(/VERSIONCHECK 2) 

(DECLAIM (FTYPE (FUNCTION (|%Shell|) (|%IntegerSection| 0))
                |INS-;characteristic;Nni;1|)) 

(PUT '|INS-;characteristic;Nni;1| '|SPADreplace| '(XLAM NIL 0)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;differentiate;2S;2|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|)
                |INS-;even?;SB;3|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|)
                |INS-;positive?;SB;4|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;copy;2S;5|)) 

(PUT '|INS-;copy;2S;5| '|SPADreplace| '(XLAM (|x|) |x|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|)
                |INS-;bit?;2SB;6|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;mask;2S;7|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|)
                |INS-;rational?;SB;8|)) 

(PUT '|INS-;rational?;SB;8| '|SPADreplace| '(XLAM (|x|) T)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%IntegerSection| 0))
                |INS-;euclideanSize;SNni;9|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;convert;SF;10|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%DoubleFloat|)
                |INS-;convert;SDf;11|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;convert;SIf;12|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Integer|)
                |INS-;retract;SI;13|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;convert;SP;14|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;factor;SF;15|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;squareFree;SF;16|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|)
                |INS-;prime?;SB;17|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;factorial;2S;18|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|)
                |INS-;binomial;3S;19|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|)
                |INS-;permutation;3S;20|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Pair|)
                |INS-;retractIfCan;SU;21|)) 

(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Thing|) |INS-;init;S;22|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Pair|)
                |INS-;nextItem;SU;23|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|)
                    |%Thing|)
                |INS-;patternMatch;SP2Pmr;24|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|)
                |INS-;rational;SF;25|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Pair|)
                |INS-;rationalIfCan;SU;26|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|)
                |INS-;symmetricRemainder;3S;27|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|)
                |INS-;invmod;3S;28|)) 

(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|)
                    |%Thing|)
                |INS-;powmod;4S;29|)) 

(DEFUN |INS-;characteristic;Nni;1| ($) (DECLARE (IGNORE $)) 0) 

(DEFUN |INS-;differentiate;2S;2| (|x| $) (|spadConstant| $ 10)) 

(DEFUN |INS-;even?;SB;3| (|x| $)
  (NOT (SPADCALL |x| (|getShellEntry| $ 13)))) 

(DEFUN |INS-;positive?;SB;4| (|x| $)
  (SPADCALL |x| (|spadConstant| $ 10) (|getShellEntry| $ 16))) 

(DEFUN |INS-;copy;2S;5| (|x| $) (DECLARE (IGNORE $)) |x|) 

(DEFUN |INS-;bit?;2SB;6| (|x| |i| $)
  (SPADCALL
      (SPADCALL |x| (SPADCALL |i| (|getShellEntry| $ 19))
          (|getShellEntry| $ 20))
      (|getShellEntry| $ 13))) 

(DEFUN |INS-;mask;2S;7| (|n| $)
  (SPADCALL (SPADCALL (|spadConstant| $ 22) |n| (|getShellEntry| $ 20))
      (|getShellEntry| $ 23))) 

(DEFUN |INS-;rational?;SB;8| (|x| $) (DECLARE (IGNORE $)) T) 

(DEFUN |INS-;euclideanSize;SNni;9| (|x| $)
  (COND
    ((SPADCALL |x| (|spadConstant| $ 10) (|getShellEntry| $ 27))
     (|error| "euclideanSize called on zero"))
    ((SPADCALL |x| (|spadConstant| $ 10) (|getShellEntry| $ 28))
     (LET ((#0=#:G1426 (- (SPADCALL |x| (|getShellEntry| $ 30)))))
       (|check-subtype| (NOT (MINUSP #0#)) '(|NonNegativeInteger|) #0#)))
    (T (LET ((#1=#:G1427 (SPADCALL |x| (|getShellEntry| $ 30))))
         (|check-subtype| (NOT (MINUSP #1#)) '(|NonNegativeInteger|)
             #1#))))) 

(DEFUN |INS-;convert;SF;10| (|x| $)
  (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30))
      (|getShellEntry| $ 34))) 

(DEFUN |INS-;convert;SDf;11| (|x| $)
  (FLOAT (SPADCALL |x| (|getShellEntry| $ 30)) |$DoubleFloatMaximum|)) 

(DEFUN |INS-;convert;SIf;12| (|x| $)
  (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30))
      (|getShellEntry| $ 40))) 

