restart; # Packages with(SolveTools):

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# These procedures display Ernst-Maxwell equations p_emq1:=proc() local i,j; global emq1; for i from 0 to 1 do for j from 0 to 1-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 1 do for j from 0 to 1-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 1 do for j from 0 to 1-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 1 do for j from 0 to 1-i do print(simplify(emq2a[i,j])); end do; end do; end proc:

# -------------------------- MAIN ---------------------------- # The expansion of E, F=conjugate(E), Phi, Alpha=conjugate(Phi) # Remark: the factorial coefficients are written explicitly # It follows from Eq. (3.1) that a[0]=b[0]=c[0]=d[0] E:=+a[1]*z+a[2]*w+1/2*a[3]*z^2+1/2*a[4]*w^2+a[5]*z*w; F:=+b[1]*w+b[2]*z+1/2*b[3]*w^2+1/2*b[4]*z^2+b[5]*w*z; Phi:=+c[1]*z+c[2]*w+1/2*c[3]*z^2+1/2*c[4]*w^2+c[5]*z*w; Alpha:=+d[1]*w+d[2]*z+1/2*d[3]*w^2+1/2*d[4]*z^2+d[5]*w*z;

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NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USZBbHBoYUYoLyUnZmFtaWx5R1EuTHVjaWRhfkJyaWdodEYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dGOC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GKC8lJ29wYXF1ZUdGOC8lK2V4ZWN1dGFibGVHRjgvJSlyZWFkb25seUdRJXRydWVGKC8lKWNvbXBvc2VkR0Y4LyUqY29udmVydGVkR0Y4LyUraW1zZWxlY3RlZEdGOC8lLHBsYWNlaG9sZGVyR0Y4LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RigvJSptYXRoY29sb3JHRkMvJS9tYXRoYmFja2dyb3VuZEdGRi8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYoLyUpbWF0aHNpemVHRjUtSSNtb0dGJTYzUSM6PUYoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRigvJSdyc3BhY2VHRltwLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lMGZvbnRfc3R5bGVfbmFtZUdGWC8lJXNpemVHRjUvJStmb3JlZ3JvdW5kR0ZDLyUrYmFja2dyb3VuZEdGRi1GJDYrLUYkNiUtSSVtc3ViR0YlNiYtRi02OVEiZEYoRjBGM0Y2L0Y6Rk1GO0Y9Rj9GQUZERkdGSUZLRk5GUEZSRlRGVkZZRmVuRmduL0ZqblEnaXRhbGljRihGXG8tRiQ2Iy1JI21uR0YlNjlGZ3BGMEYzRjZGOUY7Rj1GP0ZBRkRGR0ZJRktGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGKC8lLHBsYWNlaG9sZGVyR0Y4LUZfbzYzUTEmSW52aXNpYmxlVGltZXM7RihGYm9GZW9GZ28vRmpvUSQwZW1GKC9GXXBGYXNGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRi02OVEid0YoRjBGM0Y2RmByRjtGPUY/RkFGREZHRklGS0ZORlBGUkZURlZGWUZlbkZnbkZhckZcby1GX282M1EiK0YoRmJvRmVvRmdvL0Zqb1EwbWVkaXVtbWF0aHNwYWNlRigvRl1wRmpzRl5wRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUYkNiUtRltyNiZGXXItRiQ2Iy1GZnI2OVEiMkYoRjBGM0Y2RjlGO0Y9Rj9GQUZERkdGSUZLRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvRmhyRltzRl1zLUYtNjlRInpGKEYwRjNGNkZgckY7Rj1GP0ZBRkRGR0ZJRktGTkZQRlJGVEZWRllGZW5GZ25GYXJGXG9GZnMtRiQ2JS1JJm1mcmFjR0YlNipGZXJGYnQvJS5saW5ldGhpY2tuZXNzR1EiMUYoLyUrZGVub21hbGlnbkdRJ2NlbnRlckYoLyUpbnVtYWxpZ25HRmJ1LyUpYmV2ZWxsZWRHRjhGYnFGZHFGXXMtRiQ2JS1GW3I2JkZdci1GJDYjLUZmcjY5USIzRihGMEYzRjZGOUY7Rj1GP0ZBRkRGR0ZJRktGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG9GaHJGW3NGXXMtSSVtc3VwR0YlNiVGY3NGYnQvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZqckZmcy1GJDYlRmp0Rl1zLUYkNiUtRltyNiZGXXItRiQ2Iy1GZnI2OVEiNEYoRjBGM0Y2RjlGO0Y9Rj9GQUZERkdGSUZLRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvRmhyRltzRl1zLUZhdjYlRmV0RmJ0RmN2RmZzLUYkNictRltyNiZGXXItRiQ2Iy1GZnI2OVEiNUYoRjBGM0Y2RjlGO0Y9Rj9GQUZERkdGSUZLRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvRmhyRltzRl1zRmNzRl1zRmV0NyMtX0YpSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZBbHBoYUdGKCwsKiYmSSJkR0YoNiMiIiJGaHhJIndHRihGaHhGaHgqJiZGZng2IyIiI0ZoeEkiekdGKEZoeEZoeCooI0ZoeEZdeUZoeCZGZng2IyIiJEZoeClGaXhGXXlGaHhGaHgqKEZgeUZoeCZGZng2IyIiJUZoeClGXnlGXXlGaHhGaHgqKCZGZng2IyIiJkZoeEZpeEZoeEZeeUZoeEZoeDcjRmN4

