l*n^4 + ((-4)) *f^2*i^2*j*l*n^4 + (4) *f*h*i^2*j*l*n^4 + (2) *e^2*f*j^2*l*n^4 + (6) *f^3*j^2*l*n^4 + ((-2)) *e^2*h*j^2*l*n^4 + ((-6)) *f^2*h*j^2*l*n^4 + ((-4)) *e*f*i*j^2*l*n^4 + (4) *e*h*i*j^2*l*n^4 + (2) *f*i^2*j^2*l*n^4 + ((-2)) *h*i^2*j^2*l*n^4 + ((-4)) *f^2*j^3*l*n^4 + (4) *f*h*j^3*l*n^4 + (1) *f*j^4*l*n^4 + ((-1)) *h*j^4*l*n^4 + ((-1)) *e^5*n^5 + ((-2)) *e^3*f^2*n^5 + ((-1)) *e*f^4*n^5 + (1) *e^4*g*n^5 + (2) *e^2*f^2*g*n^5 + (1) *f^4*g*n^5 + (4) *e^4*i*n^5 + (4) *e^2*f^2*i*n^5 + ((-4)) *e^3*g*i*n^5 + ((-4)) *e*f^2*g*i*n^5 + ((-6)) *e^3*i^2*n^5 + ((-2)) *e*f^2*i^2*n^5 + (6) *e^2*g*i^2*n^5 + (2) *f^2*g*i^2*n^5 + (4) *e^2*i^3*n^5 + ((-4)) *e*g*i^3*n^5 + ((-1)) *e*i^4*n^5 + (1) *g*i^4*n^5 + (4) *e^3*f*j*n^5 + (4) *e*f^3*j*n^5 + ((-4)) *e^2*f*g*j*n^5 + ((-4)) *f^3*g*j*n^5 + ((-8)) *e^2*f*i*j*n^5 + (8) *e*f*g*i*j*n^5 + (4) *e*f*i^2*j*n^5 + ((-4)) *f*g*i^2*j*n^5 + ((-2)) *e^3*j^2*n^5 + ((-6)) *e*f^2*j^2*n^5 + (2) *e^2*g*j^2*n^5 + (6) *f^2*g*j^2*n^5 + (4) *e^2*i*j^2*n^5 + ((-4)) *e*g*i*j^2*n^5 + ((-2)) *e*i^2*j^2*n^5 + (2) *g*i^2*j^2*n^5 + (4) *e*f*j^3*n^5 + ((-4)) *f*g*j^3*n^5 + ((-1)) *e*j^4*n^5 + (1) *g*j^4*n^5
F:= [
((-1)) *i^2 + ((-1)) *j^2 + (2) *i*k + ((-2)) *k*l + (1) *l^2 + (2) *j*m + ((-2)) *m*n + (1) *n^2 ;
((-1)) *g^2 + ((-1)) *h^2 + (2) *g*k + ((-2)) *k*l + (1) *l^2 + (2) *h*m + ((-2)) *m*n + (1) *n^2 ;
((-1)) *e^2 + ((-1)) *f^2 + (2) *e*k + ((-2)) *k*l + (1) *l^2 + (2) *f*m + ((-2)) *m*n + (1) *n^2 ;
(1) *d^2 + ((-1)) *i^2 + ((-1)) *j^2 + (2) *i*l + ((-1)) *l^2 + (2) *j*n + ((-1)) *n^2 ;
(1) *c^2 + ((-1)) *e^2 + ((-1)) *f^2 + (2) *e*g + ((-1)) *g^2 + (2) *f*h + ((-1)) *h^2 ;
(1) *b^2 + ((-1)) *e^2 + ((-1)) *f^2 + (2) *e*l + ((-1)) *l^2 + (2) *f*n + ((-1)) *n^2 ;
(1) *a^2 + ((-1)) *g^2 + ((-1)) *h^2 + (2) *g*i + ((-1)) *i^2 + (2) *h*j + ((-1)) *j^2 ;
];
Certificate
calcul avec sugar
p:= ((-1)) *a^4*b^4*f*i + (2) *a^2*b^2*c^2*d^2*f*i + ((-1)) *c^4*d^4*f*i + (2) *a^2*b^2*e^2*f*g^2*i + (2) *c^2*d^2*e^2*f*g^2*i + (2) *a^2*b^2*f^3*g^2*i + (2) *c^2*d^2*f^3*g^2*i + ((-1)) *e^4*f*g^4*i + ((-2)) *e^2*f^3*g^4*i + ((-1)) *f^5*g^4*i + (1) *a^4*b^4*h*i + ((-2)) *a^2*b^2*c^2*d^2*h*i + (1) *c^4*d^4*h*i + ((-2)) *a^2*b^2*e^2*g^2*h*i + ((-2)) *c^2*d^2*e^2*g^2*h*i + ((-2)) *a^2*b^2*f^2*g^2*h*i + ((-2)) *c^2*d^2*f^2*g^2*h*i + (1) *e^4*g^4*h*i + (2) *e^2*f^2*g^4*h*i + (1) *f^4*g^4*h*i + (2) *a^2*b^2*e^2*f*h^2*i + (2) *c^2*d^2*e^2*f*h^2*i + (2) *a^2*b^2*f^3*h^2*i + (2) *c^2*d^2*f^3*h^2*i + ((-2)) *e^4*f*g^2*h^2*i + ((-4)) *e^2*f^3*g^2*h^2*i + ((-2)) *f^5*g^2*h^2*i + ((-2)) *a^2*b^2*e^2*h^3*i + ((-2)) *c^2*d^2*e^2*h^3*i + ((-2)) *a^2*b^2*f^2*h^3*i + ((-2)) *c^2*d^2*f^2*h^3*i + (2) *e^4*g^2*h^3*i + (4) *e^2*f^2*g^2*h^3*i + (2) *f^4*g^2*h^3*i + ((-1)) *e^4*f*h^4*i + ((-2)) *e^2*f^3*h^4*i + ((-1)) *f^5*h^4*i + (1) *e^4*h^5*i + (2) *e^2*f^2*h^5*i + (1) *f^4*h^5*i + ((-4)) *a^2*b^2*e*f*g^2*i^2 + ((-4)) *c^2*d^2*e*f*g^2*i^2 + (4) *e^3*f*g^4*i^2 + (4) *e*f^3*g^4*i^2 + (4) *a^2*b^2*e*g^2*h*i^2 + (4) *c^2*d^2*e*g^2*h*i^2 + ((-4)) *e^3*g^4*h*i^2 + ((-4)) *e*f^2*g^4*h*i^2 + ((-4)) *a^2*b^2*e*f*h^2*i^2 + ((-4)) *c^2*d^2*e*f*h^2*i^2 + (8) *e^3*f*g^2*h^2*i^2 + (8) *e*f^3*g^2*h^2*i^2 + (4) *a^2*b^2*e*h^3*i^2 + (4) *c^2*d^2*e*h^3*i^2 + ((-8)) *e^3*g^2*h^3*i^2 + ((-8)) *e*f^2*g^2*h^3*i^2 + (4) *e^3*f*h^4*i^2 + (4) *e*f^3*h^4*i^2 + ((-4)) *e^3*h^5*i^2 + ((-4)) *e*f^2*h^5*i^2 + (2) *a^2*b^2*f*g^2*i^3 + (2) *c^2*d^2*f*g^2*i^3 + ((-6)) *e^2*f*g^4*i^3 + ((-2)) *f^3*g^4*i^3 + ((-2)) *a^2*b^2*g^2*h*i^3 + ((-2)) *c^2*d^2*g^2*h*i^3 + (6) *e^2*g^4*h*i^3 + (2) *f^2*g^4*h*i^3 + (2) *a^2*b^2*f*h^2*i^3 + (2) *c^2*d^2*f*h^2*i^3 + ((-12)) *e^2*f*g^2*h^2*i^3 + ((-4)) *f^3*g^2*h^2*i^3 + ((-2)) *a^2*b^2*h^3*i^3 + ((-2)) *c^2*d^2*h^3*i^3 + (12) *e^2*g^2*h^3*i^3 + (4) *f^2*g^2*h^3*i^3 + ((-6)) *e^2*f*h^4*i^3 + ((-2)) *f^3*h^4*i^3 + (6) *e^2*h^5*i^3 + (2) *f^2*h^5*i^3 + (4) *e*f*g^4*i^4 + ((-4)) *e*g^4*h*i^4 + (8) *e*f*g^2*h^2*i^4 + ((-8)) *e*g^2*h^3*i^4 + (4) *e*f*h^4*i^4 + ((-4)) *e*h^5*i^4 + ((-1)) *f*g^4*i^5 + (1) *g^4*h*i^5 + ((-2)) *f*g^2*h^2*i^5 + (2) *g^2*h^3*i^5 + ((-1)) *f*h^4*i^5 + (1) *h^5*i^5 + (1) *a^4*b^4*e*j + ((-2)) *a^2*b^2*c^2*d^2*e*j + (1) *c^4*d^4*e*j + ((-1)) *a^4*b^4*g*j + (2) *a^2*b^2*c^2*d^2*g*j + ((-1)) *c^4*d^4*g*j + ((-2)) *a^2*b^2*e^3*g^2*j + ((-2)) *c^2*d^2*e^3*g^2*j + ((-2)) *a^2*b^2*e*f^2*g^2*j + ((-2)) *c^2*d^2*e*f^2*g^2*j + (2) *a^2*b^2*e^2*g^3*j + (2) *c^2*d^2*e^2*g^3*j + (2) *a^2*b^2*f^2*g^3*j + (2) *c^2*d^2*f^2*g^3*j + (1) *e^5*g^4*j + (2) *e^3*f^2*g^4*j + (1) *e*f^4*g^4*j + ((-1)) *e^4*g^5*j + ((-2)) *e^2*f^2*g^5*j + ((-1)) *f^4*g^5*j + ((-2)) *a^2*b^2*e^3*h^2*j + ((-2)) *c^2*d^2*e^3*h^2*j + ((-2)) *a^2*b^2*e*f^2*h^2*j + ((-2)) *c^2*d^2*e*f^2*h^2*j + (2) *a^2*b^2*e^2*g*h^2*j + (2) *c^2*d^2*e^2*g*h^2*j + (2) *a^2*b^2*f^2*g*h^2*j + (2) *c^2*d^2*f^2*g*h^2*j + (2) *e^5*g^2*h^2*j + (4) *e^3*f^2*g^2*h^2*j + (2) *e*f^4*g^2*h^2*j + ((-2)) *e^4*g^3*h^2*j + ((-4)) *e^2*f^2*g^3*h^2*j + ((-2)) *f^4*g^3*h^2*j + (1) *e^5*h^4*j + (2) *e^3*f^2*h^4*j + (1) *e*f^4*h^4*j + ((-1)) *e^4*g*h^4*j + ((-2)) *e^2*f^2*g*h^4*j + ((-1)) *f^4*g*h^4*j + (4) *a^2*b^2*e^2*g^2*i*j + (4) *c^2*d^2*e^2*g^2*i*j + ((-4)) *a^2*b^2*f^2*g^2*i*j + ((-4)) *c^2*d^2*f^2*g^2*i*j + ((-4)) *a^2*b^2*e*g^3*i*j + ((-4)) *c^2*d^2*e*g^3*i*j + ((-4)) *e^4*g^4*i*j + (4) *f^4*g^4*i*j + (4) *e^3*g^5*i*j + (4) *e*f^2*g^5*i*j + (4) *a^2*b^2*f*g^2*h*i*j + (4) *c^2*d^2*f*g^2*h*i*j + ((-4)) *e^2*f*g^4*h*i*j + ((-4)) *f^3*g^4*h*i*j + (4) *a^2*b^2*e^2*h^2*i*j + (4) *c^2*d^2*e^2*h^2*i*j + ((-4)) *a^2*b^2*f^2*h^2*i*j + ((-4)) *c^2*d^2*f^2*h^2*i*j + ((-4)) *a^2*b^2*e*g*h^2*i*j + ((-4)) *c^2*d^2*e*g*h^2*i*j + ((-8)) *e^4*g^2*h^2*i*j + (8) *f^4*g^2*h^2*i*j + (8) *e^3*g^3*h^2*i*j + (8) *e*f^2*g^3*h^2*i*j + (4) *a^2*b^2*f*h^3*i*j + (4) *c^2*d^2*f*h^3*i*j + ((-8)) *e^2*f*g^2*h^3*i*j + ((-8)) *f^3*g^2*h^3*i*j + ((-4)) *e^4*h^4*i*j + (4) *f^4*h^4*i*j + (4) *e^3*g*h^4*i*j + (4) 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(6) *e^5*g^2*j*l^2 + (12) *e^3*f^2*g^2*j*l^2 + (6) *e*f^4*g^2*j*l^2 + ((-6)) *e^4*g^3*j*l^2 + (4) *e^2*f^2*g^3*j*l^2 + (10) *f^4*g^3*j*l^2 + (8) *a^2*b^2*f*g*h*j*l^2 + (8) *c^2*d^2*f*g*h*j*l^2 + ((-16)) *e^2*f*g^3*h*j*l^2 + ((-16)) *f^3*g^3*h*j*l^2 + (2) *e^5*h^2*j*l^2 + (4) *e^3*f^2*h^2*j*l^2 + (2) *e*f^4*h^2*j*l^2 + ((-2)) *e^4*g*h^2*j*l^2 + (12) *e^2*f^2*g*h^2*j*l^2 + (14) *f^4*g*h^2*j*l^2 + ((-16)) *e^2*f*g*h^3*j*l^2 + ((-16)) *f^3*g*h^3*j*l^2 + (4) *a^2*b^2*e^2*i*j*l^2 + (4) *c^2*d^2*e^2*i*j*l^2 + ((-4)) *a^2*b^2*f^2*i*j*l^2 + ((-4)) *c^2*d^2*f^2*i*j*l^2 + ((-4)) *a^2*b^2*e*g*i*j*l^2 + ((-4)) *c^2*d^2*e*g*i*j*l^2 + ((-24)) *e^4*g^2*i*j*l^2 + (24) *f^4*g^2*i*j*l^2 + (24) *e^3*g^3*i*j*l^2 + ((-8)) *e*f^2*g^3*i*j*l^2 + (4) *a^2*b^2*f*h*i*j*l^2 + (4) *c^2*d^2*f*h*i*j*l^2 + ((-24)) *e^2*f*g^2*h*i*j*l^2 + ((-24)) *f^3*g^2*h*i*j*l^2 + (32) *e*f*g^3*h*i*j*l^2 + ((-8)) *e^4*h^2*i*j*l^2 + (8) *f^4*h^2*i*j*l^2 + (8) *e^3*g*h^2*i*j*l^2 + ((-24)) *e*f^2*g*h^2*i*j*l^2 + ((-8)) 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+ ((-4)) *c^2*d^2*g*h*j^2*l^2 + (8) *e^2*g^3*h*j^2*l^2 + (24) *f^2*g^3*h*j^2*l^2 + ((-8)) *e^3*f*h^2*j^2*l^2 + ((-8)) *e*f^3*h^2*j^2*l^2 + ((-16)) *f^3*g*h^2*j^2*l^2 + (8) *e^2*g*h^3*j^2*l^2 + (24) *f^2*g*h^3*j^2*l^2 + (2) *a^2*b^2*f*i*j^2*l^2 + (2) *c^2*d^2*f*i*j^2*l^2 + (36) *e^2*f*g^2*i*j^2*l^2 + ((-36)) *f^3*g^2*i*j^2*l^2 + ((-32)) *e*f*g^3*i*j^2*l^2 + ((-2)) *a^2*b^2*h*i*j^2*l^2 + ((-2)) *c^2*d^2*h*i*j^2*l^2 + (12) *e^2*g^2*h*i*j^2*l^2 + (36) *f^2*g^2*h*i*j^2*l^2 + ((-16)) *e*g^3*h*i*j^2*l^2 + (12) *e^2*f*h^2*i*j^2*l^2 + ((-12)) *f^3*h^2*i*j^2*l^2 + (4) *e^2*h^3*i*j^2*l^2 + (12) *f^2*h^3*i*j^2*l^2 + ((-16)) *e*g*h^3*i*j^2*l^2 + (16) *f*g^3*i^2*j^2*l^2 + ((-24)) *e*g^2*h*i^2*j^2*l^2 + (8) *g^3*h*i^2*j^2*l^2 + ((-8)) *e*h^3*i^2*j^2*l^2 + (8) *g*h^3*i^2*j^2*l^2 + ((-12)) *f*g^2*i^3*j^2*l^2 + (12) *g^2*h*i^3*j^2*l^2 + ((-4)) *f*h^2*i^3*j^2*l^2 + (4) *h^3*i^3*j^2*l^2 + ((-2)) *a^2*b^2*e*j^3*l^2 + ((-2)) *c^2*d^2*e*j^3*l^2 + (2) *a^2*b^2*g*j^3*l^2 + (2) *c^2*d^2*g*j^3*l^2 + (12) 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*c^2*d^2*f^3*l^3 + (6) *e^4*f*g^2*l^3 + (12) *e^2*f^3*g^2*l^3 + (6) *f^5*g^2*l^3 + (2) *a^2*b^2*e^2*h*l^3 + (2) *c^2*d^2*e^2*h*l^3 + (2) *a^2*b^2*f^2*h*l^3 + (2) *c^2*d^2*f^2*h*l^3 + ((-6)) *e^4*g^2*h*l^3 + ((-12)) *e^2*f^2*g^2*h*l^3 + ((-6)) *f^4*g^2*h*l^3 + (2) *e^4*f*h^2*l^3 + (4) *e^2*f^3*h^2*l^3 + (2) *f^5*h^2*l^3 + ((-2)) *e^4*h^3*l^3 + ((-4)) *e^2*f^2*h^3*l^3 + ((-2)) *f^4*h^3*l^3 + (4) *a^2*b^2*e*f*i*l^3 + (4) *c^2*d^2*e*f*i*l^3 + (4) *e^4*f*g*i*l^3 + (8) *e^2*f^3*g*i*l^3 + (4) *f^5*g*i*l^3 + ((-24)) *e^3*f*g^2*i*l^3 + ((-24)) *e*f^3*g^2*i*l^3 + ((-4)) *a^2*b^2*e*h*i*l^3 + ((-4)) *c^2*d^2*e*h*i*l^3 + ((-4)) *e^4*g*h*i*l^3 + ((-8)) *e^2*f^2*g*h*i*l^3 + ((-4)) *f^4*g*h*i*l^3 + (24) *e^3*g^2*h*i*l^3 + (24) *e*f^2*g^2*h*i*l^3 + ((-8)) *e^3*f*h^2*i*l^3 + ((-8)) *e*f^3*h^2*i*l^3 + (8) *e^3*h^3*i*l^3 + (8) *e*f^2*h^3*i*l^3 + ((-2)) *a^2*b^2*f*i^2*l^3 + ((-2)) *c^2*d^2*f*i^2*l^3 + ((-16)) *e^3*f*g*i^2*l^3 + ((-16)) *e*f^3*g*i^2*l^3 + (36) *e^2*f*g^2*i^2*l^3 + (12) *f^3*g^2*i^2*l^3 + (2) *a^2*b^2*h*i^2*l^3 + (2) *c^2*d^2*h*i^2*l^3 + (16) *e^3*g*h*i^2*l^3 + (16) *e*f^2*g*h*i^2*l^3 + ((-36)) *e^2*g^2*h*i^2*l^3 + ((-12)) *f^2*g^2*h*i^2*l^3 + (12) *e^2*f*h^2*i^2*l^3 + (4) *f^3*h^2*i^2*l^3 + ((-12)) *e^2*h^3*i^2*l^3 + ((-4)) *f^2*h^3*i^2*l^3 + (24) *e^2*f*g*i^3*l^3 + (8) *f^3*g*i^3*l^3 + ((-24)) *e*f*g^2*i^3*l^3 + ((-24)) *e^2*g*h*i^3*l^3 + ((-8)) *f^2*g*h*i^3*l^3 + (24) *e*g^2*h*i^3*l^3 + ((-8)) *e*f*h^2*i^3*l^3 + (8) *e*h^3*i^3*l^3 + ((-16)) *e*f*g*i^4*l^3 + (6) *f*g^2*i^4*l^3 + (16) *e*g*h*i^4*l^3 + ((-6)) *g^2*h*i^4*l^3 + (2) *f*h^2*i^4*l^3 + ((-2)) *h^3*i^4*l^3 + (4) *f*g*i^5*l^3 + ((-4)) *g*h*i^5*l^3 + (4) *a^2*b^2*f^2*j*l^3 + (4) *c^2*d^2*f^2*j*l^3 + ((-4)) *e^5*g*j*l^3 + ((-8)) *e^3*f^2*g*j*l^3 + ((-4)) *e*f^4*g*j*l^3 + (4) *e^4*g^2*j*l^3 + ((-16)) *e^2*f^2*g^2*j*l^3 + ((-20)) *f^4*g^2*j*l^3 + ((-4)) *a^2*b^2*f*h*j*l^3 + ((-4)) *c^2*d^2*f*h*j*l^3 + (24) *e^2*f*g^2*h*j*l^3 + (24) *f^3*g^2*h*j*l^3 + ((-8)) *e^2*f^2*h^2*j*l^3 + ((-8)) *f^4*h^2*j*l^3 + (8) *e^2*f*h^3*j*l^3 + (8) *f^3*h^3*j*l^3 + (16) *e^4*g*i*j*l^3 + ((-16)) *f^4*g*i*j*l^3 + ((-16)) *e^3*g^2*i*j*l^3 + (32) *e*f^2*g^2*i*j*l^3 + (16) *e^2*f*g*h*i*j*l^3 + (16) *f^3*g*h*i*j*l^3 + ((-48)) *e*f*g^2*h*i*j*l^3 + (16) *e*f^2*h^2*i*j*l^3 + ((-16)) *e*f*h^3*i*j*l^3 + ((-24)) *e^3*g*i^2*j*l^3 + (24) *e*f^2*g*i^2*j*l^3 + (24) *e^2*g^2*i^2*j*l^3 + ((-16)) *f^2*g^2*i^2*j*l^3 + ((-32)) *e*f*g*h*i^2*j*l^3 + (24) *f*g^2*h*i^2*j*l^3 + ((-8)) *f^2*h^2*i^2*j*l^3 + (8) *f*h^3*i^2*j*l^3 + (16) *e^2*g*i^3*j*l^3 + ((-16)) *f^2*g*i^3*j*l^3 + ((-16)) *e*g^2*i^3*j*l^3 + (16) *f*g*h*i^3*j*l^3 + ((-4)) *e*g*i^4*j*l^3 + (4) *g^2*i^4*j*l^3 + ((-2)) *a^2*b^2*f*j^2*l^3 + ((-2)) *c^2*d^2*f*j^2*l^3 + (16) *e^3*f*g*j^2*l^3 + (16) *e*f^3*g*j^2*l^3 + ((-4)) *e^2*f*g^2*j^2*l^3 + (20) *f^3*g^2*j^2*l^3 + (2) *a^2*b^2*h*j^2*l^3 + (2) *c^2*d^2*h*j^2*l^3 + ((-12)) *e^2*g^2*h*j^2*l^3 + ((-36)) *f^2*g^2*h*j^2*l^3 + (4) *e^2*f*h^2*j^2*l^3 + (12) *f^3*h^2*j^2*l^3 + ((-4)) *e^2*h^3*j^2*l^3 + ((-12)) *f^2*h^3*j^2*l^3 + 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*f*g^2*h*i^3*j*n^2 + ((-24)) *e^2*h^2*i^3*j*n^2 + (24) *f^2*h^2*i^3*j*n^2 + (24) *e*g*h^2*i^3*j*n^2 + ((-24)) *f*h^3*i^3*j*n^2 + (2) *e*g^2*i^4*j*n^2 + ((-2)) *g^3*i^4*j*n^2 + (6) *e*h^2*i^4*j*n^2 + ((-6)) *g*h^2*i^4*j*n^2 + (4) *a^2*b^2*e*f*j^2*n^2 + (4) *c^2*d^2*e*f*j^2*n^2 + ((-4)) *a^2*b^2*f*g*j^2*n^2 + ((-4)) *c^2*d^2*f*g*j^2*n^2 + ((-8)) *e^3*f*g^2*j^2*n^2 + ((-8)) *e*f^3*g^2*j^2*n^2 + (8) *e^2*f*g^3*j^2*n^2 + (8) *f^3*g^3*j^2*n^2 + ((-4)) *a^2*b^2*e*h*j^2*n^2 + ((-4)) *c^2*d^2*e*h*j^2*n^2 + (4) *a^2*b^2*g*h*j^2*n^2 + (4) *c^2*d^2*g*h*j^2*n^2 + (8) *e^3*g^2*h*j^2*n^2 + (24) *e*f^2*g^2*h*j^2*n^2 + ((-8)) *e^2*g^3*h*j^2*n^2 + ((-24)) *f^2*g^3*h*j^2*n^2 + ((-24)) *e^3*f*h^2*j^2*n^2 + ((-24)) *e*f^3*h^2*j^2*n^2 + (24) *e^2*f*g*h^2*j^2*n^2 + (24) *f^3*g*h^2*j^2*n^2 + (8) *e^3*h^3*j^2*n^2 + (24) *e*f^2*h^3*j^2*n^2 + ((-8)) *e^2*g*h^3*j^2*n^2 + ((-24)) *f^2*g*h^3*j^2*n^2 + (2) *a^2*b^2*f*i*j^2*n^2 + (2) *c^2*d^2*f*i*j^2*n^2 + (12) *e^2*f*g^2*i*j^2*n^2 + ((-12)) *f^3*g^2*i*j^2*n^2 + ((-16)) *e*f*g^3*i*j^2*n^2 + ((-2)) *a^2*b^2*h*i*j^2*n^2 + ((-2)) *c^2*d^2*h*i*j^2*n^2 + ((-12)) *e^2*g^2*h*i*j^2*n^2 + (12) *f^2*g^2*h*i*j^2*n^2 + (16) *e*g^3*h*i*j^2*n^2 + (36) *e^2*f*h^2*i*j^2*n^2 + ((-36)) *f^3*h^2*i*j^2*n^2 + ((-48)) *e*f*g*h^2*i*j^2*n^2 + ((-4)) *e^2*h^3*i*j^2*n^2 + (36) *f^2*h^3*i*j^2*n^2 + (16) *e*g*h^3*i*j^2*n^2 + (8) *f*g^3*i^2*j^2*n^2 + ((-8)) *g^3*h*i^2*j^2*n^2 + (24) *f*g*h^2*i^2*j^2*n^2 + ((-16)) *e*h^3*i^2*j^2*n^2 + ((-8)) *g*h^3*i^2*j^2*n^2 + ((-4)) *f*g^2*i^3*j^2*n^2 + (4) *g^2*h*i^3*j^2*n^2 + ((-12)) *f*h^2*i^3*j^2*n^2 + (12) *h^3*i^3*j^2*n^2 + ((-2)) *a^2*b^2*e*j^3*n^2 + ((-2)) *c^2*d^2*e*j^3*n^2 + (2) *a^2*b^2*g*j^3*n^2 + (2) *c^2*d^2*g*j^3*n^2 + (4) *e^3*g^2*j^3*n^2 + (12) *e*f^2*g^2*j^3*n^2 + ((-4)) *e^2*g^3*j^3*n^2 + ((-12)) *f^2*g^3*j^3*n^2 + ((-16)) *e*f*g^2*h*j^3*n^2 + (16) *f*g^3*h*j^3*n^2 + (12) *e^3*h^2*j^3*n^2 + (36) *e*f^2*h^2*j^3*n^2 + ((-12)) *e^2*g*h^2*j^3*n^2 + ((-36)) *f^2*g*h^2*j^3*n^2 + ((-16)) *e*f*h^3*j^3*n^2 + (16) *f*g*h^3*j^3*n^2 + ((-8)) *e^2*g^2*i*j^3*n^2 + (8) *f^2*g^2*i*j^3*n^2 + (8) *e*g^3*i*j^3*n^2 + ((-8)) *f*g^2*h*i*j^3*n^2 + ((-24)) *e^2*h^2*i*j^3*n^2 + (24) *f^2*h^2*i*j^3*n^2 + (24) *e*g*h^2*i*j^3*n^2 + ((-24)) *f*h^3*i*j^3*n^2 + (4) *e*g^2*i^2*j^3*n^2 + ((-4)) *g^3*i^2*j^3*n^2 + (12) *e*h^2*i^2*j^3*n^2 + ((-12)) *g*h^2*i^2*j^3*n^2 + ((-8)) *e*f*g^2*j^4*n^2 + (8) *f*g^3*j^4*n^2 + (4) *e*g^2*h*j^4*n^2 + ((-4)) *g^3*h*j^4*n^2 + ((-24)) *e*f*h^2*j^4*n^2 + (24) *f*g*h^2*j^4*n^2 + (4) *e*h^3*j^4*n^2 + ((-4)) *g*h^3*j^4*n^2 + ((-2)) *f*g^2*i*j^4*n^2 + (2) *g^2*h*i*j^4*n^2 + ((-6)) *f*h^2*i*j^4*n^2 + (6) *h^3*i*j^4*n^2 + (2) *e*g^2*j^5*n^2 + ((-2)) *g^3*j^5*n^2 + (6) *e*h^2*j^5*n^2 + ((-6)) *g*h^2*j^5*n^2 + ((-2)) *a^2*b^2*e^2*f*l*n^2 + ((-2)) *c^2*d^2*e^2*f*l*n^2 + ((-2)) *a^2*b^2*f^3*l*n^2 + ((-2)) *c^2*d^2*f^3*l*n^2 + (2) *e^4*f*g^2*l*n^2 + (4) *e^2*f^3*g^2*l*n^2 + (2) *f^5*g^2*l*n^2 + (2) *a^2*b^2*e^2*h*l*n^2 + (2) *c^2*d^2*e^2*h*l*n^2 + (2) *a^2*b^2*f^2*h*l*n^2 + (2) 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+ (8) *f^2*i*j^3*l^2*n^2 + (8) *e*g*i*j^3*l^2*n^2 + ((-8)) *f*h*i*j^3*l^2*n^2 + (4) *e*i^2*j^3*l^2*n^2 + ((-4)) *g*i^2*j^3*l^2*n^2 + ((-8)) *e*f*j^4*l^2*n^2 + (4) *f*g*j^4*l^2*n^2 + (4) *e*h*j^4*l^2*n^2 + ((-2)) *f*i*j^4*l^2*n^2 + (2) *h*i*j^4*l^2*n^2 + (2) *e*j^5*l^2*n^2 + ((-2)) *g*j^5*l^2*n^2 + (2) *e^4*f*l^3*n^2 + (4) *e^2*f^3*l^3*n^2 + (2) *f^5*l^3*n^2 + ((-2)) *e^4*h*l^3*n^2 + ((-4)) *e^2*f^2*h*l^3*n^2 + ((-2)) *f^4*h*l^3*n^2 + ((-8)) *e^3*f*i*l^3*n^2 + ((-8)) *e*f^3*i*l^3*n^2 + (8) *e^3*h*i*l^3*n^2 + (8) *e*f^2*h*i*l^3*n^2 + (12) *e^2*f*i^2*l^3*n^2 + (4) *f^3*i^2*l^3*n^2 + ((-12)) *e^2*h*i^2*l^3*n^2 + ((-4)) *f^2*h*i^2*l^3*n^2 + ((-8)) *e*f*i^3*l^3*n^2 + (8) *e*h*i^3*l^3*n^2 + (2) *f*i^4*l^3*n^2 + ((-2)) *h*i^4*l^3*n^2 + ((-8)) *e^2*f^2*j*l^3*n^2 + ((-8)) *f^4*j*l^3*n^2 + (8) *e^2*f*h*j*l^3*n^2 + (8) *f^3*h*j*l^3*n^2 + (16) *e*f^2*i*j*l^3*n^2 + ((-16)) *e*f*h*i*j*l^3*n^2 + ((-8)) *f^2*i^2*j*l^3*n^2 + (8) *f*h*i^2*j*l^3*n^2 + (4) *e^2*f*j^2*l^3*n^2 + (12) *f^3*j^2*l^3*n^2 + ((-4)) *e^2*h*j^2*l^3*n^2 + ((-12)) *f^2*h*j^2*l^3*n^2 + ((-8)) *e*f*i*j^2*l^3*n^2 + (8) *e*h*i*j^2*l^3*n^2 + (4) *f*i^2*j^2*l^3*n^2 + ((-4)) *h*i^2*j^2*l^3*n^2 + ((-8)) *f^2*j^3*l^3*n^2 + (8) *f*h*j^3*l^3*n^2 + (2) *f*j^4*l^3*n^2 + ((-2)) *h*j^4*l^3*n^2 + (2) *a^2*b^2*e^3*n^3 + (2) *c^2*d^2*e^3*n^3 + (2) *a^2*b^2*e*f^2*n^3 + (2) *c^2*d^2*e*f^2*n^3 + ((-2)) *a^2*b^2*e^2*g*n^3 + ((-2)) *c^2*d^2*e^2*g*n^3 + ((-2)) *a^2*b^2*f^2*g*n^3 + ((-2)) *c^2*d^2*f^2*g*n^3 + ((-2)) *e^5*g^2*n^3 + ((-4)) *e^3*f^2*g^2*n^3 + ((-2)) *e*f^4*g^2*n^3 + (2) *e^4*g^3*n^3 + (4) *e^2*f^2*g^3*n^3 + (2) *f^4*g^3*n^3 + ((-6)) *e^5*h^2*n^3 + ((-12)) *e^3*f^2*h^2*n^3 + ((-6)) *e*f^4*h^2*n^3 + (6) *e^4*g*h^2*n^3 + (12) *e^2*f^2*g*h^2*n^3 + (6) *f^4*g*h^2*n^3 + ((-4)) *a^2*b^2*e^2*i*n^3 + ((-4)) *c^2*d^2*e^2*i*n^3 + (4) *a^2*b^2*e*g*i*n^3 + (4) *c^2*d^2*e*g*i*n^3 + (8) *e^4*g^2*i*n^3 + (8) *e^2*f^2*g^2*i*n^3 + ((-8)) *e^3*g^3*i*n^3 + ((-8)) *e*f^2*g^3*i*n^3 + (4) *e^4*f*h*i*n^3 + (8) *e^2*f^3*h*i*n^3 + (4) *f^5*h*i*n^3 + (20) *e^4*h^2*i*n^3 + (16) *e^2*f^2*h^2*i*n^3 + ((-4)) *f^4*h^2*i*n^3 + ((-24)) *e^3*g*h^2*i*n^3 + ((-24)) *e*f^2*g*h^2*i*n^3 + (2) *a^2*b^2*e*i^2*n^3 + (2) *c^2*d^2*e*i^2*n^3 + ((-2)) *a^2*b^2*g*i^2*n^3 + ((-2)) *c^2*d^2*g*i^2*n^3 + ((-12)) *e^3*g^2*i^2*n^3 + ((-4)) *e*f^2*g^2*i^2*n^3 + (12) *e^2*g^3*i^2*n^3 + (4) *f^2*g^3*i^2*n^3 + ((-16)) *e^3*f*h*i^2*n^3 + ((-16)) *e*f^3*h*i^2*n^3 + ((-20)) *e^3*h^2*i^2*n^3 + (4) *e*f^2*h^2*i^2*n^3 + (36) *e^2*g*h^2*i^2*n^3 + (12) *f^2*g*h^2*i^2*n^3 + (8) *e^2*g^2*i^3*n^3 + ((-8)) *e*g^3*i^3*n^3 + (24) *e^2*f*h*i^3*n^3 + (8) *f^3*h*i^3*n^3 + ((-8)) *f^2*h^2*i^3*n^3 + ((-24)) *e*g*h^2*i^3*n^3 + ((-2)) *e*g^2*i^4*n^3 + (2) *g^3*i^4*n^3 + ((-16)) *e*f*h*i^4*n^3 + (10) *e*h^2*i^4*n^3 + (6) *g*h^2*i^4*n^3 + (4) *f*h*i^5*n^3 + ((-4)) *h^2*i^5*n^3 + ((-4)) *a^2*b^2*e*f*j*n^3 + ((-4)) *c^2*d^2*e*f*j*n^3 + (4) *a^2*b^2*f*g*j*n^3 + (4) *c^2*d^2*f*g*j*n^3 + (8) *e^3*f*g^2*j*n^3 + (8) *e*f^3*g^2*j*n^3 + ((-8)) *e^2*f*g^3*j*n^3 + ((-8)) *f^3*g^3*j*n^3 + ((-4)) *e^5*h*j*n^3 + ((-8)) *e^3*f^2*h*j*n^3 + ((-4)) *e*f^4*h*j*n^3 + (4) *e^4*g*h*j*n^3 + (8) *e^2*f^2*g*h*j*n^3 + (4) *f^4*g*h*j*n^3 + (24) *e^3*f*h^2*j*n^3 + (24) *e*f^3*h^2*j*n^3 + ((-24)) *e^2*f*g*h^2*j*n^3 + ((-24)) *f^3*g*h^2*j*n^3 + ((-16)) *e^2*f*g^2*i*j*n^3 + (16) *e*f*g^3*i*j*n^3 + (16) *e^4*h*i*j*n^3 + ((-16)) *f^4*h*i*j*n^3 + ((-16)) *e^3*g*h*i*j*n^3 + ((-16)) *e*f^2*g*h*i*j*n^3 + ((-32)) *e^2*f*h^2*i*j*n^3 + (16) *f^3*h^2*i*j*n^3 + (48) *e*f*g*h^2*i*j*n^3 + (8) *e*f*g^2*i^2*j*n^3 + ((-8)) *f*g^3*i^2*j*n^3 + ((-24)) *e^3*h*i^2*j*n^3 + (24) *e*f^2*h*i^2*j*n^3 + (24) *e^2*g*h*i^2*j*n^3 + (8) *f^2*g*h*i^2*j*n^3 + ((-8)) *e*f*h^2*i^2*j*n^3 + ((-24)) *f*g*h^2*i^2*j*n^3 + (16) *e^2*h*i^3*j*n^3 + ((-16)) *f^2*h*i^3*j*n^3 + ((-16)) *e*g*h*i^3*j*n^3 + (16) *f*h^2*i^3*j*n^3 + ((-4)) *e*h*i^4*j*n^3 + (4) *g*h*i^4*j*n^3 + (2) *a^2*b^2*e*j^2*n^3 + (2) *c^2*d^2*e*j^2*n^3 + ((-2)) *a^2*b^2*g*j^2*n^3 + ((-2)) *c^2*d^2*g*j^2*n^3 + ((-4)) *e^3*g^2*j^2*n^3 + ((-12)) *e*f^2*g^2*j^2*n^3 + (4) *e^2*g^3*j^2*n^3 + (12) *f^2*g^3*j^2*n^3 + (16) *e^3*f*h*j^2*n^3 + (16) *e*f^3*h*j^2*n^3 + ((-16)) *e^2*f*g*h*j^2*n^3 + ((-16)) *f^3*g*h*j^2*n^3 + ((-12)) *e^3*h^2*j^2*n^3 + ((-36)) *e*f^2*h^2*j^2*n^3 + (12) *e^2*g*h^2*j^2*n^3 + (36) *f^2*g*h^2*j^2*n^3 + (8) *e^2*g^2*i*j^2*n^3 + ((-8)) *e*g^3*i*j^2*n^3 + ((-24)) *e^2*f*h*i*j^2*n^3 + (24) *f^3*h*i*j^2*n^3 + (32) *e*f*g*h*i*j^2*n^3 + (16) *e^2*h^2*i*j^2*n^3 + ((-24)) *f^2*h^2*i*j^2*n^3 + ((-24)) *e*g*h^2*i*j^2*n^3 + ((-4)) *e*g^2*i^2*j^2*n^3 + (4) *g^3*i^2*j^2*n^3 + ((-16)) *f*g*h*i^2*j^2*n^3 + (4) *e*h^2*i^2*j^2*n^3 + (12) *g*h^2*i^2*j^2*n^3 + (8) *f*h*i^3*j^2*n^3 + ((-8)) *h^2*i^3*j^2*n^3 + (8) *e*f*g^2*j^3*n^3 + ((-8)) *f*g^3*j^3*n^3 + ((-8)) *e^3*h*j^3*n^3 + ((-24)) *e*f^2*h*j^3*n^3 + (8) *e^2*g*h*j^3*n^3 + (24) *f^2*g*h*j^3*n^3 + (24) *e*f*h^2*j^3*n^3 + ((-24)) *f*g*h^2*j^3*n^3 + (16) *e^2*h*i*j^3*n^3 + ((-16)) *f^2*h*i*j^3*n^3 + ((-16)) *e*g*h*i*j^3*n^3 + (16) *f*h^2*i*j^3*n^3 + ((-8)) *e*h*i^2*j^3*n^3 + (8) *g*h*i^2*j^3*n^3 + ((-2)) *e*g^2*j^4*n^3 + (2) *g^3*j^4*n^3 + (16) *e*f*h*j^4*n^3 + ((-16)) *f*g*h*j^4*n^3 + ((-6)) *e*h^2*j^4*n^3 + (6) *g*h^2*j^4*n^3 + (4) *f*h*i*j^4*n^3 + ((-4)) *h^2*i*j^4*n^3 + ((-4)) *e*h*j^5*n^3 + (4) *g*h*j^5*n^3 + (4) *e^5*g*l*n^3 + (8) *e^3*f^2*g*l*n^3 + (4) *e*f^4*g*l*n^3 + ((-4)) *e^4*g^2*l*n^3 + ((-8)) *e^2*f^2*g^2*l*n^3 + ((-4)) *f^4*g^2*l*n^3 + ((-4)) *e^4*f*h*l*n^3 + ((-8)) *e^2*f^3*h*l*n^3 + ((-4)) *f^5*h*l*n^3 + (4) *e^4*h^2*l*n^3 + (8) *e^2*f^2*h^2*l*n^3 + (4) *f^4*h^2*l*n^3 + ((-16)) *e^4*g*i*l*n^3 + ((-16)) *e^2*f^2*g*i*l*n^3 + (16) *e^3*g^2*i*l*n^3 + (16) *e*f^2*g^2*i*l*n^3 + (16) *e^3*f*h*i*l*n^3 + (16) *e*f^3*h*i*l*n^3 + ((-16)) *e^3*h^2*i*l*n^3 + ((-16)) *e*f^2*h^2*i*l*n^3 + (24) *e^3*g*i^2*l*n^3 + (8) *e*f^2*g*i^2*l*n^3 + ((-24)) *e^2*g^2*i^2*l*n^3 + ((-8)) *f^2*g^2*i^2*l*n^3 + ((-24)) *e^2*f*h*i^2*l*n^3 + ((-8)) *f^3*h*i^2*l*n^3 + (24) *e^2*h^2*i^2*l*n^3 + (8) *f^2*h^2*i^2*l*n^3 + ((-16)) *e^2*g*i^3*l*n^3 + (16) *e*g^2*i^3*l*n^3 + (16) *e*f*h*i^3*l*n^3 + ((-16)) *e*h^2*i^3*l*n^3 + (4) *e*g*i^4*l*n^3 + ((-4)) *g^2*i^4*l*n^3 + ((-4)) *f*h*i^4*l*n^3 + (4) *h^2*i^4*l*n^3 + ((-16)) *e^3*f*g*j*l*n^3 + ((-16)) *e*f^3*g*j*l*n^3 + (16) *e^2*f*g^2*j*l*n^3 + (16) *f^3*g^2*j*l*n^3 + (16) *e^2*f^2*h*j*l*n^3 + (16) *f^4*h*j*l*n^3 + ((-16)) *e^2*f*h^2*j*l*n^3 + ((-16)) *f^3*h^2*j*l*n^3 + (32) *e^2*f*g*i*j*l*n^3 + ((-32)) *e*f*g^2*i*j*l*n^3 + ((-32)) *e*f^2*h*i*j*l*n^3 + (32) *e*f*h^2*i*j*l*n^3 + ((-16)) *e*f*g*i^2*j*l*n^3 + (16) *f*g^2*i^2*j*l*n^3 + (16) *f^2*h*i^2*j*l*n^3 + ((-16)) *f*h^2*i^2*j*l*n^3 + (8) *e^3*g*j^2*l*n^3 + (24) *e*f^2*g*j^2*l*n^3 + ((-8)) *e^2*g^2*j^2*l*n^3 + ((-24)) *f^2*g^2*j^2*l*n^3 + ((-8)) *e^2*f*h*j^2*l*n^3 + ((-24)) *f^3*h*j^2*l*n^3 + (8) *e^2*h^2*j^2*l*n^3 + (24) *f^2*h^2*j^2*l*n^3 + ((-16)) *e^2*g*i*j^2*l*n^3 + (16) *e*g^2*i*j^2*l*n^3 + (16) *e*f*h*i*j^2*l*n^3 + ((-16)) *e*h^2*i*j^2*l*n^3 + (8) *e*g*i^2*j^2*l*n^3 + ((-8)) *g^2*i^2*j^2*l*n^3 + ((-8)) *f*h*i^2*j^2*l*n^3 + (8) *h^2*i^2*j^2*l*n^3 + ((-16)) *e*f*g*j^3*l*n^3 + (16) *f*g^2*j^3*l*n^3 + (16) *f^2*h*j^3*l*n^3 + ((-16)) *f*h^2*j^3*l*n^3 + (4) *e*g*j^4*l*n^3 + ((-4)) *g^2*j^4*l*n^3 + ((-4)) *f*h*j^4*l*n^3 + (4) *h^2*j^4*l*n^3 + ((-2)) *e^5*l^2*n^3 + ((-4)) *e^3*f^2*l^2*n^3 + ((-2)) *e*f^4*l^2*n^3 + (2) *e^4*g*l^2*n^3 + (4) *e^2*f^2*g*l^2*n^3 + (2) *f^4*g*l^2*n^3 + (8) *e^4*i*l^2*n^3 + (8) *e^2*f^2*i*l^2*n^3 + ((-8)) *e^3*g*i*l^2*n^3 + ((-8)) *e*f^2*g*i*l^2*n^3 + ((-12)) *e^3*i^2*l^2*n^3 + ((-4)) *e*f^2*i^2*l^2*n^3 + (12) *e^2*g*i^2*l^2*n^3 + (4) *f^2*g*i^2*l^2*n^3 + (8) *e^2*i^3*l^2*n^3 + ((-8)) *e*g*i^3*l^2*n^3 + ((-2)) *e*i^4*l^2*n^3 + (2) *g*i^4*l^2*n^3 + (8) *e^3*f*j*l^2*n^3 + (8) *e*f^3*j*l^2*n^3 + ((-8)) *e^2*f*g*j*l^2*n^3 + ((-8)) *f^3*g*j*l^2*n^3 + ((-16)) *e^2*f*i*j*l^2*n^3 + (16) *e*f*g*i*j*l^2*n^3 + (8) *e*f*i^2*j*l^2*n^3 + ((-8)) *f*g*i^2*j*l^2*n^3 + ((-4)) *e^3*j^2*l^2*n^3 + ((-12)) *e*f^2*j^2*l^2*n^3 + (4) *e^2*g*j^2*l^2*n^3 + (12) *f^2*g*j^2*l^2*n^3 + (8) *e^2*i*j^2*l^2*n^3 + ((-8)) *e*g*i*j^2*l^2*n^3 + ((-4)) *e*i^2*j^2*l^2*n^3 + (4) *g*i^2*j^2*l^2*n^3 + (8) *e*f*j^3*l^2*n^3 + ((-8)) *f*g*j^3*l^2*n^3 + ((-2)) *e*j^4*l^2*n^3 + (2) *g*j^4*l^2*n^3 + (4) *e^5*h*n^4 + (8) *e^3*f^2*h*n^4 + (4) *e*f^4*h*n^4 + ((-4)) *e^4*g*h*n^4 + ((-8)) *e^2*f^2*g*h*n^4 + ((-4)) *f^4*g*h*n^4 + ((-1)) *e^4*f*i*n^4 + ((-2)) *e^2*f^3*i*n^4 + ((-1)) *f^5*i*n^4 + ((-15)) *e^4*h*i*n^4 + ((-14)) *e^2*f^2*h*i*n^4 + (1) *f^4*h*i*n^4 + (16) *e^3*g*h*i*n^4 + (16) *e*f^2*g*h*i*n^4 + (4) *e^3*f*i^2*n^4 + (4) *e*f^3*i^2*n^4 + (20) *e^3*h*i^2*n^4 + (4) *e*f^2*h*i^2*n^4 + ((-24)) *e^2*g*h*i^2*n^4 + ((-8)) *f^2*g*h*i^2*n^4 + ((-6)) *e^2*f*i^3*n^4 + ((-2)) *f^3*i^3*n^4 + ((-10)) *e^2*h*i^3*n^4 + (2) *f^2*h*i^3*n^4 + (16) *e*g*h*i^3*n^4 + (4) *e*f*i^4*n^4 + ((-4)) *g*h*i^4*n^4 + ((-1)) *f*i^5*n^4 + (1) *h*i^5*n^4 + (1) *e^5*j*n^4 + (2) *e^3*f^2*j*n^4 + (1) *e*f^4*j*n^4 + ((-1)) *e^4*g*j*n^4 + ((-2)) *e^2*f^2*g*j*n^4 + ((-1)) *f^4*g*j*n^4 + ((-16)) *e^3*f*h*j*n^4 + ((-16)) *e*f^3*h*j*n^4 + (16) *e^2*f*g*h*j*n^4 + (16) *f^3*g*h*j*n^4 + ((-4)) *e^4*i*j*n^4 + (4) *f^4*i*j*n^4 + (4) *e^3*g*i*j*n^4 + (4) *e*f^2*g*i*j*n^4 + (28) *e^2*f*h*i*j*n^4 + ((-4)) *f^3*h*i*j*n^4 + ((-32)) *e*f*g*h*i*j*n^4 + (6) *e^3*i^2*j*n^4 + ((-6)) *e*f^2*i^2*j*n^4 + ((-6)) *e^2*g*i^2*j*n^4 + ((-2)) *f^2*g*i^2*j*n^4 + ((-8)) *e*f*h*i^2*j*n^4 + (16) *f*g*h*i^2*j*n^4 + ((-4)) *e^2*i^3*j*n^4 + (4) *f^2*i^3*j*n^4 + (4) *e*g*i^3*j*n^4 + ((-4)) *f*h*i^3*j*n^4 + (1) *e*i^4*j*n^4 + ((-1)) *g*i^4*j*n^4 + ((-4)) *e^3*f*j^2*n^4 + ((-4)) *e*f^3*j^2*n^4 + (4) *e^2*f*g*j^2*n^4 + (4) *f^3*g*j^2*n^4 + (8) *e^3*h*j^2*n^4 + (24) *e*f^2*h*j^2*n^4 + ((-8)) *e^2*g*h*j^2*n^4 + ((-24)) *f^2*g*h*j^2*n^4 + (6) *e^2*f*i*j^2*n^4 + ((-6)) *f^3*i*j^2*n^4 + ((-8)) *e*f*g*i*j^2*n^4 + ((-14)) *e^2*h*i*j^2*n^4 + (6) *f^2*h*i*j^2*n^4 + (16) *e*g*h*i*j^2*n^4 + (4) *f*g*i^2*j^2*n^4 + (4) *e*h*i^2*j^2*n^4 + ((-8)) *g*h*i^2*j^2*n^4 + ((-2)) *f*i^3*j^2*n^4 + (2) *h*i^3*j^2*n^4 + (2) *e^3*j^3*n^4 + (6) *e*f^2*j^3*n^4 + ((-2)) *e^2*g*j^3*n^4 + ((-6)) *f^2*g*j^3*n^4 + ((-16)) *e*f*h*j^3*n^4 + (16) *f*g*h*j^3*n^4 + ((-4)) *e^2*i*j^3*n^4 + (4) *f^2*i*j^3*n^4 + (4) *e*g*i*j^3*n^4 + ((-4)) *f*h*i*j^3*n^4 + (2) *e*i^2*j^3*n^4 + ((-2)) *g*i^2*j^3*n^4 + ((-4)) *e*f*j^4*n^4 + (4) *f*g*j^4*n^4 + (4) *e*h*j^4*n^4 + ((-4)) *g*h*j^4*n^4 + ((-1)) *f*i*j^4*n^4 + (1) *h*i*j^4*n^4 + (1) *e*j^5*n^4 + ((-1)) *g*j^5*n^4 + (1) *e^4*f*l*n^4 + (2) *e^2*f^3*l*n^4 + (1) *f^5*l*n^4 + ((-1)) *e^4*h*l*n^4 + ((-2)) *e^2*f^2*h*l*n^4 + ((-1)) *f^4*h*l*n^4 + ((-4)) *e^3*f*i*l*n^4 + ((-4)) *e*f^3*i*l*n^4 + (4) *e^3*h*i*l*n^4 + (4) *e*f^2*h*i*l*n^4 + (6) *e^2*f*i^2*l*n^4 + (2) *f^3*i^2*l*n^4 + ((-6)) *e^2*h*i^2*l*n^4 + ((-2)) *f^2*h*i^2*l*n^4 + ((-4)) *e*f*i^3*l*n^4 + (4) *e*h*i^3*l*n^4 + (1) *f*i^4*l*n^4 + ((-1)) *h*i^4*l*n^4 + ((-4)) *e^2*f^2*j*l*n^4 + ((-4)) *f^4*j*l*n^4 + (4) *e^2*f*h*j*l*n^4 + (4) *f^3*h*j*l*n^4 + (8) *e*f^2*i*j*l*n^4 + ((-8)) *e*f*h*i*j*l*n^4 + ((-4)) *f^2*i^2*j*l*n^4 + (4) *f*h*i^2*j*l*n^4 + (2) *e^2*f*j^2*l*n^4 + (6) *f^3*j^2*l*n^4 + ((-2)) *e^2*h*j^2*l*n^4 + ((-6)) *f^2*h*j^2*l*n^4 + ((-4)) *e*f*i*j^2*l*n^4 + (4) *e*h*i*j^2*l*n^4 + (2) *f*i^2*j^2*l*n^4 + ((-2)) *h*i^2*j^2*l*n^4 + ((-4)) *f^2*j^3*l*n^4 + (4) *f*h*j^3*l*n^4 + (1) *f*j^4*l*n^4 + ((-1)) *h*j^4*l*n^4 + ((-1)) *e^5*n^5 + ((-2)) *e^3*f^2*n^5 + ((-1)) *e*f^4*n^5 + (1) *e^4*g*n^5 + (2) *e^2*f^2*g*n^5 + (1) *f^4*g*n^5 + (4) *e^4*i*n^5 + (4) *e^2*f^2*i*n^5 + ((-4)) *e^3*g*i*n^5 + ((-4)) *e*f^2*g*i*n^5 + ((-6)) *e^3*i^2*n^5 + ((-2)) *e*f^2*i^2*n^5 + (6) *e^2*g*i^2*n^5 + (2) *f^2*g*i^2*n^5 + (4) *e^2*i^3*n^5 + ((-4)) *e*g*i^3*n^5 + ((-1)) *e*i^4*n^5 + (1) *g*i^4*n^5 + (4) *e^3*f*j*n^5 + (4) *e*f^3*j*n^5 + ((-4)) *e^2*f*g*j*n^5 + ((-4)) *f^3*g*j*n^5 + ((-8)) *e^2*f*i*j*n^5 + (8) *e*f*g*i*j*n^5 + (4) *e*f*i^2*j*n^5 + ((-4)) *f*g*i^2*j*n^5 + ((-2)) *e^3*j^2*n^5 + ((-6)) *e*f^2*j^2*n^5 + (2) *e^2*g*j^2*n^5 + (6) *f^2*g*j^2*n^5 + (4) *e^2*i*j^2*n^5 + ((-4)) *e*g*i*j^2*n^5 + ((-2)) *e*i^2*j^2*n^5 + (2) *g*i^2*j^2*n^5 + (4) *e*f*j^3*n^5 + ((-4)) *f*g*j^3*n^5 + ((-1)) *e*j^4*n^5 + (1) *g*j^4*n^5
F:= [
((-1)) *i^2 + ((-1)) *j^2 + (2) *i*k + ((-2)) *k*l + (1) *l^2 + (2) *j*m + ((-2)) *m*n + (1) *n^2 ;
((-1)) *g^2 + ((-1)) *h^2 + (2) *g*k + ((-2)) *k*l + (1) *l^2 + (2) *h*m + ((-2)) *m*n + (1) *n^2 ;
((-1)) *e^2 + ((-1)) *f^2 + (2) *e*k + ((-2)) *k*l + (1) *l^2 + (2) *f*m + ((-2)) *m*n + (1) *n^2 ;
(1) *d^2 + ((-1)) *i^2 + ((-1)) *j^2 + (2) *i*l + ((-1)) *l^2 + (2) *j*n + ((-1)) *n^2 ;
(1) *c^2 + ((-1)) *e^2 + ((-1)) *f^2 + (2) *e*g + ((-1)) *g^2 + (2) *f*h + ((-1)) *h^2 ;
(1) *b^2 + ((-1)) *e^2 + ((-1)) *f^2 + (2) *e*l + ((-1)) *l^2 + (2) *f*n + ((-1)) *n^2 ;
(1) *a^2 + ((-1)) *g^2 + ((-1)) *h^2 + (2) *g*i + ((-1)) *i^2 + (2) *h*j + ((-1)) *j^2 ;
];
polynomes homogenes
reste: 0
polynome reduit a 0
r: 0
verif somme: 0
coefficient: (1)
temps: 199.451s
spolynomes inutiles: 0
spolynomes utiles: 1
coeffient de p: 1
pgcd des contenus des coeffients du tz: 1
pgcd avec le coefficient de p: 1
----------------------- tz:
taille des coefficients du tz: 571931
taille des coefficients du certificat: 571931
Certificat:
CR:=[
(4) *a^2*f^3*i*k^2 + ((-4)) *a^2*f^2*h*i*k^2 + ((-4)) *a^2*e*f^2*j*k^2 + (4) *a^2*f^2*g*j*k^2 + ((-40)) *e*f^2*g*i*j*k^2 + ((-24)) *f^3*h*i*j*k^2 + ((-16)) *f^2*h^2*i*j*k^2 + ((-40)) *f^3*g*j^2*k^2 + (24) *e*f^2*h*j^2*k^2 + (16) *f^2*g*h*j^2*k^2 + ((-8)) *a^2*e*f*i*k^3 + (40) *f^3*g*i*k^3 + (8) *a^2*e*h*i*k^3 + ((-32)) *e*f^2*h*i*k^3 + ((-40)) *f^2*g*h*i*k^3 + (32) *e*f*h^2*i*k^3 + ((-8)) *a^2*f^2*j*k^3 + ((-8)) *a^2*e*g*j*k^3 + (8) *e*f^2*g*j*k^3 + (8) *f^2*h^2*j*k^3 + (8) *e*f^2*i*j*k^3 + (24) *f^2*g*i*j*k^3 + (48) *e*f*h*i*j*k^3 + (8) *f^3*j^2*k^3 + (16) *e*f*g*j^2*k^3 + (8) *f^2*h*j^2*k^3 + ((-16)) *f^3*i*k^4 + ((-16)) *e*f*g*i*k^4 + (16) *f^2*h*i*k^4 + (16) *e*g*h*i*k^4 + (16) *a^2*e*j*k^4 + ((-16)) *e*h^2*j*k^4 + (16) *f^2*i*j*k^4 + (16) *e*g*i*j*k^4 + ((-16)) *e*f*j^2*k^4 + ((-16)) *e*h*j^2*k^4 + (32) *e*f*i*k^5 + ((-32)) *e*h*i*k^5 + ((-32)) *e*i*j*k^5 + ((-8)) *a^2*f^3*i*k*l + (8) *a^2*f^2*h*i*k*l + (8) *a^2*e*f^2*j*k*l + ((-8)) *a^2*f^2*g*j*k*l + (80) *e*f^2*g*i*j*k*l + (48) *f^3*h*i*j*k*l + (32) *f^2*h^2*i*j*k*l + (80) *f^3*g*j^2*k*l + ((-48)) *e*f^2*h*j^2*k*l + ((-32)) *f^2*g*h*j^2*k*l + ((-4)) *a^2*f^3*k^2*l + (4) *a^2*f^2*h*k^2*l + (24) *a^2*e*f*i*k^2*l + ((-120)) *f^3*g*i*k^2*l + ((-24)) *a^2*e*h*i*k^2*l + (96) *e*f^2*h*i*k^2*l + (120) *f^2*g*h*i*k^2*l + ((-96)) *e*f*h^2*i*k^2*l + (24) *a^2*f^2*j*k^2*l + (24) *a^2*e*g*j*k^2*l + (16) *e*f^2*g*j*k^2*l + (24) *f^3*h*j*k^2*l + ((-8)) *f^2*h^2*j*k^2*l + (16) *e*f^2*i*j*k^2*l + ((-32)) *f^2*g*i*j*k^2*l + ((-144)) *e*f*h*i*j*k^2*l + (16) *f^3*j^2*k^2*l + ((-48)) *e*f*g*j^2*k^2*l + ((-64)) *f^2*h*j^2*k^2*l + (8) *a^2*e*f*k^3*l + ((-40)) *f^3*g*k^3*l + ((-8)) *a^2*e*h*k^3*l + (32) *e*f^2*h*k^3*l + (40) *f^2*g*h*k^3*l + ((-32)) *e*f*h^2*k^3*l + (8) *a^2*f*i*k^3*l + (24) *f^3*i*k^3*l + (64) *e*f*g*i*k^3*l + ((-8)) *a^2*h*i*k^3*l + (8) *f^2*h*i*k^3*l + ((-64)) *e*g*h*i*k^3*l + ((-32)) *f*h^2*i*k^3*l + ((-56)) *a^2*e*j*k^3*l + ((-16)) *e*f^2*j*k^3*l + (8) *a^2*g*j*k^3*l + ((-32)) *f^2*g*j*k^3*l + ((-48)) *e*f*h*j*k^3*l + (64) *e*h^2*j*k^3*l + ((-96)) *f^2*i*j*k^3*l + ((-64)) *e*g*i*j*k^3*l + ((-48)) *f*h*i*j*k^3*l + (48) *e*f*j^2*k^3*l + ((-16)) *f*g*j^2*k^3*l + (64) *e*h*j^2*k^3*l + (16) *f^3*k^4*l + (16) *e*f*g*k^4*l + ((-16)) *f^2*h*k^4*l + ((-16)) *e*g*h*k^4*l + ((-144)) *e*f*i*k^4*l + (16) *f*g*i*k^4*l + (144) *e*h*i*k^4*l + ((-16)) *g*h*i*k^4*l + ((-16)) *a^2*j*k^4*l + ((-16)) *f^2*j*k^4*l + ((-16)) *e*g*j*k^4*l + (16) *h^2*j*k^4*l + (144) *e*i*j*k^4*l + ((-16)) *g*i*j*k^4*l + (16) *f*j^2*k^4*l + (16) *h*j^2*k^4*l + ((-32)) *e*f*k^5*l + (32) *e*h*k^5*l + ((-32)) *f*i*k^5*l + (32) *h*i*k^5*l + (32) *e*j*k^5*l + (32) *i*j*k^5*l + (4) *a^2*f^3*i*l^2 + ((-4)) *a^2*f^2*h*i*l^2 + ((-4)) *a^2*e*f^2*j*l^2 + (4) *a^2*f^2*g*j*l^2 + ((-40)) *e*f^2*g*i*j*l^2 + ((-24)) *f^3*h*i*j*l^2 + ((-16)) *f^2*h^2*i*j*l^2 + ((-40)) *f^3*g*j^2*l^2 + (24) *e*f^2*h*j^2*l^2 + (16) *f^2*g*h*j^2*l^2 + (8) *a^2*f^3*k*l^2 + ((-8)) *a^2*f^2*h*k*l^2 + ((-24)) *a^2*e*f*i*k*l^2 + (120) *f^3*g*i*k*l^2 + (24) *a^2*e*h*i*k*l^2 + ((-96)) *e*f^2*h*i*k*l^2 + ((-120)) *f^2*g*h*i*k*l^2 + (96) *e*f*h^2*i*k*l^2 + ((-24)) *a^2*f^2*j*k*l^2 + ((-24)) *a^2*e*g*j*k*l^2 + ((-56)) *e*f^2*g*j*k*l^2 + ((-48)) *f^3*h*j*k*l^2 + ((-8)) *f^2*h^2*j*k*l^2 + ((-56)) *e*f^2*i*j*k*l^2 + ((-8)) *f^2*g*i*j*k*l^2 + (144) *e*f*h*i*j*k*l^2 + ((-56)) *f^3*j^2*k*l^2 + (48) *e*f*g*j^2*k*l^2 + (104) *f^2*h*j^2*k*l^2 + ((-24)) *a^2*e*f*k^2*l^2 + (120) *f^3*g*k^2*l^2 + (24) *a^2*e*h*k^2*l^2 + ((-96)) *e*f^2*h*k^2*l^2 + ((-120)) *f^2*g*h*k^2*l^2 + (96) *e*f*h^2*k^2*l^2 + ((-24)) *a^2*f*i*k^2*l^2 + (24) *f^3*i*k^2*l^2 + ((-96)) *e*f*g*i*k^2*l^2 + (24) *a^2*h*i*k^2*l^2 + ((-120)) *f^2*h*i*k^2*l^2 + (96) *e*g*h*i*k^2*l^2 + (96) *f*h^2*i*k^2*l^2 + (72) *a^2*e*j*k^2*l^2 + (8) *e*f^2*j*k^2*l^2 + ((-24)) *a^2*g*j*k^2*l^2 + (56) *f^2*g*j*k^2*l^2 + (144) *e*f*h*j*k^2*l^2 + ((-96)) *e*h^2*j*k^2*l^2 + (152) *f^2*i*j*k^2*l^2 + (96) *e*g*i*j*k^2*l^2 + (144) *f*h*i*j*k^2*l^2 + ((-48)) *e*f*j^2*k^2*l^2 + (48) *f*g*j^2*k^2*l^2 + ((-96)) *e*h*j^2*k^2*l^2 + ((-8)) *a^2*f*k^3*l^2 + ((-24)) *f^3*k^3*l^2 + ((-64)) *e*f*g*k^3*l^2 + (8) *a^2*h*k^3*l^2 + ((-8)) *f^2*h*k^3*l^2 + (64) *e*g*h*k^3*l^2 + (32) *f*h^2*k^3*l^2 + (256) *e*f*i*k^3*l^2 + ((-64)) *f*g*i*k^3*l^2 + ((-256)) *e*h*i*k^3*l^2 + (64) *g*h*i*k^3*l^2 + (56) *a^2*j*k^3*l^2 + (104) *f^2*j*k^3*l^2 + (64) *e*g*j*k^3*l^2 + (48) *f*h*j*k^3*l^2 + ((-64)) *h^2*j*k^3*l^2 + ((-256)) *e*i*j*k^3*l^2 + (64) *g*i*j*k^3*l^2 + ((-48)) *f*j^2*k^3*l^2 + ((-64)) *h*j^2*k^3*l^2 + (144) *e*f*k^4*l^2 + ((-16)) *f*g*k^4*l^2 + ((-144)) *e*h*k^4*l^2 + (16) *g*h*k^4*l^2 + (144) *f*i*k^4*l^2 + ((-144)) *h*i*k^4*l^2 + ((-144)) *e*j*k^4*l^2 + (16) *g*j*k^4*l^2 + ((-144)) *i*j*k^4*l^2 + (32) *f*k^5*l^2 + ((-32)) *h*k^5*l^2 + ((-32)) *j*k^5*l^2 + ((-4)) *a^2*f^3*l^3 + (4) *a^2*f^2*h*l^3 + (8) *a^2*e*f*i*l^3 + ((-40)) *f^3*g*i*l^3 + ((-8)) *a^2*e*h*i*l^3 + (32) *e*f^2*h*i*l^3 + (40) *f^2*g*h*i*l^3 + ((-32)) *e*f*h^2*i*l^3 + (8) *a^2*f^2*j*l^3 + (8) *a^2*e*g*j*l^3 + (32) *e*f^2*g*j*l^3 + (24) *f^3*h*j*l^3 + (8) *f^2*h^2*j*l^3 + (32) *e*f^2*i*j*l^3 + (16) *f^2*g*i*j*l^3 + ((-48)) *e*f*h*i*j*l^3 + (32) *f^3*j^2*l^3 + ((-16)) *e*f*g*j^2*l^3 + ((-48)) *f^2*h*j^2*l^3 + (24) *a^2*e*f*k*l^3 + ((-120)) *f^3*g*k*l^3 + ((-24)) *a^2*e*h*k*l^3 + (96) *e*f^2*h*k*l^3 + (120) *f^2*g*h*k*l^3 + ((-96)) *e*f*h^2*k*l^3 + (24) *a^2*f*i*k*l^3 + ((-56)) *f^3*i*k*l^3 + (64) *e*f*g*i*k*l^3 + ((-24)) *a^2*h*i*k*l^3 + (152) *f^2*h*i*k*l^3 + ((-64)) *e*g*h*i*k*l^3 + ((-96)) *f*h^2*i*k*l^3 + ((-40)) *a^2*e*j*k*l^3 + (32) *e*f^2*j*k*l^3 + (24) *a^2*g*j*k*l^3 + ((-16)) *f^2*g*j*k*l^3 + ((-144)) *e*f*h*j*k*l^3 + (64) *e*h^2*j*k*l^3 + ((-80)) *f^2*i*j*k*l^3 + ((-64)) *e*g*i*j*k*l^3 + ((-144)) *f*h*i*j*k*l^3 + (16) *e*f*j^2*k*l^3 + ((-48)) *f*g*j^2*k*l^3 + (64) *e*h*j^2*k*l^3 + (24) *a^2*f*k^2*l^3 + ((-24)) *f^3*k^2*l^3 + (96) *e*f*g*k^2*l^3 + ((-24)) *a^2*h*k^2*l^3 + (120) *f^2*h*k^2*l^3 + ((-96)) *e*g*h*k^2*l^3 + ((-96)) *f*h^2*k^2*l^3 + ((-224)) *e*f*i*k^2*l^3 + (96) *f*g*i*k^2*l^3 + (224) *e*h*i*k^2*l^3 + ((-96)) *g*h*i*k^2*l^3 + ((-72)) *a^2*j*k^2*l^3 + ((-176)) *f^2*j*k^2*l^3 + ((-96)) *e*g*j*k^2*l^3 + ((-144)) *f*h*j*k^2*l^3 + (96) *h^2*j*k^2*l^3 + (224) *e*i*j*k^2*l^3 + ((-96)) *g*i*j*k^2*l^3 + (48) *f*j^2*k^2*l^3 + (96) *h*j^2*k^2*l^3 + ((-256)) *e*f*k^3*l^3 + (64) *f*g*k^3*l^3 + (256) *e*h*k^3*l^3 + ((-64)) *g*h*k^3*l^3 + ((-256)) *f*i*k^3*l^3 + (256) *h*i*k^3*l^3 + (256) *e*j*k^3*l^3 + ((-64)) *g*j*k^3*l^3 + (256) *i*j*k^3*l^3 + ((-144)) *f*k^4*l^3 + (144) *h*k^4*l^3 + (144) *j*k^4*l^3 + ((-8)) *a^2*e*f*l^4 + (40) *f^3*g*l^4 + (8) *a^2*e*h*l^4 + ((-32)) *e*f^2*h*l^4 + ((-40)) *f^2*g*h*l^4 + (32) *e*f*h^2*l^4 + ((-8)) *a^2*f*i*l^4 + (24) *f^3*i*l^4 + ((-16)) *e*f*g*i*l^4 + (8) *a^2*h*i*l^4 + ((-56)) *f^2*h*i*l^4 + (16) *e*g*h*i*l^4 + (32) *f*h^2*i*l^4 + (8) *a^2*e*j*l^4 + ((-24)) *e*f^2*j*l^4 + ((-8)) *a^2*g*j*l^4 + ((-8)) *f^2*g*j*l^4 + (48) *e*f*h*j*l^4 + ((-16)) *e*h^2*j*l^4 + (8) *f^2*i*j*l^4 + (16) *e*g*i*j*l^4 + (48) *f*h*i*j*l^4 + (16) *f*g*j^2*l^4 + ((-16)) *e*h*j^2*l^4 + ((-24)) *a^2*f*k*l^4 + (56) *f^3*k*l^4 + ((-64)) *e*f*g*k*l^4 + (24) *a^2*h*k*l^4 + ((-152)) *f^2*h*k*l^4 + (64) *e*g*h*k*l^4 + (96) *f*h^2*k*l^4 + (96) *e*f*i*k*l^4 + ((-64)) *f*g*i*k*l^4 + ((-96)) *e*h*i*k*l^4 + (64) *g*h*i*k*l^4 + (40) *a^2*j*k*l^4 + (104) *f^2*j*k*l^4 + (64) *e*g*j*k*l^4 + (144) *f*h*j*k*l^4 + ((-64)) *h^2*j*k*l^4 + ((-96)) *e*i*j*k*l^4 + (64) *g*i*j*k*l^4 + ((-16)) *f*j^2*k*l^4 + ((-64)) *h*j^2*k*l^4 + (224) *e*f*k^2*l^4 + ((-96)) *f*g*k^2*l^4 + ((-224)) *e*h*k^2*l^4 + (96) *g*h*k^2*l^4 + (224) *f*i*k^2*l^4 + ((-224)) *h*i*k^2*l^4 + ((-224)) *e*j*k^2*l^4 + (96) *g*j*k^2*l^4 + ((-224)) *i*j*k^2*l^4 + (256) *f*k^3*l^4 + ((-256)) *h*k^3*l^4 + ((-256)) *j*k^3*l^4 + (8) *a^2*f*l^5 + ((-24)) *f^3*l^5 + (16) *e*f*g*l^5 + ((-8)) *a^2*h*l^5 + (56) *f^2*h*l^5 + ((-16)) *e*g*h*l^5 + ((-32)) *f*h^2*l^5 + ((-16)) *e*f*i*l^5 + (16) *f*g*i*l^5 + (16) *e*h*i*l^5 + ((-16)) *g*h*i*l^5 + ((-8)) *a^2*j*l^5 + ((-16)) *f^2*j*l^5 + ((-16)) *e*g*j*l^5 + ((-48)) *f*h*j*l^5 + (16) *h^2*j*l^5 + (16) *e*i*j*l^5 + ((-16)) *g*i*j*l^5 + (16) *h*j^2*l^5 + ((-96)) *e*f*k*l^5 + (64) *f*g*k*l^5 + (96) *e*h*k*l^5 + ((-64)) *g*h*k*l^5 + ((-96)) *f*i*k*l^5 + (96) *h*i*k*l^5 + (96) *e*j*k*l^5 + ((-64)) *g*j*k*l^5 + (96) *i*j*k*l^5 + ((-224)) *f*k^2*l^5 + (224) *h*k^2*l^5 + (224) *j*k^2*l^5 + (16) *e*f*l^6 + ((-16)) *f*g*l^6 + ((-16)) *e*h*l^6 + (16) *g*h*l^6 + (16) *f*i*l^6 + ((-16)) *h*i*l^6 + ((-16)) *e*j*l^6 + (16) *g*j*l^6 + ((-16)) *i*j*l^6 + (96) *f*k*l^6 + ((-96)) *h*k*l^6 + ((-96)) *j*k*l^6 + ((-16)) *f*l^7 + (16) *h*l^7 + (16) *j*l^7 + ((-8)) *a^2*e*f^2*i*k*m + (8) *a^2*e*f*h*i*k*m + ((-8)) *a^2*f^3*j*k*m + ((-8)) *a^2*e*f*g*j*k*m + ((-16)) *f^3*g*i*j*k*m + ((-16)) *e*f^2*h*i*j*k*m + (32) *e*f*h^2*i*j*k*m + (16) *e*f^2*g*j^2*k*m + ((-16)) *f^3*h*j^2*k*m + ((-32)) *e*f*g*h*j^2*k*m + ((-8)) *a^2*f^2*i*k^2*m + ((-16)) *e*f^2*g*i*k^2*m + (8) *a^2*f*h*i*k^2*m + ((-8)) *f^3*h*i*k^2*m + (16) *e*f*g*h*i*k^2*m + (8) *f^2*h^2*i*k^2*m + (24) *a^2*e*f*j*k^2*m + ((-8)) *a^2*f*g*j*k^2*m + (64) *f^3*g*j*k^2*m + ((-24)) *e*f^2*h*j*k^2*m + ((-56)) *f^2*g*h*j*k^2*m + (16) *e*f*h^2*j*k^2*m + (8) *f^3*i*j*k^2*m + (32) *e*f*g*i*j*k^2*m + (104) *f^2*h*i*j*k^2*m + ((-8)) *e*f^2*j^2*k^2*m + (40) *f^2*g*j^2*k^2*m + (32) *e*f^2*i*k^3*m + ((-16)) *f^2*g*i*k^3*m + ((-16)) *e*f*h*i*k^3*m + (16) *f*g*h*i*k^3*m + ((-16)) *e*h^2*i*k^3*m + (16) *a^2*f*j*k^3*m + ((-16)) *f^3*j*k^3*m + ((-48)) *e*f*g*j*k^3*m + (16) *f^2*h*j*k^3*m + (48) *e*g*h*j*k^3*m + ((-16)) *f*h^2*j*k^3*m + ((-32)) *e*f*i*j*k^3*m + (16) *f*g*i*j*k^3*m + ((-48)) *e*h*i*j*k^3*m + (16) *e*g*j^2*k^3*m + ((-16)) *f*h*j^2*k^3*m + (32) *f^2*i*k^4*m + ((-32)) *f*h*i*k^4*m + (32) *e*f*j*k^4*m + ((-32)) *e*h*j*k^4*m + ((-32)) *f*i*j*k^4*m + ((-32)) *e*j^2*k^4*m + (8) *a^2*e*f^2*i*l*m + ((-8)) *a^2*e*f*h*i*l*m + (8) *a^2*f^3*j*l*m + (8) *a^2*e*f*g*j*l*m + (16) *f^3*g*i*j*l*m + (16) *e*f^2*h*i*j*l*m + ((-32)) *e*f*h^2*i*j*l*m + ((-16)) *e*f^2*g*j^2*l*m + (16) *f^3*h*j^2*l*m + (32) *e*f*g*h*j^2*l*m + (8) 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C:=[
[
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*f*k*n^6 + (52) *h*k*n^6 + (24) *j*k*n^6 + (55) *f*l*n^6 + ((-39)) *h*l*n^6 + ((-48)) *j*l*n^6 + (158) *e*m*n^6 + (34) *g*m*n^6 + ((-96)) *i*m*n^6 + ((-16)) *k*m*n^6 + ((-80)) *l*m*n^6 + ((-39)) *e*n^7 + ((-9)) *g*n^7 + (24) *i*n^7 + (8) *k*n^7 + (16) *l*n^7 ; ];
];
c:=
1;