(DEFUN |INS-;retract;SI;13| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 30))) 

(DEFUN |INS-;convert;SP;14| (|x| $)
  (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30))
      (|getShellEntry| $ 44))) 

(DEFUN |INS-;factor;SF;15| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 48))) 

(DEFUN |INS-;squareFree;SF;16| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 51))) 

(DEFUN |INS-;prime?;SB;17| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 54))) 

(DEFUN |INS-;factorial;2S;18| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 57))) 

(DEFUN |INS-;binomial;3S;19| (|n| |m| $)
  (SPADCALL |n| |m| (|getShellEntry| $ 59))) 

(DEFUN |INS-;permutation;3S;20| (|n| |m| $)
  (SPADCALL |n| |m| (|getShellEntry| $ 61))) 

(DEFUN |INS-;retractIfCan;SU;21| (|x| $)
  (CONS 0 (SPADCALL |x| (|getShellEntry| $ 30)))) 

(DEFUN |INS-;init;S;22| ($) (|spadConstant| $ 10)) 

(DEFUN |INS-;nextItem;SU;23| (|n| $)
  (COND
    ((SPADCALL |n| (|getShellEntry| $ 66))
     (CONS 0 (|spadConstant| $ 22)))
    ((SPADCALL |n| (|spadConstant| $ 10) (|getShellEntry| $ 16))
     (CONS 0 (SPADCALL |n| (|getShellEntry| $ 19))))
    (T (CONS 0
             (SPADCALL (|spadConstant| $ 22) |n|
                 (|getShellEntry| $ 67)))))) 

(DEFUN |INS-;patternMatch;SP2Pmr;24| (|x| |p| |l| $)
  (SPADCALL |x| |p| |l| (|getShellEntry| $ 72))) 

(DEFUN |INS-;rational;SF;25| (|x| $)
  (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30))
      (|getShellEntry| $ 76))) 

(DEFUN |INS-;rationalIfCan;SU;26| (|x| $)
  (CONS 0
        (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30))
            (|getShellEntry| $ 76)))) 

(DEFUN |INS-;symmetricRemainder;3S;27| (|x| |n| $)
  (LET ((|r| (SPADCALL |x| |n| (|getShellEntry| $ 80))))
    (COND
      ((SPADCALL |r| (|spadConstant| $ 10) (|getShellEntry| $ 27)) |r|)
      (T (SEQ (COND
                ((SPADCALL |n| (|spadConstant| $ 10)
                     (|getShellEntry| $ 28))
                 (SETQ |n| (SPADCALL |n| (|getShellEntry| $ 19)))))
              (EXIT (COND
                      ((SPADCALL |r| (|spadConstant| $ 10)
                           (|getShellEntry| $ 16))
                       (COND
                         ((SPADCALL
                              (SPADCALL 2 |r| (|getShellEntry| $ 82))
                              |n| (|getShellEntry| $ 16))
                          (SPADCALL |r| |n| (|getShellEntry| $ 67)))
                         (T |r|)))
                      ((NOT (SPADCALL
                                (SPADCALL
                                    (SPADCALL 2 |r|
                                     (|getShellEntry| $ 82))
                                    |n| (|getShellEntry| $ 83))
                                (|spadConstant| $ 10)
                                (|getShellEntry| $ 16)))
                       (SPADCALL |r| |n| (|getShellEntry| $ 83)))
                      (T |r|)))))))) 

