(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)