(message "
This is the \"answer key\" for quiz 1, multivariate calculus
")

(message "
Problem 1: plotting points:
")
(data points (1 -1 2) (-1 2 1) (-2 1 -2))
;; (plot points)  doesn't work, because it understands by this a collection of
;; x-coordinates, y-coordinates, and z-coordinates
(title "Three points")
(plot
 (xs points)
 (ys points)
 (zs points)
 )
(send my-plot :showing-axes nil)

(message "
Problem 2: distance between points:
")

(data points (1 2 3) (3 2 1) (1 1 0))
(func distance (x y) sqrt (sum ((x - y) ^ 2))) ; operates component-wise
(print (distance (first points) (second points)))
(print (distance (first points) (third points)))
(print (distance (third points) (second points)))
(print "second and third is smallest")

(message "
Problem 3: plotting functions and cross-sections
")

(func f(x y) x ^ 2 - y)

(title "f(x y)=x ^ 2 - y")
(spin-domain -3 3 -3 3)
(spin-points 20)
(plot f)
(send my-plot :showing-axes nil)

(title "Cross-section for x=1")
(section f 1 1)
(plot my-func -3 3)

(title "Cross-section for y=-1")
(section f 2 -1)
(plot my-func -3 3)

(domain -3 3)
(range -3 12)
(animate f (grid -3 3 11) :loops 3)

(func f(y x) x ^ 2 - y)
(animate f (grid -3 3 11) :loops 3)

(new-plot)