chapter-9.txt

MIT/GNU Scheme running under OS X
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;  ... done
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1 (user) => (define d (lambda (x1 y1 x2 y2)
                        (sqrt (+ (square (- x2 x1)) (square (- y2 y1))))))
#| d |#

1 (user) => (d 0.0 0.0 3.0 4.0)
#| 5. |#

1 (user) => (define h (compose cube sin))
#| h |#

1 (user) => (h 2)
#| .7518269446689928 |#

1 (user) => (cube (sin 2))
#| .7518269446689928 |#

1 (user) => (equal? (h 2) (cube (sin 2)))
#| #t |#

1 (user) => (define g (* cube sin))
#| g |#

1 (user) => (g 2)
#| 7.274379414605454 |#

1 (user) => (compose cube sin)
#|
(lambda (x)
  ???)
|#

1 (user) => ((compose cube sin) 'a)
#|
(expt (sin a) 3)
|#

1 (user) => (- 1 (+ (square sin) (square cos)))
#|
(lambda (x)
  ???)
|#

1 (user) => ((- 1 (+ (square sin) (square cos))) 'a)
#| 0 |#

1 (user) => (print-expression (compose cube sin))
(lambda (x)
  ???)

;No return value.

1 (user) => (print-expression ((compose cube sin) 'a))

;Application of a number not allowed a ((#[compiled-closure 27 (lambda "mathutil" #x1c) #x11e1 #x130182df1 ...]))
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (print-expression ((compose cube sin) 'a))
(expt (sin a) 3)

;No return value.

2 error> (restart 1)

;Abort!

1 (user) => (literal-function 'f)
#| f |#

1 (user) => ((literal-function 'f) 'x)
#|
(f x)
|#

1 (user) => (define f (literal-function 'f))
#| f |#

1 (user) => (define g (literal-function 'g))
#| g |#

1 (user) => (compose f g)
#|
(lambda (x)
  ???)
|#

1 (user) => ((compose f g) 'x)
#|
(f (g x))
|#

1 (user) => (define g (literal-function 'g (-> (X Real Real) Real)))
#| g |#

1 (user) => (g 'a 'b)
#|
(g a b)
|#

1 (user) => (g 'a 'b 'c)

;The procedure #[compiled-closure 28 (lambda "litfun" #x1c) #x45a #x130254182 ...] has been called with 3 arguments; it requires exactly 2 arguments.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Unbalanced close parenthesis: #\)
;To continue, call RESTART with an option number:
; (RESTART 2) => Return to read-eval-print level 2.
; (RESTART 1) => Return to read-eval-print level 1.

3 error> (restart 1)

;Abort!

1 (user) => (D g)
#|
(lambda (x y)
  ???)
|#

1 (user) => ((D g) 'a 'b)
#|
(down (((partial 0) g) a b) (((partial 1) g) a b))
|#

1 (user) => (define v (up 'v^0 'v^1 'v^2))
#| v |#

1 (user) => v
#|
(up v^0 v^1 v^2)
|#

1 (user) => (define u (down 'u_0 'u_1 'u_2))
#| u |#

1 (user) => u
#|
(down u_0 u_1 u_2)
|#

1 (user) => (define p (down 'p_0 'p_1 'p_2))
#| p |#

1 (user) => p
#|
(down p_0 p_1 p_2)
|#

1 (user) => clear
#| #[compiled-closure 29 (lambda "output-port" #x1c) #x84 #x12ead8584 ...] |#

1 (user) => (define s (up 't (up 'x 'y) (down 'p_x 'p_y)))
#| s |#

1 (user) => s
#|
(up t (up x y) (down p_x p_y))
|#

1 (user) => (component s)
#|
(lambda (x)
  ???)
|#

1 (user) => ((component 0) s)
#| t |#

1 (user) => ((component 1) s)
#|
(up x y)
|#

1 (user) => ((component 1 0) s)
#| x |#

1 (user) => ((ref s 1 0))

;Application of a number not allowed x (())
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (ref s 1 0)
#| x |#

