egison-3.7.8: sample/math/geometry/riemann-curvature-tensor-of-S2xS3-integral.egi
(define $ret3 (/ (+ (* 8 a (sin θ) y) (* -4 a^2 (sin θ) y) (* -4 (sin θ) y)) (* 45 '(+ 1 (* -1 y))^5)))
(define $ret4 (- (let {[$θ π]} (/ (+ (* 8 a (sin θ) y) (* -4 a^2 (sin θ) y) (* -4 (sin θ) y)) (* 45 '(+ 1 (* -1 y))^5)))
(let {[$θ 0]} (/ (+ (* 8 a (sin θ) y) (* -4 a^2 (sin θ) y) (* -4 (sin θ) y)) (* 45 '(+ 1 (* -1 y))^5)))))
"ret4"
ret4
;(/ (+ (* 16 a y) (* -8 a^2 y) (* -8 y)) (* 45 '(+ 1 (* -1 y))^5))
(define $ret5 (d/d (/ (* 2 (+ 1 (* -1 a))^2 (- 1 (* 4 y))) (* 135 '(+ 1 (* -1 y))^4)) y))
"ret5"
ret5
(define $ret6 (/ (expand-all' (numerator ret5)) (denominator ret5)))
"ret6"
ret6
(define $ret7 (/ (* 2 (+ 1 (* -1 a))^2 (- 1 (* 4 y))) (* 135 '(+ 1 (* -1 y))^4)))
(define $y1 (* (/ 1 2) (+ 1 (* -1 λ) (* -1 (sqrt (- 1 (/ λ^2 3)))))))
(define $y2 (+ y1 λ))
(let {[$y y2]} ret7)
(let {[$y y1]} ret7)
(define $ret8 (- (let {[$y y2]} (/ (* 2 (+ 1 (* -1 a))^2 (- 1 (* 4 y))) (* 135 '(+ 1 (* -1 y))^4)))
(let {[$y y1]} (/ (* 2 (+ 1 (* -1 a))^2 (- 1 (* 4 y))) (* 135 '(+ 1 (* -1 y))^4)))))
"ret8"
ret8
;(/ (+ (* -6 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 12 a '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 24 a λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -8 a (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -6 a^2 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 a^2 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 4 a^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 6 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 a '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 24 a λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 8 a (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 6 a^2 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 a^2 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -4 a^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4)) (* 405 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4))
(define $ret9 (let {[$a (- (* 3 y1^2) (* 2 y2^3))]}
(/ (+ (* -6 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 12 a '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 24 a λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -8 a (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -6 a^2 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 a^2 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 4 a^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 6 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 a '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 24 a λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 8 a (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 6 a^2 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -12 a^2 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -4 a^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4)) (* 405 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4))))
"ret9"
ret9
;(/ (+ (* -324 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 54 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -108 λ (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 5742 λ^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -17793 λ^2 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 5544 λ^3 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 162 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -15390 λ^3 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 1548 λ^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 2808 λ^5 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 912 λ^6 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 360 λ^4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 96 λ^7 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -288 λ^5 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -32 λ^6 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -324 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -54 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -108 λ (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -5742 λ^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 17793 λ^2 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 2520 λ^3 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -162 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -6966 λ^3 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -8028 λ^4 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 216 λ^5 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 816 λ^6 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 1368 λ^4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 96 λ^7 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 288 λ^5 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 32 λ^6 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4)) (* 21870 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4))
(define $ret10 (let {[$λ (/ (* 3 q) (* 2 p))]}
(/ (+ (* -324 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 54 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -108 λ (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 5742 λ^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -17793 λ^2 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 5544 λ^3 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 162 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -15390 λ^3 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 1548 λ^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 2808 λ^5 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 912 λ^6 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 360 λ^4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 96 λ^7 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -288 λ^5 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -32 λ^6 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -324 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -54 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -108 λ (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -5742 λ^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 17793 λ^2 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 2520 λ^3 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -162 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -6966 λ^3 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -8028 λ^4 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 216 λ^5 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 816 λ^6 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 1368 λ^4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 96 λ^7 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 288 λ^5 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 32 λ^6 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4)) (* 21870 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4))))
"ret10"
ret10
(define $ret11 (let* {[$p 7]
[$q 3]
[$λ (/ (* 3 q) (* 2 p))]}
(* (/ (+ (* -324 λ '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 54 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -108 λ (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 5742 λ^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -17793 λ^2 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 5544 λ^3 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 162 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -15390 λ^3 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 1548 λ^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 2808 λ^5 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 912 λ^6 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 360 λ^4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 96 λ^7 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -288 λ^5 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -32 λ^6 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -324 λ '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -54 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -108 λ (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -5742 λ^2 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 17793 λ^2 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 2520 λ^3 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -162 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -6966 λ^3 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* -8028 λ^4 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 216 λ^5 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 816 λ^6 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 1368 λ^4 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 96 λ^7 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 288 λ^5 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4) (* 32 λ^6 (sqrt (+ 9 (* -3 λ^2))) '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4)) (* 21870 '(/ (+ 3 (* -3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4 '(/ (+ 3 (* 3 λ) (sqrt (+ 9 (* -3 λ^2)))) 6)^4))
(* 2^4 π^4 (/ q (+ (* 3 q^2) (* -2 p^2) (* p (sqrt (+ (* 4 p^2) (* -3 q^2))))))))))
(expand-all ret11)
;(/ (* -1849 π^4) 22050)