# We assume the second order zero of f=-(Re(E)+Alpha*Phi) and consider solutions that have E=a[5]*z*w+O(|z|^3).
restart;
# Definitions
p_emq1:=proc()
local i,j;
global emq1;
for i from 0 to 2 do
for j from 0 to 2-i do
print(simplify(emq1[i,j]));
end do;
end do;
end proc;
p_emq1a:=proc()
local i,j;
global emq1a;
for i from 0 to 2 do
for j from 0 to 2-i do
print(simplify(emq1a[i,j]));
end do;
end do;
end proc;
p_emq2:=proc()
local i,j;
global emq2;
for i from 0 to 2 do
for j from 0 to 2-i do
print(simplify(emq2[i,j]));
end do;
end do;
end proc;
p_emq2a:=proc()
local i,j;
global emq2a;
for i from 0 to 2 do
for j from 0 to 2-i do
print(simplify(emq2a[i,j]));
end do;
end do;
end proc;
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
# -------------------------- MAIN ----------------------------
# Taylor expansions (F is conjugate to E and Alpha is conjugate to Phi)
E:=a[3]*z^2+a[4]*w^2+a[5]*z*w+a[6]*z^3+a[7]*z^2*w+a[8]*z*w^2+a[9]*w^3;
F:=b[3]*w^2+b[4]*z^2+b[5]*z*w+b[6]*w^3+b[7]*w^2*z+b[8]*w*z^2+b[9]*z^3;
Phi:=c[1]*z+c[2]*w+c[3]*z^2+c[4]*w^2+c[5]*z*w+c[6]*z^3+c[7]*z^2*w+c[8]*z*w^2+c[9]*w^3;
Alpha:=d[1]*w+d[2]*z+d[3]*w^2+d[4]*z^2+d[5]*z*w+d[6]*w^3+d[7]*w^2*z+d[8]*w*z^2+d[9]*z^3;
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
NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USZBbHBoYUYoLyUnZmFtaWx5R1EuTHVjaWRhfkJyaWdodEYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dGOC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GKC8lJ29wYXF1ZUdGOC8lK2V4ZWN1dGFibGVHRjgvJSlyZWFkb25seUdRJXRydWVGKC8lKWNvbXBvc2VkR0Y4LyUqY29udmVydGVkR0Y4LyUraW1zZWxlY3RlZEdGOC8lLHBsYWNlaG9sZGVyR0Y4LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RigvJSptYXRoY29sb3JHRkMvJS9tYXRoYmFja2dyb3VuZEdGRi8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYoLyUpbWF0aHNpemVHRjUtSSNtb0dGJTYzUSM6PUYoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRigvJSdyc3BhY2VHRltwLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lMGZvbnRfc3R5bGVfbmFtZUdGWC8lJXNpemVHRjUvJStmb3JlZ3JvdW5kR0ZDLyUrYmFja2dyb3VuZEdGRi1GJDYzLUYkNiUtSSVtc3ViR0YlNiYtRi02OVEiZEYoRjBGM0Y2L0Y6Rk1GO0Y9Rj9GQUZERkdGSUZLRk5GUEZSRlRGVkZZRmVuRmduL0ZqblEnaXRhbGljRihGXG8tRiQ2Iy1JI21uR0YlNjlGZ3BGMEYzRjZGOUY7Rj1GP0ZBRkRGR0ZJRktGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGKC8lLHBsYWNlaG9sZGVyR0Y4LUZfbzYzUTEmSW52aXNpYmxlVGltZXM7RihGYm9GZW9GZ28vRmpvUSQwZW1GKC9GXXBGYXNGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRi02OVEid0YoRjBGM0Y2RmByRjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZhckZcby1GX282M1EiK0YoRmJvRmVvRmdvL0Zqb1EwbWVkaXVtbWF0aHNwYWNlRigvRl1wRmpzRl5wRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUYkNiUtRltyNiZGXXItRiQ2Iy1GZnI2OVEiMkYoRjBGM0Y2RjlGO0Y9Rj9GQUZERkdGSUZLRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvRmhyRltzRl1zLUYtNjlRInpGKEYwRjNGNkZgckY7Rj1GP0ZBRkRGR0ZJRktGTkZQRlJGVEZWRllGZW5GZ25GYXJGXG9GZnMtRiQ2JS1GW3I2JkZdci1GJDYjLUZmcjY5USIzRihGMEYzRjZGOUY7Rj1GP0ZBRkRGR0ZJRktGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG9GaHJGW3NGXXMtSSVtc3VwR0YlNiVGY3NGYnQvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZqckZmcy1GJDYlLUZbcjYmRl1yLUYkNiMtRmZyNjlRIjRGKEYwRjNGNkY5RjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0ZockZbc0Zdcy1GYnU2JUZldEZidEZkdUZmcy1GJDYnLUZbcjYmRl1yLUYkNiMtRmZyNjlRIjVGKEYwRjNGNkY5RjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0ZockZbc0Zdc0ZldEZdc0Zjc0Zmcy1GJDYlLUZbcjYmRl1yLUYkNiMtRmZyNjlRIjZGKEYwRjNGNkY5RjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0ZockZbc0Zdcy1GYnU2JUZjc0ZedUZkdUZmcy1GJDYnLUZbcjYmRl1yLUYkNiMtRmZyNjlRIjdGKEYwRjNGNkY5RjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0ZockZbc0Zdc0ZhdUZdc0ZldEZmcy1GJDYnLUZbcjYmRl1yLUYkNiMtRmZyNjlRIjhGKEYwRjNGNkY5RjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0ZockZbc0Zdc0Zjc0Zdc0ZfdkZmcy1GJDYlLUZbcjYmRl1yLUYkNiMtRmZyNjlRIjlGKEYwRjNGNkY5RjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0ZockZbc0Zdcy1GYnU2JUZldEZedUZkdTcjLV9GKUksbXByaW50c2xhc2hHRig2JDcjPkkmQWxwaGFHRigsNComJkkiZEdGKDYjIiIiRl96SSJ3R0YoRl96Rl96KiYmRl16NiMiIiNGX3pJInpHRihGX3pGX3oqJiZGXXo2IyIiJEZfeilGYHpGZHpGX3pGX3oqJiZGXXo2IyIiJUZfeilGZXpGZHpGX3pGX3oqKCZGXXo2IyIiJkZfekZlekZfekZgekZfekZfeiomJkZdejYjIiInRl96KUZgekZpekZfekZfeiooJkZdejYjIiIoRl96Rmp6Rl96RmV6Rl96Rl96KigmRl16NiMiIilGX3pGYHpGX3pGX1tsRl96Rl96KiYmRl16NiMiIipGX3opRmV6Rml6Rl96Rl96NyNGank=
# E takes the form E=a[5]*z*w+O(|z|^3)
a[3]:=0;b[3]:=0;a[4]:=0;b[4]:=0;
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# Definitions of functions: f, sigma_I, sigma_II, kappa (sigmas do not have hats nor dots).
f:=-1/2*(E+F+2*Alpha*Phi);
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
sigma_I:=1/2*(2*rho0+z+w)*(diff(E,z)+2*Alpha*diff(Phi,z)+f/(2*rho0+z+w));
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
sigma_II:=-1/2*(2*rho0+z+w)*(diff(F,z)+2*Phi*diff(Alpha,z)+f/(2*rho0+z+w));
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
kappa:=-2/(2*rho0+z+w)*(sigma_I*sigma_II+1/4*f^2)+2*(2*rho0+z+w)*diff(Alpha,z)*diff(Phi,z)*f;
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# Ernst-Maxwell equations
em1:=(E+F+2*Alpha*Phi)*(2*(2*rho0+w+z)*diff(E,w,z)+(diff(E,z)+diff(E,w)))-4*(2*rho0+w+z)*(diff(E,z)*diff(E,w)+Alpha*(diff(E,z)*diff(Phi,w)+diff(E,w)*diff(Phi,z))):
em1a:=(E+F+2*Alpha*Phi)*(2*(2*rho0+w+z)*diff(F,z,w)+(diff(F,w)+diff(F,z)))-4*(2*rho0+w+z)*(diff(F,w)*diff(F,z)+Phi*(diff(F,w)*diff(Alpha,z)+diff(F,z)*diff(Alpha,w))):
em2:=(E+F+2*Alpha*Phi)*(2*(2*rho0+w+z)*diff(Phi,w,z)+(diff(Phi,z)+diff(Phi,w)))-2*(2*rho0+w+z)*(diff(E,z)*diff(Phi,w)+diff(E,w)*diff(Phi,z)+4*Alpha*diff(Phi,z)*diff(Phi,w)):
em2a:=(E+F+2*Alpha*Phi)*(2*(2*rho0+w+z)*diff(Alpha,z,w)+(diff(Alpha,w)+diff(Alpha,z)))-2*(2*rho0+w+z)*(diff(F,w)*diff(Alpha,z)+diff(F,z)*diff(Alpha,w)+4*Phi*diff(Alpha,w)*diff(Alpha,z)):
em1:=mtaylor(em1,[z,w],3):
em2:=mtaylor(em2,[z,w],3):
em1a:=mtaylor(em1a,[z,w],3):
em2a:=mtaylor(em2a,[z,w],3):
# Expansion of the Ernst-Maxwell equations
print("++++++++++++++++++++++++++em1+++++++++++++++++++++++++++++");
for i from 0 to 2 do
for j from 0 to 2-i do
emq1[i,j]:=factor(coeftayl(em1,[z,w]=[0,0],[i,j]));
print(i,j);
print(factor(simplify(emq1[i,j])));
end do;
end do;
print("++++++++++++++++++++++++++em1a+++++++++++++++++++++++++++++");