1 (user) => (= ((component 1 0) s) (ref s 1 0))
#| #f |#

1 (user) => (equal? ((component 1 0) s) (ref s 1 0))
#| #t |#

1 (user) => p
#|
(down p_0 p_1 p_2)
|#

1 (user) => v
#|
(up v^0 v^1 v^2)
|#

1 (user) => (* p v)
#|
(+ (* p_0 v^0) (* p_1 v^1) (* p_2 v^2))
|#

1 (user) => (* p v)
#|
(+ (* p_0 v^0) (* p_1 v^1) (* p_2 v^2))
|#

1 (user) => ((D sin) 'x)
#|
(cos x)
|#

1 (user) => (D sin)
#| a-euclidean-derivative |#

1 (user) => (sin 'x)
#|
(sin x)
|#

1 (user) => ((D cos) 'x)
#|
(* -1 (sin x))
|#

1 (user) => (D (cos 'x))

;Generic operator inapplicable: #[compiled-closure 30 (lambda "ghelper" #x3) #x59b #x12ff0c9cb ...] partial-derivative ((*number* (expression (cos x))) ())
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (cos 'x)
#|
(cos x)
|#

1 (user) => ((g(* 5 D) cos) 'x)
#|
(* -5 (sin x))
|#

1 (user) => 
#| #f |#

1 (user) => (+ D I)
#|
(+ D (lambda x ???))
|#

1 (user) => (* (+ D I) (- D I))
#|
(+ (expt D 2) (* -1 (expt (lambda x ???) 2)))
|#

1 (user) => (((* (+ D I) (- D I)) (literal-function 'f)) 'x)
#|
(+ (((expt D 2) f) x) (* -1 (f x)))
|#

1 (user) => g
#| g |#

1 (user) => ((D g) 'x 'y)
#|
(down (((partial 0) g) x y) (((partial 1) g) x y))
|#

1 (user) => h
#| h |#

1 (user) => (define (h s) (g (ref s 0) (ref s 1)))
#| h |#

1 (user) => (h (up 'x 'y))
#|
(g x y)
|#

1 (user) => h
#| h |#

1 (user) => g
#| g |#

1 (user) => (define g (literal-function 'g (-> (X Real Real) Real)))
#| g |#

1 (user) => (g 'x 'y)
#|
(g x y)
|#

1 (user) => s
#|
(up t (up x y) (down p_x p_y))
|#

1 (user) => (ref s 0)
#| t |#

1 (user) => (ref s 1)
#|
(up x y)
|#

1 (user) => (define (h s)
              (g (ref s 0) (ref s 1)))
#| h |#

1 (user) => (h (up 'x 'y))
#|
(g x y)
|#

1 (user) => s
#|
(up t (up x y) (down p_x p_y))
|#

1 (user) => (h s)

;Assertion failed: (&and (map (lambda (p x) (p x)) dpreds args)) "Wrong type argument -- LITERAL-FUNCTION" (g t #(x y))
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (g 'x 'y)
#|
(g x y)
|#

1 (user) => ((D g) (up 'x 'y))

;The procedure #[compiled-closure 31 (lambda "deriv" #x2) #x8cc #x13019492c ...] has been called with 1 argument; it requires exactly 2 arguments.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => ((D g) 'x 'y)
#|
(down (((partial 0) g) x y) (((partial 1) g) x y))
|#

1 (user) => ((D h) (up 'x 'y))
#|
(down (((partial 0) g) x y) (((partial 1) g) x y))
|#

1 (user) => s
#|
(up t (up x y) (down p_x p_y))
|#

1 (user) => (define helix (up cos sin identity))
#| helix |#

1 (user) => (helix 't)
#|
(up (cos t) (sin t) t)
|#

1 (user) => (D helix)
#| a-euclidean-derivative |#

1 (user) => ((D helix) 't)
#|
(up (* -1 (sin t)) (cos t) 1)
|#

1 (user) => (define (g x y))

;Ill-formed syntax: (define (g x y))
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (define (g x y)
(up (square (+ x y)) (cube (- y x)) (exp (+ x y))))
#| g |#

1 (user) => g
#| g |#

1 (user) => (g 'x 'y)
#|
(up (+ (expt x 2) (* 2 x y) (expt y 2))
    (+ (* -1 (expt x 3)) (* 3 (expt x 2) y) (* -3 x (expt y 2)) (expt y 3))
    (* (exp y) (exp x)))
|#

