
(/VERSIONCHECK 2) 

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

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

(DEFUN |INS-;differentiate;2S;2| (|x| $) (|spadConstant| $ 9)) 

(DEFUN |INS-;even?;SB;3| (|x| $)
  (COND ((SPADCALL |x| (QREFELT $ 12)) 'NIL) ('T 'T))) 

(DEFUN |INS-;positive?;SB;4| (|x| $)
  (SPADCALL (|spadConstant| $ 9) |x| (QREFELT $ 14))) 

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

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

(DEFUN |INS-;bit?;2SB;6| (|x| |i| $)
  (SPADCALL (SPADCALL |x| (SPADCALL |i| (QREFELT $ 17)) (QREFELT $ 18))
            (QREFELT $ 12))) 

(DEFUN |INS-;mask;2S;7| (|n| $)
  (SPADCALL (SPADCALL (|spadConstant| $ 20) |n| (QREFELT $ 18)) (QREFELT $ 21))) 

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

(DEFUN |INS-;rational?;SB;8| (|x| $) 'T) 

(DEFUN |INS-;euclideanSize;SNni;9| (|x| $)
  (PROG (#1=#:G8325 #2=#:G8324)
    (RETURN
     (COND
      ((SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 24))
       (|error| "euclideanSize called on zero"))
      ((SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 14))
       (PROG1
           (LETT #2# (- (SPADCALL |x| (QREFELT $ 26)))
                 . #3=(|INS-;euclideanSize;SNni;9|))
         (|check-subtype| (>= #2# 0) '(|NonNegativeInteger|) #2#)))
      ('T
       (PROG1 (LETT #1# (SPADCALL |x| (QREFELT $ 26)) . #3#)
         (|check-subtype| (>= #1# 0) '(|NonNegativeInteger|) #1#))))))) 

(DEFUN |INS-;convert;SF;10| (|x| $)
  (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 29))) 

(DEFUN |INS-;convert;SDf;11| (|x| $)
  (FLOAT (SPADCALL |x| (QREFELT $ 26)) MOST-POSITIVE-DOUBLE-FLOAT)) 

(DEFUN |INS-;convert;SIf;12| (|x| $)
  (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 34))) 

(DEFUN |INS-;retract;SI;13| (|x| $) (SPADCALL |x| (QREFELT $ 26))) 

(DEFUN |INS-;convert;SP;14| (|x| $)
  (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 38))) 

(DEFUN |INS-;factor;SF;15| (|x| $) (SPADCALL |x| (QREFELT $ 42))) 

(DEFUN |INS-;squareFree;SF;16| (|x| $) (SPADCALL |x| (QREFELT $ 45))) 

(DEFUN |INS-;prime?;SB;17| (|x| $) (SPADCALL |x| (QREFELT $ 48))) 

(DEFUN |INS-;factorial;2S;18| (|x| $) (SPADCALL |x| (QREFELT $ 51))) 

(DEFUN |INS-;binomial;3S;19| (|n| |m| $) (SPADCALL |n| |m| (QREFELT $ 53))) 

(DEFUN |INS-;permutation;3S;20| (|n| |m| $) (SPADCALL |n| |m| (QREFELT $ 55))) 

(DEFUN |INS-;retractIfCan;SU;21| (|x| $) (CONS 0 (SPADCALL |x| (QREFELT $ 26)))) 

(DEFUN |INS-;init;S;22| ($) (|spadConstant| $ 9)) 

(DEFUN |INS-;nextItem;SU;23| (|n| $)
  (COND ((SPADCALL |n| (QREFELT $ 60)) (CONS 0 (|spadConstant| $ 20)))
        ((SPADCALL (|spadConstant| $ 9) |n| (QREFELT $ 14))
         (CONS 0 (SPADCALL |n| (QREFELT $ 17))))
        ('T (CONS 0 (SPADCALL (|spadConstant| $ 20) |n| (QREFELT $ 61)))))) 

(DEFUN |INS-;patternMatch;SP2Pmr;24| (|x| |p| |l| $)
  (SPADCALL |x| |p| |l| (QREFELT $ 66))) 

(DEFUN |INS-;rational;SF;25| (|x| $)
  (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 70))) 

(DEFUN |INS-;rationalIfCan;SU;26| (|x| $)
  (CONS 0 (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 70)))) 