# The metric function f f:=-1/2*(E+F+2*Alpha*Phi);

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

# Ernst-Maxwell equations # em1a, em2a are the conjugate equations of em1, em2, respectively 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):

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for i from 0 to 1 do for j from 0 to 1-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:

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for i from 0 to 1 do for j from 0 to 1-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:

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

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNjMtRiQ2KS1JI21uR0YlNjlRIjRGKC8lJ2ZhbWlseUdRLkx1Y2lkYX5CcmlnaHRGKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHRjovJSp1bmRlcmxpbmVHRjovJSpzdWJzY3JpcHRHRjovJSxzdXBlcnNjcmlwdEdGOi8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUShbMCwwLDBdRigvJSdvcGFxdWVHRjovJStleGVjdXRhYmxlR0Y6LyUpcmVhZG9ubHlHUSV0cnVlRigvJSljb21wb3NlZEdGOi8lKmNvbnZlcnRlZEdGOi8lK2ltc2VsZWN0ZWRHRjovJSxwbGFjZWhvbGRlckdGOi8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZFLyUvbWF0aGJhY2tncm91bmRHRkgvJStmb250ZmFtaWx5R0Y0LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGKC8lKW1hdGhzaXplR0Y3LUkjbW9HRiU2M1ExJkludmlzaWJsZVRpbWVzO0YoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lJ2xzcGFjZUdRJDBlbUYoLyUncnNwYWNlR0ZdcC8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJTBmb250X3N0eWxlX25hbWVHRlovJSVzaXplR0Y3LyUrZm9yZWdyb3VuZEdGRS8lK2JhY2tncm91bmRHRkgtSSVtc3ViR0YlNiYtSSNtaUdGJTY5USJhRihGMkY1RjgvRjxGT0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluL0Zcb1EnaXRhbGljRihGXm8tRiQ2Iy1GLzY5USIyRihGMkY1RjhGO0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vLyUvc3Vic2NyaXB0c2hpZnRHUSIwRigvJSxwbGFjZWhvbGRlckdGOkZgby1GXHI2OVEnJnJobzswRihGMkY1RjhGX3JGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZgckZeb0Zgby1GaXE2Ji1GXHI2OVEiYkYoRjJGNUY4Rl9yRj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GYHJGXm8tRiQ2Iy1GLzY5USI1RihGMkY1RjhGO0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vRmdyRmpyLUZhbzYzUSIrRihGZG9GZ29GaW8vRlxwUTBtZWRpdW1tYXRoc3BhY2VGKC9GX3BGXXRGYHBGYnBGZHBGZ3BGanBGXHFGXnFGYHFGYnFGZHFGZnEtRiQ2JS1GaXE2JkZhc0ZickZnckZqckZgb0ZocUZpcy1GJDYlLUZpcTYmRmFzLUYkNiMtRi82OUZpcEYyRjVGOEY7Rj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GW29GXm9GZ3JGanJGYG9GaHEtRmFvNjNRKCZtaW51cztGKEZkb0Znb0Zpb0ZcdEZedEZgcEZicEZkcEZncEZqcEZccUZecUZgcUZicUZkcUZmcS1GJDYpRi5GYG9GZXRGYG9GXHNGYG9GX3NGW3UtRiQ2Jy1GLzY5USIzRihGMkY1RjhGO0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vRmBvRmV0RmBvRmF0RmlzLUYkNiMtSShtc3Vic3VwR0YlNidGYXNGZ3RGZHIvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZpckZnckZbdS1GJDYpLUYvNjlRIjhGKEYyRjVGOEY7Rj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GW29GXm9GYG9GXHNGYG8tRmlxNiZGYXMtRiQ2I0ZidUZnckZqckZgb0ZhdEZbdS1GJDYrRl52RmBvRlxzRmBvLUZpcTYmLUZccjY5USJjRihGMkY