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Created
January 14, 2024 18:00
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IBP identity for I(2,2) w.r.t. {I(1,1), I(1,2)} of MI
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(%i1) eqn:I12 = I11*(((-d)+3)/(pp-4*m2))+I10*((d-2)/((2*m2)*pp-8*m2^2)) | |
I10 (d - 2) I11 (3 - d) | |
(%o1) I12 = --------------- + ----------- | |
2 pp - 4 m2 | |
2 m2 pp - 8 m2 | |
(%i2) sol:solve(eqn,[I10]) | |
2 | |
2 I12 m2 pp - 8 I12 m2 + (2 I11 d - 6 I11) m2 | |
(%o2) [I10 = ----------------------------------------------] | |
d - 2 | |
(%i3) I22:ev(I11*(((d^2-9*d+18)*pp+(4*d-12)*m2) | |
/(pp^3+((-8)*m2)*pp^2+(16*m2^2)*pp)) | |
+I10*(((d-2)*pp+((-2)*d^2+10*d-12)*m2) | |
/(m2*pp^3+((-8)*m2^2)*pp^2+(16*m2^3)*pp)),sol) | |
2 | |
(%o3) (((d - 2) pp + ((- 2 d ) + 10 d - 12) m2) | |
2 | |
(2 I12 m2 pp - 8 I12 m2 + (2 I11 d - 6 I11) m2)) | |
3 2 2 3 | |
/((d - 2) (m2 pp - 8 m2 pp + 16 m2 pp)) | |
2 | |
I11 ((d - 9 d + 18) pp + (4 d - 12) m2) | |
+ ---------------------------------------- | |
3 2 2 | |
pp - 8 m2 pp + 16 m2 pp | |
(%i4) factor(radcan(coeff(expand(I22),I11))) | |
(d - 4) (d - 3) | |
(%o4) --------------- | |
pp (pp - 4 m2) | |
(%i5) factor(radcan(coeff(expand(I22),I12))) | |
2 (pp - 2 d m2 + 6 m2) | |
(%o5) ---------------------- | |
pp (pp - 4 m2) | |
(%o5) /home/rds/Desktop/test.mac |
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