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(in-package #:geodesics)
(eval-when (:compile-toplevel)
(declaim (optimize (speed 3) (safety 0))))
#| This set of functions is for a more interesting case (translated from
Geodesics2.nb). Should reduce to the above no matter equations for c=0,
but don't. We think we understand why -- see above. |#
(defun-with-z-and-chi a (time y)
(declare (double-float time y))
(/ (* A (sqrt (+ 4 (* (- z 1) chi (+ -4 (* 2 c (- z 1)) (* (- z 1) chi))))))
(* (sqrt z) (expt chi 1/4))))
(defun-with-z-and-chi n (time y)
(declare (double-float time y))
(- (/ (+ -4 (* (- z 1) chi (+ -4 (* 2 c (- z 1)) (* 3 (- z 1) chi))))
(* 2 (sqrt z) (sqrt (+ 4 (* (- z 1) chi (+ -4 (* 2 c (- z 1)) (* (- z 1) chi)))))))))
(defun-with-z-and-chi adash (time y)
(declare (double-float time y))
(* dz/dy (/ (* A (+ -4 (* chi (+ -4 (* 2 c (- (* z z) 1)) (* (- (* z z) 1) chi)))))
(* 2 (expt z 3/2) (expt chi 1/4)
(sqrt (+ 4 (* (- z 1) chi (+ -4 (* 2 c (- z 1)) (* (- z 1) chi)))))))))
(defun-with-z-and-chi ndash (time y)
(declare (double-float time y))
(/ (* dz/dy
(- (+ 16
(* 48 (+ -1 (* c (- z 1))) z chi)
(* 4 (- z 1) (+ 6 (* 12 z) (* c (- z 1) (+ (* -2 (+ 2 z)) (* c (- (* z z) 1))) chi chi)))
(* 4 (expt (- z 1) 2) (+ -4 (* -5 z) (* 2 c (- (* z z) 1))) (expt chi 3))
(* 3 (expt (- z 1) 3) (+ z 1) (expt chi 4)))))
(* 4 (expt z 3/2) (expt (+ 4 (* (- z 1) chi (+ -4 (* 2 c (- z 1)) (* (- z 1) chi)))) 3/2))))
(defun-with-z-and-chi da/dt (time y)
(declare (double-float time y))
;; wow!
(* dchi/dt (n time y) (/ (- A) 2 (expt chi 5/4))))
(defun-with-z-and-chi dn/dt (time y)
(declare (double-float time y))
(* dchi/dt
(/ (- (* (- z 1) (+ (* 2 c c (expt (- z 1) 3) chi)
(* 3 (expt (+ -2 (* (- z 1) chi)) 3))
(* c (- z 1) (+ 12 (* (- z 1) chi (+ -8 (* 9 (- z 1) chi))))))))
(* (sqrt z)
(sqrt (+ 4 (* (- z 1) chi (+ -4 (* 2 c (- z 1)) (* (- z 1) chi)))))
(+ 8 (* 2 (- z 1) chi (+ -4 (* 2 c (- z 1)) (* (- z 1) chi))))))))
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