1 (user) => (g 'a 'b)
#|
(up (+ (expt a 2) (* 2 a b) (expt b 2))
    (+ (* -1 (expt a 3)) (* 3 (expt a 2) b) (* -3 a (expt b 2)) (expt b 3))
    (* (exp b) (exp a)))
|#

1 (user) => helix
#|
(up cos sin identity)
|#

1 (user) => (D helix)
#| a-euclidean-derivative |#

1 (user) => ((D helix) 't)
#|
(up (* -1 (sin t)) (cos t) 1)
|#

1 (user) => (define g (up (square (+ 'x 'y)) (expt (cube (- 'y 'x) 3)) (expt (+ 'x 'y))))

;The procedure #[compiled-procedure 32 (g:expt "generic" #x1f) #x14 #x12ff0f9cc] has been called with 1 argument; it requires exactly 2 arguments.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (define (g x y)
              (up (square (+ x y)) (cube (- y x)) (exp (+ x y))))
#| g |#

1 (user) => g
#| g |#

1 (user) => (g 'a 'b)
#|
(up (+ (expt a 2) (* 2 a b) (expt b 2))
    (+ (* -1 (expt a 3)) (* 3 (expt a 2) b) (* -3 a (expt b 2)) (expt b 3))
    (* (exp b) (exp a)))
|#

1 (user) => ((D g) 'x 'y)
#|
(down (up (+ (* 2 x) (* 2 y)) (+ (* -3 (expt x 2)) (* 6 x y) (* -3 (expt y 2))) (* (exp y) (exp x)))
      (up (+ (* 2 x) (* 2 y)) (+ (* 3 (expt x 2)) (* -6 x y) (* 3 (expt y 2))) (* (exp y) (exp x))))
|#

1 (user) => (define (F x y) (* (square x) (cube y)))
#| F |#

1 (user) => (F 'x 'y)
#|
(* (expt x 2) (expt y 3))
|#

1 (user) => (define (G x y) (up (F x y) y))
#| G |#

1 (user) => (G 'x 'y)
#|
(up (* (expt x 2) (expt y 3)) y)
|#

1 (user) => (define H (compose F G))
#| H |#

1 (user) => (H 'x 'y)

;The procedure #[compound-procedure 33 F] has been called with 1 argument; it requires exactly 2 arguments.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => H
#| H |#

1 (user) => (define (h x y)
              (f (f x y) y))
#| h |#

1 (user) => (define (H x y)
              (f (f x y) y))
#| H |#

1 (user) => F
#| F |#

1 (user) => G
#| G |#

1 (user) => H
#| H |#

1 (user) => (F 'x 'y)
#|
(* (expt x 2) (expt y 3))
|#

1 (user) => (G 'x 'y)
#|
(up (* (expt x 2) (expt y 3)) y)
|#

1 (user) => (H 'x 'y)

;The procedure #[compiled-closure 34 (lambda "litfun" #x1c) #x420 #x1300671d0 ...] has been called with 2 arguments; it requires exactly 1 argument.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (define (f x y)
  (* (square x) (cube y)))

(define (g x y)
  (up (f x y) y))

(define (h x y)
  (f (f x y) y))
#| f |#

2 error> #| g |#

2 error> #| h |#

2 error> (restart 1)

;Abort!

1 (user) => (define (f x y)
  (* (square x) (cube y)))

(define (g x y)
  (up (f x y) y))

(define (h x y)
  (f (f x y) y))
#| f |#

1 (user) => #| g |#

1 (user) => #| h |#

1 (user) => (g 'x 'y)
#|
(up (* (expt x 2) (expt y 3)) y)
|#

1 (user) => (h 'x 'y)
#|
(* (expt x 4) (expt y 9))
|#

1 (user) => F
#| F |#

1 (user) => (F 'x 'y)
#|
(* (expt x 2) (expt y 3))
|#

1 (user) => ((D F) 'x 'y)
#|
(down (* 2 x (expt y 3)) (* 3 (expt x 2) (expt y 2)))
|#