(DEFUN |INS-;invmod;3S;28| (|a| |b| $)
  (PROG (|c| |c1| |d| |d1| |q| |r| |r1|)
    (RETURN
      (SEQ (COND
             ((SPADCALL |a| (|getShellEntry| $ 85))
              (SETQ |a| (SPADCALL |a| |b| (|getShellEntry| $ 86)))))
           (LETT |c| |a| |INS-;invmod;3S;28|)
           (LETT |c1| (|spadConstant| $ 22) |INS-;invmod;3S;28|)
           (LETT |d| |b| |INS-;invmod;3S;28|)
           (LETT |d1| (|spadConstant| $ 10) |INS-;invmod;3S;28|)
           (LOOP
             (COND
               ((NOT (NOT (SPADCALL |d| (|getShellEntry| $ 66))))
                (RETURN NIL))
               (T (SEQ (LETT |q|
                             (SPADCALL |c| |d| (|getShellEntry| $ 87))
                             |INS-;invmod;3S;28|)
                       (LETT |r|
                             (SPADCALL |c|
                                 (SPADCALL |q| |d|
                                     (|getShellEntry| $ 88))
                                 (|getShellEntry| $ 67))
                             |INS-;invmod;3S;28|)
                       (LETT |r1|
                             (SPADCALL |c1|
                                 (SPADCALL |q| |d1|
                                     (|getShellEntry| $ 88))
                                 (|getShellEntry| $ 67))
                             |INS-;invmod;3S;28|)
                       (SETQ |c| |d|) (SETQ |c1| |d1|) (SETQ |d| |r|)
                       (EXIT (SETQ |d1| |r1|))))))
           (COND
             ((NOT (SPADCALL |c| (|getShellEntry| $ 89)))
              (EXIT (|error| "inverse does not exist"))))
           (EXIT (COND
                   ((SPADCALL |c1| (|getShellEntry| $ 85))
                    (SPADCALL |c1| |b| (|getShellEntry| $ 83)))
                   (T |c1|))))))) 

(DEFUN |INS-;powmod;4S;29| (|x| |n| |p| $)
  (PROG (|y| |z|)
    (RETURN
      (SEQ (COND
             ((SPADCALL |x| (|getShellEntry| $ 85))
              (SETQ |x| (SPADCALL |x| |p| (|getShellEntry| $ 86)))))
           (EXIT (COND
                   ((SPADCALL |x| (|getShellEntry| $ 66))
                    (|spadConstant| $ 10))
                   ((SPADCALL |n| (|getShellEntry| $ 66))
                    (|spadConstant| $ 22))
                   (T (SEQ (LETT |y| (|spadConstant| $ 22)
                                 |INS-;powmod;4S;29|)
                           (LETT |z| |x| |INS-;powmod;4S;29|)
                           (EXIT (LOOP
                                   (COND
                                     (NIL (RETURN NIL))
                                     (T
                                      (SEQ
                                       (COND
                                         ((SPADCALL |n|
                                           (|getShellEntry| $ 13))
                                          (SETQ |y|
                                           (SPADCALL |y| |z| |p|
                                            (|getShellEntry| $ 91)))))
                                       (EXIT
                                        (COND
                                          ((SPADCALL
                                            (SETQ |n|
                                             (SPADCALL |n|
                                              (SPADCALL
                                               (|spadConstant| $ 22)
                                               (|getShellEntry| $ 19))
                                              (|getShellEntry| $ 20)))
                                            (|getShellEntry| $ 66))
                                           (RETURN-FROM
                                            |INS-;powmod;4S;29|
                                             |y|))
                                          (T
                                           (SETQ |z|
                                            (SPADCALL |z| |z| |p|
                                             (|getShellEntry| $ 91))))))))))))))))))) 

(DEFUN |IntegerNumberSystem&| (|#1|)
  (LET* ((|dv$1| (|devaluate| |#1|))
         (|dv$| (LIST '|IntegerNumberSystem&| |dv$1|))
         ($ (|newShell| 93)) (|pv$| (|buildPredVector| 0 0 NIL)))
    (|setShellEntry| $ 0 |dv$|)
    (|setShellEntry| $ 3 |pv$|)
    (|stuffDomainSlots| $)
    (|setShellEntry| $ 6 |#1|)
    $)) 