1RjhGX3JGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZgckZeb0ZickZnckZqckZgb0ZldEZgby1GaXE2Ji1GXHI2OVEiZEYoRjJGNUY4Rl9yRj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GYHJGXm9GYnJGZ3JGanJGW3UtRiQ2K0ZedkZgb0Zcc0Zgb0ZndkZgb0ZhdEZgby1GaXE2JkZed0ZndEZnckZqcjcjLDQqKiIiJSIiIiZJImFHRig2IyIiI0Zpd0klcmhvMEdGKEZpdyZJImJHRig2IyIiJkZpd0ZpdyomJkZgeEZceEZpd0Zqd0Zpd0ZpdyomJkZgeDYjRml3Rml3Rmp3Rml3Rml3KipGaHdGaXdGZnhGaXdGXnhGaXdGX3hGaXchIiIqKCIiJEZpd0ZmeEZpd0ZkeEZpd0ZpeCokKUZmeEZdeEZpd0ZpdyoqIiIpRml3Rl54Rml3JkZgeDYjRlt5Rml3RmR4Rml3Rml4KixGX3lGaXdGXnhGaXcmSSJjR0YoRlx4Rml3RmZ4Rml3JkkiZEdGKEZceEZpd0ZpeCosRl95Rml3Rl54Rml3RmN5Rml3RmR4Rml3JkZmeUZneEZpd0ZpeA==

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

for i from 0 to 1 do for j from 0 to 1-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:

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for i from 0 to 1 do for j from 0 to 1-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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# It follows from emq1[0,0], emq1a[0,0] that a[1]=b[1]=0 or a[2]=b[2]=0

# It is straightforward to solve the equations above with "solve" command, however we prefer to solve them step by step.

# Firstly, we choose a[2]=b[2]=0 (remaining possibility will be examined later) a[2]:=0; b[2]:=0;

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

# Now, the Ernst-Maxwell equations take the form

p_emq1();

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p_emq1a();

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p_emq2();

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p_emq2a();

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

# Since Df does not equal to zero, all solutions such that a[1]=0 or b[1]=0 have to be rejected (b[1]=conjugate(a[1])). This implies that c[2]=d[2]=0

c[2]:=0; d[2]:=0;

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# Again, we look at the Ernst-Maxwell equations p_emq1();

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p_emq1a();

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

p_emq2();

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

p_emq2a();

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

# Repeating the previous argument, we have a[1]:=4*rho0*a[5]; b[1]:=4*rho0*b[5];

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

# Since now, we know that a[5], b[5] are not equal to 0

# Once more we look at the Ernst-Maxwell equations p_emq1();

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

p_emq1a();

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

p_emq2();

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

p_emq2a();

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

# Thus, a[4]:=b[5]; b[4]:=a[5];

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

# The Ernst-Maxwell equations take the form p_emq1();

p_emq1a();

p_emq2();