for i from 0 to 2 do
for j from 0 to 2-i do
emq1a[i,j]:=factor(coeftayl(em1a,[z,w]=[0,0],[i,j]));
print(i,j);
print(factor(simplify(emq1a[i,j])));
end do;
end do;
print("++++++++++++++++++++++++++em2+++++++++++++++++++++++++++++");
for i from 0 to 2 do
for j from 0 to 2-i do
emq2[i,j]:=coeftayl(em2,[z,w]=[0,0],[i,j]);
print(i,j);
print(simplify(emq2[i,j]));
end do;
end do;
print("++++++++++++++++++++++++++em2a+++++++++++++++++++++++++++++");
for i from 0 to 2 do
for j from 0 to 2-i do
emq2a[i,j]:=coeftayl(em2a,[z,w]=[0,0],[i,j]);
print(i,j);
print(simplify(emq2a[i,j]));
end do;
end do;
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E;
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Phi;
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
# We assign the solution that satisfy the Ernst-Maxwell equations up to first order
b[5]:=a[5];
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
a[5]:=-4*d[2]*c[2];
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
c[2]:=d[1]*c[1]/d[2];
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# Taylor expansion of f, sigma_I, sigma_II
mtaylor(f,[z,w],3);
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
mtaylor(sigma_I,[z,w],2);
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
mtaylor(sigma_II,[z,w],2);
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
# Finally, we turn to notation such that
c[1]:=alpha;
d[1]:=conjugate(alpha);
d[2]:=gamma;
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
NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSVtc3ViR0YlNiYtSSNtaUdGJTY5USJkRigvJSdmYW1pbHlHUS5MdWNpZGF+QnJpZ2h0RigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR1EldHJ1ZUYoLyUqdW5kZXJsaW5lR0Y7LyUqc3Vic2NyaXB0R0Y7LyUsc3VwZXJzY3JpcHRHRjsvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLyUnb3BhcXVlR0Y7LyUrZXhlY3V0YWJsZUdGOy8lKXJlYWRvbmx5R0Y+LyUpY29tcG9zZWRHRjsvJSpjb252ZXJ0ZWRHRjsvJStpbXNlbGVjdGVkR0Y7LyUscGxhY2Vob2xkZXJHRjsvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRy8lL21hdGhiYWNrZ3JvdW5kR0ZKLyUrZm9udGZhbWlseUdGNS8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGOC1GJDYjLUkjbW5HRiU2OVEiMkYoRjNGNkY5L0Y9RjtGP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbi9GXW9RJ25vcm1hbEYoRl9vLyUvc3Vic2NyaXB0c2hpZnRHUSIwRigvJSxwbGFjZWhvbGRlckdGOy1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGXHEvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUwZm9udF9zdHlsZV9uYW1lR0Zlbi8lJXNpemVHRjgvJStmb3JlZ3JvdW5kR0ZHLyUrYmFja2dyb3VuZEdGSi1GMDY5USZnYW1tYUYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX283Iy1fRilJLG1wcmludHNsYXNoR0YoNiQ3Iz4mSSJkR0YoNiMiIiNJJmdhbW1hRyUqcHJvdGVjdGVkRzcjRmVz
# Taylor expansion of E, Phi, f, sigma_I, sigma_II (new notation)
mtaylor(E,[z,w],3);
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
mtaylor(Phi,[z,w],2);
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
mtaylor(f,[z,w],3);
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
simplify(mtaylor(sigma_I,[z,w],2));
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
simplify(mtaylor(sigma_II,[z,w],2));
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