(MAKEPROP '|IntegerNumberSystem&| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|)
             (|NonNegativeInteger|) (0 . |Zero|)
             |INS-;characteristic;Nni;1| (4 . |Zero|)
             |INS-;differentiate;2S;2| (|Boolean|) (8 . |odd?|)
             (13 . |not|) |INS-;even?;SB;3| (18 . >)
             |INS-;positive?;SB;4| |INS-;copy;2S;5| (24 . -)
             (29 . |shift|) |INS-;bit?;2SB;6| (35 . |One|) (39 . |dec|)
             |INS-;mask;2S;7| (44 . |true|) |INS-;rational?;SB;8|
             (48 . =) (54 . <) (|Integer|) (60 . |convert|) (65 . -)
             |INS-;euclideanSize;SNni;9| (|Float|) (70 . |coerce|)
             |INS-;convert;SF;10| (|DoubleFloat|) (75 . |coerce|)
             |INS-;convert;SDf;11| (|InputForm|) (80 . |convert|)
             |INS-;convert;SIf;12| |INS-;retract;SI;13| (|Pattern| 29)
             (85 . |coerce|) |INS-;convert;SP;14| (|Factored| 6)
             (|IntegerFactorizationPackage| 6) (90 . |factor|)
             (|Factored| $) |INS-;factor;SF;15| (95 . |squareFree|)
             |INS-;squareFree;SF;16| (|IntegerPrimesPackage| 6)
             (100 . |prime?|) |INS-;prime?;SB;17|
             (|IntegerCombinatoricFunctions| 6) (105 . |factorial|)
             |INS-;factorial;2S;18| (110 . |binomial|)
             |INS-;binomial;3S;19| (116 . |permutation|)
             |INS-;permutation;3S;20| (|Union| 29 '"failed")
             |INS-;retractIfCan;SU;21| |INS-;init;S;22| (122 . |zero?|)
             (127 . -) (|Union| $ '"failed") |INS-;nextItem;SU;23|
             (|PatternMatchResult| 29 6)
             (|PatternMatchIntegerNumberSystem| 6)
             (133 . |patternMatch|) (|PatternMatchResult| 29 $)
             |INS-;patternMatch;SP2Pmr;24| (|Fraction| 29)
             (140 . |coerce|) |INS-;rational;SF;25|
             (|Union| 75 '"failed") |INS-;rationalIfCan;SU;26|
             (145 . |rem|) (|PositiveInteger|) (151 . *) (157 . +)
             |INS-;symmetricRemainder;3S;27| (163 . |negative?|)
             (168 . |positiveRemainder|) (174 . |quo|) (180 . *)
             (186 . |one?|) |INS-;invmod;3S;28| (191 . |mulmod|)
             |INS-;powmod;4S;29|)
          '#(|symmetricRemainder| 198 |squareFree| 204 |retractIfCan|
             209 |retract| 214 |rationalIfCan| 219 |rational?| 224
             |rational| 229 |prime?| 234 |powmod| 239 |positive?| 246
             |permutation| 251 |patternMatch| 257 |nextItem| 264 |mask|
             269 |invmod| 274 |init| 280 |factorial| 284 |factor| 289
             |even?| 294 |euclideanSize| 299 |differentiate| 304 |copy|
             309 |convert| 314 |characteristic| 334 |bit?| 338
             |binomial| 344)
          'NIL
          (CONS (|makeByteWordVec2| 1 'NIL)
                (CONS '#()
                      (CONS '#()
                            (|makeByteWordVec2| 92
                                '(0 7 0 8 0 6 0 10 1 6 12 0 13 1 12 0 0
                                  14 2 6 12 0 0 16 1 6 0 0 19 2 6 0 0 0
                                  20 0 6 0 22 1 6 0 0 23 0 12 0 25 2 6
                                  12 0 0 27 2 6 12 0 0 28 1 6 29 0 30 1
                                  29 0 0 31 1 33 0 29 34 1 36 0 29 37 1
                                  39 0 29 40 1 43 0 29 44 1 47 46 6 48
                                  1 47 46 6 51 1 53 12 6 54 1 56 6 6 57
                                  2 56 6 6 6 59 2 56 6 6 6 61 1 6 12 0
                                  66 2 6 0 0 0 67 3 71 70 6 43 70 72 1
                                  75 0 29 76 2 6 0 0 0 80 2 6 0 81 0 82
                                  2 6 0 0 0 83 1 6 12 0 85 2 6 0 0 0 86
                                  2 6 0 0 0 87 2 6 0 0 0 88 1 6 12 0 89
                                  3 6 0 0 0 0 91 2 0 0 0 0 84 1 0 49 0
                                  52 1 0 63 0 64 1 0 29 0 42 1 0 78 0
                                  79 1 0 12 0 26 1 0 75 0 77 1 0 12 0
                                  55 3 0 0 0 0 0 92 1 0 12 0 17 2 0 0 0
                                  0 62 3 0 73 0 43 73 74 1 0 68 0 69 1
                                  0 0 0 24 2 0 0 0 0 90 0 0 0 65 1 0 0
                                  0 58 1 0 49 0 50 1 0 12 0 15 1 0 7 0
                                  32 1 0 0 0 11 1 0 0 0 18 1 0 36 0 38
                                  1 0 33 0 35 1 0 43 0 45 1 0 39 0 41 0
                                  0 7 9 2 0 12 0 0 21 2 0 0 0 0 60)))))
          '|lookupComplete|))