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

p_emq2a();

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

# Therefore, c[4]:=b[5]*c[5]/a[5]; d[4]:=a[5]*d[5]/b[5];

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

# Finally, the Ernst-Maxwell equations

p_emq1();

p_emq1a();

p_emq2();

p_emq2a();

# and we are done

# The solution E;

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

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiktRiQ2KS1JI21uR0YlNjlRIjRGKC8lJ2ZhbWlseUdRLkx1Y2lkYX5CcmlnaHRGKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHRjovJSp1bmRlcmxpbmVHRjovJSpzdWJzY3JpcHRHRjovJSxzdXBlcnNjcmlwdEdGOi8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUShbMCwwLDBdRigvJSdvcGFxdWVHRjovJStleGVjdXRhYmxlR0Y6LyUpcmVhZG9ubHlHUSV0cnVlRigvJSljb21wb3NlZEdGOi8lKmNvbnZlcnRlZEdGOi8lK2ltc2VsZWN0ZWRHRjovJSxwbGFjZWhvbGRlckdGOi8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZFLyUvbWF0aGJhY2tncm91bmRHRkgvJStmb250ZmFtaWx5R0Y0LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGKC8lKW1hdGhzaXplR0Y3LUkjbW9HRiU2M1ExJkludmlzaWJsZVRpbWVzO0YoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lJ2xzcGFjZUdRJDBlbUYoLyUncnNwYWNlR0ZdcC8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJTBmb250X3N0eWxlX25hbWVHRlovJSVzaXplR0Y3LyUrZm9yZWdyb3VuZEdGRS8lK2JhY2tncm91bmRHRkgtSSNtaUdGJTY5UScmcmhvOzBGKEYyRjVGOC9GPEZPRj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW4vRlxvUSdpdGFsaWNGKEZeb0Zgby1JJW1zdWJHRiU2Ji1GaXE2OVEiYkYoRjJGNUY4RlxyRj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GXXJGXm8tRiQ2Iy1GLzY5USI1RihGMkY1RjhGO0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vLyUvc3Vic2NyaXB0c2hpZnRHUSIwRigvJSxwbGFjZWhvbGRlckdGOkZgby1GaXE2OVEid0YoRjJGNUY4RlxyRj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GXXJGXm8tRmFvNjNRIitGKEZkb0Znb0Zpby9GXHBRMG1lZGl1bW1hdGhzcGFjZUYoL0ZfcEZmc0ZgcEZicEZkcEZncEZqcEZccUZecUZgcUZicUZkcUZmcS1GJDYlLUkmbWZyYWNHRiU2Ki1GLzY5RmlwRjJGNUY4RjtGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZbb0Zeby1GLzY5USIyRihGMkY1RjhGO0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vLyUubGluZXRoaWNrbmVzc0dRIjFGKC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGKC8lKW51bWFsaWduR0ZndC8lKWJldmVsbGVkR0Y6RmRxRmZxRmBvLUYkNiUtRmByNiZGYnItRiQ2Iy1GLzY5USIzRihGMkY1RjhGO0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vRmpyRl1zRmBvLUklbXN1cEdGJTYlRl9zRl90LyUxc3VwZXJzY3JpcHRzaGlmdEdGXHNGYnMtRiQ2JUZqc0Zgby1GJDYlLUZgcjYmLUZpcTY5USJhRihGMkY1RjhGXHJGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZdckZeb0ZlckZqckZdc0Zgby1GZnU2JS1GaXE2OVEiekYoRjJGNUY4RlxyRj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GXXJGXm9GX3RGaHVGYnMtRiQ2J0ZfckZgb0Zfc0Zgb0ZldjcjLCoqKiIiJSIiIkklcmhvMEdGKEZedyZJImJHRig2IyIiJkZed0kid0dGKEZed0ZedyooI0ZedyIiI0ZedyZGYXc2IyIiJEZedylGZHdGZ3dGXndGXncqKEZmd0ZedyZJImFHRihGYndGXncpSSJ6R0YoRmd3Rl53Rl53KihGYHdGXndGZHdGXndGYHhGXndGXnc=