(DEFUN |INS-;symmetricRemainder;3S;27| (|x| |n| $)
  (PROG (|r|)
    (RETURN
     (SEQ
      (LETT |r| (SPADCALL |x| |n| (QREFELT $ 74))
            . #1=(|INS-;symmetricRemainder;3S;27|))
      (EXIT
       (COND ((SPADCALL |r| (|spadConstant| $ 9) (QREFELT $ 24)) |r|)
             (#2='T
              (SEQ
               (COND
                ((SPADCALL |n| (|spadConstant| $ 9) (QREFELT $ 14))
                 (LETT |n| (SPADCALL |n| (QREFELT $ 17)) . #1#)))
               (EXIT
                (COND
                 ((SPADCALL (|spadConstant| $ 9) |r| (QREFELT $ 14))
                  (COND
                   ((SPADCALL |n| (SPADCALL 2 |r| (QREFELT $ 76))
                              (QREFELT $ 14))
                    (SPADCALL |r| |n| (QREFELT $ 61)))
                   (#2# |r|)))
                 ((NULL
                   (SPADCALL (|spadConstant| $ 9)
                             (SPADCALL (SPADCALL 2 |r| (QREFELT $ 76)) |n|
                                       (QREFELT $ 77))
                             (QREFELT $ 14)))
                  (SPADCALL |r| |n| (QREFELT $ 77)))
                 ('T |r|))))))))))) 

(DEFUN |INS-;invmod;3S;28| (|a| |b| $)
  (PROG (|d1| |d| |c1| |c| |r1| |r| |q|)
    (RETURN
     (SEQ
      (COND
       ((SPADCALL |a| (QREFELT $ 79))
        (LETT |a| (SPADCALL |a| |b| (QREFELT $ 80))
              . #1=(|INS-;invmod;3S;28|))))
      (LETT |c| |a| . #1#) (LETT |c1| (|spadConstant| $ 20) . #1#)
      (LETT |d| |b| . #1#) (LETT |d1| (|spadConstant| $ 9) . #1#)
      (SEQ G190
           (COND
            ((NULL (COND ((SPADCALL |d| (QREFELT $ 60)) 'NIL) ('T 'T)))
             (GO G191)))
           (SEQ (LETT |q| (SPADCALL |c| |d| (QREFELT $ 81)) . #1#)
                (LETT |r|
                      (SPADCALL |c| (SPADCALL |q| |d| (QREFELT $ 82))
                                (QREFELT $ 61))
                      . #1#)
                (LETT |r1|
                      (SPADCALL |c1| (SPADCALL |q| |d1| (QREFELT $ 82))
                                (QREFELT $ 61))
                      . #1#)
                (LETT |c| |d| . #1#) (LETT |c1| |d1| . #1#)
                (LETT |d| |r| . #1#) (EXIT (LETT |d1| |r1| . #1#)))
           NIL (GO G190) G191 (EXIT NIL))
      (EXIT
       (COND
        ((SPADCALL |c| (|spadConstant| $ 20) (QREFELT $ 24))
         (COND
          ((SPADCALL |c1| (QREFELT $ 79)) (SPADCALL |c1| |b| (QREFELT $ 77)))
          (#2='T |c1|)))
        (#2# (|error| "inverse does not exist")))))))) 

(DEFUN |INS-;powmod;4S;29| (|x| |n| |p| $)
  (PROG (|z| #1=#:G8389 |y|)
    (RETURN
     (SEQ
      (EXIT
       (SEQ
        (COND
         ((SPADCALL |x| (QREFELT $ 79))
          (LETT |x| (SPADCALL |x| |p| (QREFELT $ 80))
                . #2=(|INS-;powmod;4S;29|))))
        (EXIT
         (COND ((SPADCALL |x| (QREFELT $ 60)) (|spadConstant| $ 9))
               ((SPADCALL |n| (QREFELT $ 60)) (|spadConstant| $ 20))
               ('T
                (SEQ (LETT |y| (|spadConstant| $ 20) . #2#)
                     (LETT |z| |x| . #2#)
                     (EXIT
                      (SEQ G190 NIL
                           (SEQ
                            (COND
                             ((SPADCALL |n| (QREFELT $ 12))
                              (LETT |y| (SPADCALL |y| |z| |p| (QREFELT $ 84))
                                    . #2#)))
                            (EXIT
                             (COND
                              ((SPADCALL
                                (LETT |n|
                                      (SPADCALL |n|
                                                (SPADCALL (|spadConstant| $ 20)
                                                          (QREFELT $ 17))
                                                (QREFELT $ 18))
                                      . #2#)
                                (QREFELT $ 60))
                               (PROGN (LETT #1# |y| . #2#) (GO #1#)))
                              ('T
                               (LETT |z| (SPADCALL |z| |z| |p| (QREFELT $ 84))
                                     . #2#)))))
                           NIL (GO G190) G191 (EXIT NIL)))))))))
      #1# (EXIT #1#))))) 

(DEFUN |IntegerNumberSystem&| (|#1|)
  (PROG (|pv$| $ |dv$| DV$1)
    (RETURN
     (PROGN
      (LETT DV$1 (|devaluate| |#1|) . #1=(|IntegerNumberSystem&|))
      (LETT |dv$| (LIST '|IntegerNumberSystem&| DV$1) . #1#)
      (LETT $ (GETREFV 86) . #1#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
      (|stuffDomainSlots| $)
      (QSETREFV $ 6 |#1|)
      $)))) 

