Mathematica for Section 7.2 (evaluated)

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Section 7.2 (pages 66-69)

B[1,1][z_]=w[1,1][z]-(w[0,1][z])^2;

B[1,2][z_]=w[1,2][z]-w[0,1][z]*w[0,2][z];

B[2,2][z_]=w[2,2][z]-(w[0,2][z])^2;

D2[z_]=B[1,1][z]*B[2,2][z]-(B[1,2][z])^2;

E6[z_]=(B[1,1][z]*B[2,2][z]-2(B[1,2][z])^2+w[0,1][z]*B[1,1][z]*B[1,2][z]-w[0,2][z](B[1,1][z])^2+B[1,1][z]*D[B[1,2][z],z]-D[B[1,1][z],z]*B[1,2][z]);

H7[z_]=(B[1,1][z]*D[B[2,2][z],z]-D[B[1,1][z],z]*B[2,2][z]-2B[1,2][z]*B[2,2][z]+2w[0,1][z]*B[1,1][z]*B[2,2][z]-2w[0,2][z]*B[1,1][z]*B[1,2][z]);

E7[z_]=(H7[z]-(1/6)(D[E6[z],z]+6w[0,1][z]*E6[z]));

x[2,2][z_]=(inv[2,2][z]+w[0,1][z]*w[1,2][z]-(1/5)w[0,2][z]*w[1,1][z]+(w[0,2][z])^2-(1/5)(w[0,1][z])^2*w[1,1][z]-(4/5)(w[0,1][z])^2*w[0,2][z]+(1/5)(w[0,1][z])^4+(1/3)D[w[1,2][z],z]-(1/30)D[w[1,1][z],{z,2}]-(1/6)w[0,1][z]*D[w[1,1][z],z]-(1/15)D[w[0,1][z],z]*w[1,1][z]-(1/3)w[0,1][z]*D[w[0,2][z],z]-(1/3)D[w[0,1][z],z]*w[0,2][z]+(1/15)w[0,1][z]*D[w[0,1][z],{z,2}]+(1/15)(D[w[0,1][z],z])^2+(2/5)(w[0,1][z])^2*D[w[0,1][z],z]);

x[1,2][z_]=(inv[1,2][z]+(1/2)w[0,1][z]*w[1,1][z]+w[0,1][z]*w[0,2][z]-(1/2)(w[0,1][z])^3+(1/4)D[w[1,1][z],z]-(1/2)w[0,1][z]*D[w[0,1][z],z]);

x[1,1][z_]=(inv[1,1][z]+(w[0,1][z])^2);

x[0,2][z_]=(a[2,2][z]+(1/2)D[w[0,1][z],z]+(1/4)(w[0,1][z])^2);

{a1,b1,c1}=Expand[{E6[z],E7[z],D2[z]}/.w[2,2]'[z]->x[2,2]'[z]];

{a2,b2,c2}=Expand[{a1,b1,c1}/.w[2,2][z]->x[2,2][z]];

{a3,b3,c3}=Expand[{a2,b2,c2}/.w[1,2]''[z]->x[1,2]''[z]];

{a4,b4,c4}=Expand[{a3,b3,c3}/.w[1,2]'[z]->x[1,2]'[z]];

{a5,b5,c5}=Expand[{a4,b4,c4}/.w[1,2][z]->x[1,2][z]];

{a6,b6,c6}=Expand[{a5,b5,c5}/.w[1,1]''[z]->x[1,1]''[z]];

{a7,b7,c7}=Expand[{a6,b6,c6}/.w[1,1]'[z]->x[1,1]'[z]];

{a8,b8,c8}=Expand[{a7,b7,c7}/.w[1,1][z]->x[1,1][z]];

{a9,b9,c9}=Expand[{a8,b8,c8}/.w[0,2][z]->x[0,2][z]]