Phi;

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiktRiQ2JS1JJW1zdWJHRiU2Ji1JI21pR0YlNjlRImNGKC8lJ2ZhbWlseUdRLkx1Y2lkYX5CcmlnaHRGKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRj0vJSpzdWJzY3JpcHRHRj0vJSxzdXBlcnNjcmlwdEdGPS8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUShbMCwwLDBdRigvJSdvcGFxdWVHRj0vJStleGVjdXRhYmxlR0Y9LyUpcmVhZG9ubHlHRkAvJSljb21wb3NlZEdGPS8lKmNvbnZlcnRlZEdGPS8lK2ltc2VsZWN0ZWRHRj0vJSxwbGFjZWhvbGRlckdGPS8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZJLyUvbWF0aGJhY2tncm91bmRHRkwvJStmb250ZmFtaWx5R0Y3LyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y6LUYkNiMtSSNtbkdGJTY5USIxRihGNUY4RjsvRj9GPUZBRkNGRUZHRkpGTUZPRlFGU0ZVRldGWUZlbkZobkZqbkZcby9GX29RJ25vcm1hbEYoRmFvLyUvc3Vic2NyaXB0c2hpZnRHUSIwRigvJSxwbGFjZWhvbGRlckdGPS1JI21vR0YlNjNRMSZJbnZpc2libGVUaW1lcztGKC8lJWZvcm1HUSZpbmZpeEYoLyUmZmVuY2VHRj0vJSpzZXBhcmF0b3JHRj0vJSdsc3BhY2VHUSQwZW1GKC8lJ3JzcGFjZUdGXnEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdGaG8vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lMGZvbnRfc3R5bGVfbmFtZUdGZ24vJSVzaXplR0Y6LyUrZm9yZWdyb3VuZEdGSS8lK2JhY2tncm91bmRHRkwtRjI2OVEiekYoRjVGOEY7Rj5GQUZDRkVGR0ZKRk1GT0ZRRlNGVUZXRllGZW5GaG5Gam5GXG9GXm9GYW8tRmJwNjNRIitGKEZlcEZocEZqcC9GXXFRMG1lZGl1bW1hdGhzcGFjZUYoL0ZgcUZfc0ZhcUZjcUZlcUZocUZqcUZcckZeckZgckZickZkckZmci1GJDYlLUkmbWZyYWNHRiU2KkZlby1GZm82OVEiMkYoRjVGOEY7RmlvRkFGQ0ZFRkdGSkZNRk9GUUZTRlVGV0ZZRmVuRmhuRmpuRlxvRmpvRmFvLyUubGluZXRoaWNrbmVzc0dRIjFGKC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGKC8lKW51bWFsaWduR0ZedC8lKWJldmVsbGVkR0Y9RmRyRmZyRmFwLUYkNiUtRi82JkYxLUYkNiMtRmZvNjlRIjNGKEY1RjhGO0Zpb0ZBRkNGRUZHRkpGTUZPRlFGU0ZVRldGWUZlbkZobkZqbkZcb0Zqb0Zhb0ZccEZfcEZhcC1JJW1zdXBHRiU2JUZockZmcy8lMXN1cGVyc2NyaXB0c2hpZnRHRl5wRltzLUYkNiVGY3NGYXAtRmRzNiotRiQ2Jy1GLzYmLUYyNjlRImJGKEY1RjhGO0Y+RkFGQ0ZFRkdGSkZNRk9GUUZTRlVGV0ZZRmVuRmhuRmpuRlxvRl5vRmFvLUYkNiMtRmZvNjlRIjVGKEY1RjhGO0Zpb0ZBRkNGRUZHRkpGTUZPRlFGU0ZVRldGWUZlbkZobkZqbkZcb0Zqb0Zhb0ZccEZfcEZhcC1GLzYmRjFGXHZGXHBGX3BGYXAtRl11NiUtRjI2OVEid0YoRjVGOEY7Rj5GQUZDRkVGR0ZKRk1GT0ZRRlNGVUZXRllGZW5GaG5Gam5GXG9GXm9GYW9GZnNGX3UtRiQ2Iy1GLzYmLUYyNjlRImFGKEY1RjhGO0Y+RkFGQ0ZFRkdGSkZNRk9GUUZTRlVGV0ZZRmVuRmhuRmpuRlxvRl5vRmFvRlx2RlxwRl9wRmlzRlx0Rl90RmF0RmRyRmZyRltzLUYkNidGYXZGYXBGaHJGYXBGZXY3IywqKiYmSSJjR0YoNiMiIiJGZ3dJInpHRihGZ3dGZ3cqKCNGZ3ciIiNGZ3cmRmV3NiMiIiRGZ3cpRmh3Rlt4Rmd3Rmd3KixGandGZ3cmSSJiR0YoNiMiIiZGZ3cmRmV3RmN4Rmd3JkkiYUdGKEZjeCEiIilJIndHRihGW3hGZ3dGZ3cqKEZleEZnd0Zod0Znd0ZqeEZnd0Zndw==

