; Subspace Intersection stress test
(lambda (sg zer? zer one fa fm / fneg) (let* (
; (ex (lambda (m v)(write (list m v))(newline) v))
  (I (((fileVal "gIntersect") zer zer? one fa fneg fm /) 'inter))
  (R ((fileVal "gRREF") zer? zer one / fm (lambda (x y) (fa x (fneg y))) #t))
  (rref (R 'rref)) (rank (R 'rank))
  (DoL ((fileVal "Do") 'DoL)))
(ylppa ((fileVal "Matrix") sg zer zer? one fa fneg fm /)
     (lambda (rmg mm inv ip tr det i? v= m=)
     (let ((scr (lambda (a) (mm (let rx () (let ((m (rmg (length a))))
          (if (zer? (det m)) (rx) m))) a))))
(lambda (n a b c)
    (and (>= n (+ a b c)) (let (
  (vsg (lambda (j) (DoL j (lambda (_) (DoL n (lambda (_) (sg))))))))
  (let ss () (let ((A (vsg a)) (B (vsg b)) (C (vsg c)))
    (if (= (+ a b c) (rank (append A B C)))
  (m= (rref (I (scr (append A B)) (scr (append A C))))
      (rref (scr A))) (ss))))))))))))

; tests
(define za ((fileVal "testInter")
 (if #f (let ((w (((fileVal "RC4") "vip4w") 'nb))) (lambda () (modulo (w 1) 7)))
 ((fileVal "rr") "Seed3"))
  zero? 0 1 + * / -))
(za  3 1 1 1) ; => #t
(za  8 3 2 3) ; => #t
(za 10 1 2 2) ; => #t
(za 11 3 4 4) ; => #t
(za 10 4 2 3) ; => #t

; the following version of za tests intersection for finite fields.
; (define (ex m v) (write (list m v))(newline) v)
(define za (ylppa ((fileVal "GFpq") 11 3 "Px")
     (lambda (sg zero zero? one + - * /)
     ((fileVal "testInter") sg zero? zero one + * / -))))
(za  3 1 1 1) ; => #t
(za  8 3 2 3) ; => #t
(za 10 1 2 2) ; => #t
(za 11 3 4 4) ; => #t
(za 10 4 2 3) ; => #t