1 (user) => (ref ((D F) 'x 'y)) 0)
#|
(down (* 2 x (expt y 3)) (* 3 (expt x 2) (expt y 2)))
|#

1 (user) => #| 0 |#

1 (user) => (ref (D F) 'x 'y) 0)
#|
(lambda (x y)
  ???)
|#

1 (user) => #| 0 |#

1 (user) => (ref (D F)) 0)
#|
(lambda (x y)
  ???)
|#

1 (user) => #| 0 |#

1 (user) => ((ref (D F)) 0) 'x 'y)

;The procedure #[compiled-closure 35 (lambda "deriv" #x2) #x8cc #x13019492c ...] has been called with 1 argument; it requires exactly 2 arguments.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> #| x |#

2 error> #| y |#

2 error> (restart 1)

;Abort!

1 (user) => ((component 0) (D F))
#|
(lambda (x y)
  ???)
|#

1 (user) => ((component 0) ((D F) 'x 'y))
#|
(* 2 x (expt y 3))
|#

1 (user) => ((component 1) ((D F) 'x 'y))
#|
(* 3 (expt x 2) (expt y 2))
|#

1 (user) => ((D H) 'x 'y)
#|
(down (* 4 (expt x 3) (expt y 9)) (* 9 (expt x 4) (expt y 8)))
|#

1 (user) => ((component 0) ((D H) 'x 'y))
#|
(* 4 (expt x 3) (expt y 9))
|#

1 (user) => ((component 1) ((D H) 'x 'y))
#|
(* 9 (expt x 4) (expt y 8))
|#

1 (user) => (H 'x 'y)
#|
(* (expt x 4) (expt y 9))
|#

1 (user) => F
#| F |#

1 (user) => (F 'x 'y)
#|
(* (expt x 2) (expt y 3))
|#

1 (user) => (G 'x 'y)
#|
(up (* (expt x 2) (expt y 3)) y)
|#

1 (user) => (define (H x y)
              (f (f x y) y))
#| h |#

1 (user) => (define (H x y)
              (f (f x y) y))
#| H |#

1 (user) => ((component 0) ((D H) 'x 'y))
#|
(* 4 (expt x 3) (expt y 9))
|#

1 (user) => (let ((f (down ((partial 0) F) ((partial 1) F))))
  (->tex-equation
   (f 'x 'y)))

;Unbound variable: ->tex-equation
;To continue, call RESTART with an option number:
; (RESTART 3) => Specify a value to use instead of ->tex-equation.
; (RESTART 2) => Define ->tex-equation to a given value.
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (F 'x 'y)
#|
(* (expt x 2) (expt y 3))
|#

1 (user) => (G 'x 'y)
#|
(up (* (expt x 2) (expt y 3)) y)
|#

1 (user) => (H 'x 'y)
#|
(* (expt x 4) (expt y 9))
|#

1 (user) => (((component 0) (D G)) 'x 'y)
#|
(up (* 2 x (expt y 3)) 0)
|#

1 (user) => (((component 1) (D G)) 'x 'y)
#|
(up (* 3 (expt x 2) (expt y 2)) 1)
|#

1 (user) => ((partial 0) F)
#|
(lambda (x y)
  ???)
|#

1 (user) => (((partial 0) F) 'x 'y)
#|
(* 2 x (expt y 3))
|#

1 (user) => (down (((partial 0) F) 'x 'y))
#|
(down (* 2 x (expt y 3)))
|#

1 (user) => ((D H) 'x 'y)
#|
(down (* 4 (expt x 3) (expt y 9)) (* 9 (expt x 4) (expt y 8)))
|#

1 (user) => (H 'x 'y)
#|
(* (expt x 4) (expt y 9))
|#

1 (user) => (F 'x 'y)
#|
(* (expt x 2) (expt y 3))
|#

1 (user) => ((D F) 'x 'y)
#|
(down (* 2 x (expt y 3)) (* 3 (expt x 2) (expt y 2)))
|#

1 (user) => (G 'x 'y)
#|
(up (* (expt x 2) (expt y 3)) y)
|#

1 (user) => (((D G) 'x 'y)
#|
(down (up (* 2 x (expt y 3)) 0) (up (* 3 (expt x 2) (expt y 2)) 1))
|#

1 (user) => (((D G) 'x 'y) ref 0)

;Application of a number not allowed (*number* (expression (* 2 x y y ...))) ((#[compiled-procedure 36 (g:ref "mathutil" #x13) #x14 #x130126f7c] 0))
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart)

;Choose an option by number:
;  1: Return to read-eval-print level 1.