Alpha;

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

# Moreover, Df does not vanish (a[5], b[5] cannot be equal to 0) mtaylor(f,[z,w],2);

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

# Now, we explore the remaining possibility, namely a[1]=b[1]=0 # We clear our coefficients a:='a':b:='b':c:='c':d:='d':

# From the previous analysis we have a[1]:=0; b[1]:=0;

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

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSVtc3ViR0YlNiYtSSNtaUdGJTY5USJiRigvJSdmYW1pbHlHUS5MdWNpZGF+QnJpZ2h0RigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR1EldHJ1ZUYoLyUqdW5kZXJsaW5lR0Y7LyUqc3Vic2NyaXB0R0Y7LyUsc3VwZXJzY3JpcHRHRjsvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLyUnb3BhcXVlR0Y7LyUrZXhlY3V0YWJsZUdGOy8lKXJlYWRvbmx5R0Y+LyUpY29tcG9zZWRHRjsvJSpjb252ZXJ0ZWRHRjsvJStpbXNlbGVjdGVkR0Y7LyUscGxhY2Vob2xkZXJHRjsvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRy8lL21hdGhiYWNrZ3JvdW5kR0ZKLyUrZm9udGZhbWlseUdGNS8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGOC1GJDYjLUkjbW5HRiU2OVEiMUYoRjNGNkY5L0Y9RjtGP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbi9GXW9RJ25vcm1hbEYoRl9vLyUvc3Vic2NyaXB0c2hpZnRHUSIwRigvJSxwbGFjZWhvbGRlckdGOy1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGXHEvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdGZm8vJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lMGZvbnRfc3R5bGVfbmFtZUdGZW4vJSVzaXplR0Y4LyUrZm9yZWdyb3VuZEdGRy8lK2JhY2tncm91bmRHRkotRmRvNjlRIjBGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vNyMtX0YpSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIiIiIhNyNGZHM=

# We repeat our calculations. The Ernst-Maxwell equations take the form

p_emq1();

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p_emq1a();

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p_emq2();

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p_emq2a();

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

# Since Df does not equal to zero, all solutions such that a[2]=0 or b[2]=0 have to be rejected (b[2]=conjugate(a[2])). This implies that c[1]=d[1]=0

c[1]:=0; d[1]:=0;

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# Again, we look at the Ernst-Maxwell equations p_emq1();

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p_emq1a();

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

p_emq2();

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

p_emq2a();

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

# Repeating the previous argument, we have a[2]:=4*rho0*a[5]; b[2]:=4*rho0*b[5];

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

# Since now, we know that a[5], b[5] are not equal to 0

# Once more we look at the Ernst-Maxwell equations p_emq1();

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

p_emq1a();