(MAKEPROP '|IntegerNumberSystem&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|NonNegativeInteger|)
              |INS-;characteristic;Nni;1| (0 . |Zero|)
              |INS-;differentiate;2S;2| (|Boolean|) (4 . |odd?|)
              |INS-;even?;SB;3| (9 . <) |INS-;positive?;SB;4| |INS-;copy;2S;5|
              (15 . -) (20 . |shift|) |INS-;bit?;2SB;6| (26 . |One|)
              (30 . |dec|) |INS-;mask;2S;7| |INS-;rational?;SB;8| (35 . =)
              (|Integer|) (41 . |convert|) |INS-;euclideanSize;SNni;9|
              (|Float|) (46 . |coerce|) |INS-;convert;SF;10| (|DoubleFloat|)
              |INS-;convert;SDf;11| (|InputForm|) (51 . |convert|)
              |INS-;convert;SIf;12| |INS-;retract;SI;13| (|Pattern| 25)
              (56 . |coerce|) |INS-;convert;SP;14| (|Factored| 6)
              (|IntegerFactorizationPackage| 6) (61 . |factor|) (|Factored| $)
              |INS-;factor;SF;15| (66 . |squareFree|) |INS-;squareFree;SF;16|
              (|IntegerPrimesPackage| 6) (71 . |prime?|) |INS-;prime?;SB;17|
              (|IntegerCombinatoricFunctions| 6) (76 . |factorial|)
              |INS-;factorial;2S;18| (81 . |binomial|) |INS-;binomial;3S;19|
              (87 . |permutation|) |INS-;permutation;3S;20|
              (|Union| 25 '"failed") |INS-;retractIfCan;SU;21| |INS-;init;S;22|
              (93 . |zero?|) (98 . -) (|Union| $ '"failed")
              |INS-;nextItem;SU;23| (|PatternMatchResult| 25 6)
              (|PatternMatchIntegerNumberSystem| 6) (104 . |patternMatch|)
              (|PatternMatchResult| 25 $) |INS-;patternMatch;SP2Pmr;24|
              (|Fraction| 25) (111 . |coerce|) |INS-;rational;SF;25|
              (|Union| 69 '"failed") |INS-;rationalIfCan;SU;26| (116 . |rem|)
              (|PositiveInteger|) (122 . *) (128 . +)
              |INS-;symmetricRemainder;3S;27| (134 . |negative?|)
              (139 . |positiveRemainder|) (145 . |quo|) (151 . *)
              |INS-;invmod;3S;28| (157 . |mulmod|) |INS-;powmod;4S;29|)
           '#(|symmetricRemainder| 164 |squareFree| 170 |retractIfCan| 175
              |retract| 180 |rationalIfCan| 185 |rational?| 190 |rational| 195
              |prime?| 200 |powmod| 205 |positive?| 212 |permutation| 217
              |patternMatch| 223 |nextItem| 230 |mask| 235 |invmod| 240 |init|
              246 |factorial| 250 |factor| 255 |even?| 260 |euclideanSize| 265
              |differentiate| 270 |copy| 275 |convert| 280 |characteristic| 300
              |bit?| 304 |binomial| 310)
           'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 85
                                                 '(0 6 0 9 1 6 11 0 12 2 6 11 0
                                                   0 14 1 6 0 0 17 2 6 0 0 0 18
                                                   0 6 0 20 1 6 0 0 21 2 6 11 0
                                                   0 24 1 6 25 0 26 1 28 0 25
                                                   29 1 33 0 25 34 1 37 0 25 38
                                                   1 41 40 6 42 1 41 40 6 45 1
                                                   47 11 6 48 1 50 6 6 51 2 50
                                                   6 6 6 53 2 50 6 6 6 55 1 6
                                                   11 0 60 2 6 0 0 0 61 3 65 64
                                                   6 37 64 66 1 69 0 25 70 2 6
                                                   0 0 0 74 2 6 0 75 0 76 2 6 0
                                                   0 0 77 1 6 11 0 79 2 6 0 0 0
                                                   80 2 6 0 0 0 81 2 6 0 0 0 82
                                                   3 6 0 0 0 0 84 2 0 0 0 0 78
                                                   1 0 43 0 46 1 0 57 0 58 1 0
                                                   25 0 36 1 0 72 0 73 1 0 11 0
                                                   23 1 0 69 0 71 1 0 11 0 49 3
                                                   0 0 0 0 0 85 1 0 11 0 15 2 0
                                                   0 0 0 56 3 0 67 0 37 67 68 1
                                                   0 62 0 63 1 0 0 0 22 2 0 0 0
                                                   0 83 0 0 0 59 1 0 0 0 52 1 0
                                                   43 0 44 1 0 11 0 13 1 0 7 0
                                                   27 1 0 0 0 10 1 0 0 0 16 1 0
                                                   31 0 32 1 0 28 0 30 1 0 37 0
                                                   39 1 0 33 0 35 0 0 7 8 2 0
                                                   11 0 0 19 2 0 0 0 0 54)))))
           '|lookupComplete|)) 