Option number: 1

;Abort!

1 (user) => ((D G) 'x 'y))

#|
(down (up (* 2 x (expt y 3)) 0) (up (* 3 (expt x 2) (expt y 2)) 1))
|#

1 (user) => ((D F) 'a 'b)
#|
(down (* 2 a (expt b 3)) (* 3 (expt a 2) (expt b 2)))
|#

1 (user) => ((D G) 3 5)
#|
(down (up 750 0) (up 675 1))
|#

1 (user) => ((D H) (* 3 (expt 'a 2)) (* 5 (expt b 3)))

;Unbound variable: b
;To continue, call RESTART with an option number:
; (RESTART 3) => Specify a value to use instead of b.
; (RESTART 2) => Define b to a given value.
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (* 3 (expt 'a 2))
#|
(* 3 (expt a 2))
|#

1 (user) => (* 5 (expt b 3))

;Unbound variable: b
;To continue, call RESTART with an option number:
; (RESTART 3) => Specify a value to use instead of b.
; (RESTART 2) => Define b to a given value.
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (* 5 (expt 'b 3))
#|
(* 5 (expt b 3))
|#

1 (user) => ((D H) (* 3 (expt 'a 2)) (* 5 (expt 'b 3)))
#|
(down (* 210937500 (expt a 6) (expt b 27)) (* 284765625 (expt a 8) (expt b 24)))
|#

1 (user) => (define F2 (lambda v) 
              (v))

;Ill-formed syntax: (lambda v)
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (define F2 (lambda (v) 
              (v)))
#| F2 |#

2 error> (define F2 (lambda (v) 
              ()))
#| F2 |#
z3
2 error> (define F2 (lambda (v) 
              (let ((x (ref v 0))
                    (y (ref v 1))
                    (* (square x) (cube y))))))

;Ill-formed syntax: (let ((x (ref v 0)) (y (ref v 1)) (* (square x) (cube y))))
;To continue, call RESTART with an option number:
; (RESTART 2) => Return to read-eval-print level 2.
; (RESTART 1) => Return to read-eval-print level 1.

3 error> (restart 1)

;Abort!
x
1 (user) => (define a (lambda (b) (square b)))
#| a |#

1 (user) => (a 2)
#| 4 |#

1 (user) => (define (a b) (square b))
#| a |#

1 (user) => (a 3)
#| 9 |#

1 (user) => ((partial 0 F) 'x 'y)

;The procedure #[compiled-closure 37 (lambda "generic" #x10) #x9b #x13002d4a3 ...] has been called with 2 arguments; it requires exactly 1 argument.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (return 1)

;Unbound variable: return
;To continue, call RESTART with an option number:
; (RESTART 4) => Specify a value to use instead of return.
; (RESTART 3) => Define return to a given value.
; (RESTART 2) => Return to read-eval-print level 2.
; (RESTART 1) => Return to read-eval-print level 1.

3 error> (restart 1)

;Abort!

1 (user) => ((D F) 'x 'y)
#|
(down (* 2 x (expt y 3)) (* 3 (expt x 2) (expt y 2)))
|#

1 (user) => ((component 0) ((D F) 'x 'y))
#|
(* 2 x (expt y 3))
|#

1 (user) => ((component 1) ((D F) 'x 'y))
#|
(* 3 (expt x 2) (expt y 2))
|#

1 (user) => ((component 0) ((D H) 'x 'y))
#|
(* 4 (expt x 3) (expt y 9))
|#

1 (user) => ((component 1) ((D H) 'x 'y))
#|
(* 9 (expt x 4) (expt y 8))
|#

1 (user) => ((component 0) ((D G) 'x 'y))
#|
(up (* 2 x (expt y 3)) 0)
|#

1 (user) => ((component 1) ((D G) 'x 'y))
#|
(up (* 3 (expt x 2) (expt y 2)) 1)
|#