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtRiQ2KS1JI21uR0YlNjlRIzMyRigvJSdmYW1pbHlHUS5MdWNpZGF+QnJpZ2h0RigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR0Y6LyUqdW5kZXJsaW5lR0Y6LyUqc3Vic2NyaXB0R0Y6LyUsc3VwZXJzY3JpcHRHRjovJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLyUnb3BhcXVlR0Y6LyUrZXhlY3V0YWJsZUdGOi8lKXJlYWRvbmx5R1EldHJ1ZUYoLyUpY29tcG9zZWRHRjovJSpjb252ZXJ0ZWRHRjovJStpbXNlbGVjdGVkR0Y6LyUscGxhY2Vob2xkZXJHRjovJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRS8lL21hdGhiYWNrZ3JvdW5kR0ZILyUrZm9udGZhbWlseUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRigvJSltYXRoc2l6ZUdGNy1JI21vR0YlNjNRMSZJbnZpc2libGVUaW1lcztGKC8lJWZvcm1HUSZpbmZpeEYoLyUmZmVuY2VHRjovJSpzZXBhcmF0b3JHRjovJSdsc3BhY2VHUSQwZW1GKC8lJ3JzcGFjZUdGXXAvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUwZm9udF9zdHlsZV9uYW1lR0ZaLyUlc2l6ZUdGNy8lK2ZvcmVncm91bmRHRkUvJStiYWNrZ3JvdW5kR0ZILUklbXN1cEdGJTYlLUkjbWlHRiU2OVEnJnJobzswRihGMkY1RjgvRjxGT0Y9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluL0Zcb1EnaXRhbGljRihGXm8tRi82OVEiMkYoRjJGNUY4RjtGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZbb0Zeby8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRihGYG8tSSVtc3ViR0YlNiYtRlxyNjlRImJGKEYyRjVGOEZfckY9Rj9GQUZDRkZGSUZLRk1GUEZSRlRGVkZYRmVuRmduRmluRmByRl5vLUYkNiMtRi82OVEiNUYoRjJGNUY4RjtGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZbb0Zeby8lL3N1YnNjcmlwdHNoaWZ0R0Znci8lLHBsYWNlaG9sZGVyR0Y6RmBvLUZpcjYmLUZccjY5USJhRihGMkY1RjhGX3JGPUY/RkFGQ0ZGRklGS0ZNRlBGUkZURlZGWEZlbkZnbkZpbkZgckZeb0Zec0Zjc0Zlcy1GYW82M1EoJm1pbnVzO0YoRmRvRmdvRmlvL0ZccFEwbWVkaXVtbWF0aHNwYWNlRigvRl9wRmB0RmBwRmJwRmRwRmdwRmpwRlxxRl5xRmBxRmJxRmRxRmZxLUYkNilGLkZgb0ZocUZgby1GaXI2JkZbcy1GJDYjLUYvNjlRIjNGKEYyRjVGOEY7Rj1GP0ZBRkNGRkZJRktGTUZQRlJGVEZWRlhGZW5GZ25GaW5GW29GXm9GY3NGZXNGYG9GaHI3IywmKioiI0siIiIpSSVyaG8wR0YoIiIjRl91JkkiYkdGKDYjIiImRl91JkkiYUdGKEZldUZfdUZfdSoqRl51Rl91RmB1Rl91JkZkdTYjIiIkRl91RmN1Rl91ISIi

p_emq2();

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

p_emq2a();

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

# Thus, a[3]:=b[5]; b[3]:=a[5];

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

# The Ernst-Maxwell equations take the form p_emq1();

p_emq1a();

p_emq2();

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

p_emq2a();

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

# Therefore, c[3]:=b[5]*c[5]/a[5]; d[3]:=a[5]*d[5]/b[5];

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

# Finally, the Ernst-Maxwell equations

p_emq1();

p_emq1a();

p_emq2();

p_emq2a();

# and we are done

# The solution is conjugate to the first one E;

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

Phi;

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

Alpha;

