Bribing a computer to compute the roots of (A4f) polynomial.

  Our (A4f) polynomial was

   h(x)  =  [x + 5] * [x - 11] * [x + 37].

In class, we saw its reduction mod 8, mod 3, and  mod 5,
and we found the respective roots.
 
  Promising my computer an extra mouse, I asked its help:

=========================================================

& (defun hof (x) (* (+ x 5) (- x 11) (+ x 37)))

& (setq CRT-8-3-5 (cree-crt 8 3 5))  =>

#S(CHINESE-FUSION::CRTSTR :EUCLDOM #1=<<RING: InTeGeRs>>
   :PROD 120 :MODULI #(8 3 5)
   :OMITTEDPRODS #(15 40 24) :MAGICNUMS #(105 40 96))

& (setq U (CRTSTR-PROD CRT-8-3-5)) => 120

& (setq roots8 '(1 3 5 7)   roots3 '(1 2)   roots5 '(0 1 3))

& (print-h-table roots8 roots3 roots5)


root8 root3 root5 | URoot |  h(URoot)  | Mod-U
    1     1     0 |    25 |      26040 |   0
    1     1     1 |     1 |      -2280 |   0
    1     1     3 |   -47 |     -24360 |   0
    1     2     0 |   -55 |     -59400 |   0
    1     2     1 |    41 |     107640 |   0
    1     2     3 |    -7 |       1080 |   0
    3     1     0 |    -5 |          0 |   0
    3     1     1 |   -29 |       7680 |   0
    3     1     3 |    43 |     122880 |   0
    3     2     0 |    35 |      69120 |   0
    3     2     1 |    11 |          0 |   0
    3     2     3 |   -37 |          0 |   0
    5     1     0 |   -35 |       2760 |   0
    5     1     1 |   -59 |     -83160 |   0
    5     1     3 |    13 |       1800 |   0
    5     2     0 |     5 |      -2520 |   0
    5     2     1 |   -19 |       7560 |   0
    5     2     3 |    53 |     219240 |   0
    7     1     0 |    55 |     242880 |   0
    7     1     1 |    31 |      48960 |   0
    7     1     3 |   -17 |       6720 |   0
    7     2     0 |   -25 |       8640 |   0
    7     2     1 |   -49 |     -31680 |   0
    7     2     3 |    23 |      20160 |   0

========