1 (user) => ((D G) 3 5)
#|
(down (up 750 0) (up 675 1))
|#

1 (user) => (define expr '(integrate (* x (sin x)) x))
#| expr-tag |#

1 (user) => expr
#|
(integrate (* x (sin x)) x)
|#

1 (user) => (latexize expr)

;Unbound variable: latexize
;To continue, call RESTART with an option number:
; (RESTART 3) => Specify a value to use instead of latexize.
; (RESTART 2) => Define latexize to a given value.
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (expression->tex-string expr)
#| "\\boxit{ $$integrate\\left( x \\sin\\left( x \\right), x \\right)$$}" |#

1 (user) => (expression->tex-string ((D H) (* 3 (expt 'a 2)) (* 5 (expt 'b 3))))

;The object #((*number* (expression (* 210937500 (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt b 3) (expt b 3) (expt b 3)))) (*number* (expression (+ (* 2531250 (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt a 2) (expt a 2) (+ (* 5 (+ (* 5 (expt b 3)) (* 5 (expt b 3))) (expt b 3)) (* 25 (expt b 3) (expt b 3))) (expt b 3) (expt b 3) (expt b 3)) (* 1265625 (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (+ (* 5 (+ (* 5 (expt b 3)) (* 5 (expt b 3))) (expt b 3)) (* 25 (expt b 3) (expt b 3)))))))), passed as the first argument to car, is not the correct type.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (expression->tex-string (sin 'a))
#| "\\boxit{ $$*number*\\left( expression\\left( \\sin\\left( a \\right) \\right) \\right)$$}" |#

1 (user) => (D H) (* 3 (expt 'a 2)) (* 5 (expt 'b 3))
#|
(lambda (x y)
  ???)
|#

1 (user) => #|
(* 3 (expt a 2))
|#

1 (user) => #|
(* 5 (expt b 3))
|#

1 (user) => ((D H) (* 3 (expt 'a 2)) (* 5 (expt 'b 3)))
#|
(down (* 210937500 (expt a 6) (expt b 27)) (* 284765625 (expt a 8) (expt b 24)))
|#

1 (user) => (define expr ((D H) (* 3 (expt 'a 2)) (* 5 (expt 'b 3))))
#| expr-tag |#

1 (user) => exprt

;Unbound variable: exprt
;To continue, call RESTART with an option number:
; (RESTART 3) => Specify a value to use instead of exprt.
; (RESTART 2) => Define exprt to a given value.
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => expr
#|
(down (* 210937500 (expt a 6) (expt b 27)) (* 284765625 (expt a 8) (expt b 24)))
|#

1 (user) => (expression->tex-string expr)

;The object #((*number* (expression (* 210937500 (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt b 3) (expt b 3) (expt b 3)))) (*number* (expression (+ (* 2531250 (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt a 2) (expt a 2) (+ (* 5 (+ (* 5 (expt b 3)) (* 5 (expt b 3))) (expt b 3)) (* 25 (expt b 3) (expt b 3))) (expt b 3) (expt b 3) (expt b 3)) (* 1265625 (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (expt a 2) (expt a 2) (expt b 3) (expt b 3) (expt b 3) (+ (* 5 (+ (* 5 (expt b 3)) (* 5 (expt b 3))) (expt b 3)) (* 25 (expt b 3) (expt b 3)))))))), passed as the first argument to car, is not the correct type.
;To continue, call RESTART with an option number:
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => ((component 0) expr)
#|
(* 210937500 (expt a 6) (expt b 27))
|#

1 (user) => (expression-tex-string ((component 0) expr))

;Unbound variable: expression-tex-string
;To continue, call RESTART with an option number:
; (RESTART 3) => Specify a value to use instead of expression-tex-string.
; (RESTART 2) => Define expression-tex-string to a given value.
; (RESTART 1) => Return to read-eval-print level 1.

2 error> (restart 1)

;Abort!

1 (user) => (message "hellp")

hellp
;No return value.

1 (user) =>