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

# Moreover, Df does not vanish (a[5], b[5] cannot be equal to 0) mtaylor(f,[z,w],2);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiYtSSNtb0dGJTYzUSomdW1pbnVzMDtGKC8lJWZvcm1HUSdwcmVmaXhGKC8lJmZlbmNlR1EmZmFsc2VGKC8lKnNlcGFyYXRvckdGNS8lJ2xzcGFjZUdRJDBlbUYoLyUncnNwYWNlR0Y6LyUpc3RyZXRjaHlHRjUvJSpzeW1tZXRyaWNHRjUvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y1LyUubW92YWJsZWxpbWl0c0dGNS8lJ2FjY2VudEdGNS8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUlc2l6ZUdRIzEyRigvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLUYkNiktSSNtbkdGJTY5USIyRigvJSdmYW1pbHlHUS5MdWNpZGF+QnJpZ2h0RigvJSVzaXplR0ZSLyUlYm9sZEdGNS8lJ2l0YWxpY0dGNS8lKnVuZGVybGluZUdGNS8lKnN1YnNjcmlwdEdGNS8lLHN1cGVyc2NyaXB0R0Y1LyUrZm9yZWdyb3VuZEdGVS8lK2JhY2tncm91bmRHRlgvJSdvcGFxdWVHRjUvJStleGVjdXRhYmxlR0Y1LyUpcmVhZG9ubHlHUSV0cnVlRigvJSljb21wb3NlZEdGNS8lKmNvbnZlcnRlZEdGNS8lK2ltc2VsZWN0ZWRHRjUvJSxwbGFjZWhvbGRlckdGNS8lMGZvbnRfc3R5bGVfbmFtZUdGTy8lKm1hdGhjb2xvckdGVS8lL21hdGhiYWNrZ3JvdW5kR0ZYLyUrZm9udGZhbWlseUdGW28vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYoLyUpbWF0aHNpemVHRlItRi02M1ExJkludmlzaWJsZVRpbWVzO0YoL0YxUSZpbmZpeEYoRjNGNkY4RjtGPUY/RkFGREZHRklGS0ZNRlBGU0ZWLUkjbWlHRiU2OVEnJnJobzswRihGaW5GXG9GXm8vRmFvRmJwRmJvRmRvRmZvRmhvRmpvRlxwRl5wRmBwRmNwRmVwRmdwRmlwRltxRl1xRl9xRmFxL0ZkcVEnaXRhbGljRihGZnFGaHEtSSVtc3ViR0YlNiYtRl5yNjlRImFGKEZpbkZcb0Zeb0ZhckZib0Zkb0Zmb0Zob0Zqb0ZccEZecEZgcEZjcEZlcEZncEZpcEZbcUZdcUZfcUZhcUZickZmcS1GJDYjLUZmbjY5USI1RihGaW5GXG9GXm9GYG9GYm9GZG9GZm9GaG9Gam9GXHBGXnBGYHBGY3BGZXBGZ3BGaXBGW3FGXXFGX3FGYXFGY3FGZnEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGKC8lLHBsYWNlaG9sZGVyR0Y1RmhxLUZecjY5USJ3RihGaW5GXG9GXm9GYXJGYm9GZG9GZm9GaG9Gam9GXHBGXnBGYHBGY3BGZXBGZ3BGaXBGW3FGXXFGX3FGYXFGYnJGZnEtRi02M1EoJm1pbnVzO0YoRltyRjNGNi9GOVEwbWVkaXVtbWF0aHNwYWNlRigvRjxGW3RGPUY/RkFGREZHRklGS0ZNRlBGU0ZWLUYkNilGZW5GaHFGXXJGaHEtRmVyNiYtRl5yNjlRImJGKEZpbkZcb0Zeb0ZhckZib0Zkb0Zmb0Zob0Zqb0ZccEZecEZgcEZjcEZlcEZncEZpcEZbcUZdcUZfcUZhcUZickZmcUZqckZfc0Zic0ZocS1GXnI2OVEiekYoRmluRlxvRl5vRmFyRmJvRmRvRmZvRmhvRmpvRlxwRl5wRmBwRmNwRmVwRmdwRmlwRltxRl1xRl9xRmFxRmJyRmZxNyMsJioqIiIjIiIiSSVyaG8wR0YoRlt1JkkiYUdGKDYjIiImRlt1SSJ3R0YoRlt1ISIiKipGanRGW3VGXHVGW3UmSSJiR0YoRl91Rlt1SSJ6R0YoRlt1RmJ1