
(PUT '|DIHGRP;rep| '|SPADreplace| '(XLAM (|x|) |x|)) 

(SDEFUN |DIHGRP;rep| ((|x| (%)) (% (|Rep|))) |x|) 

(PUT '|DIHGRP;per| '|SPADreplace| '(XLAM (|r|) |r|)) 

(SDEFUN |DIHGRP;per| ((|r| (|Rep|)) (% (%))) |r|) 

(SDEFUN |DIHGRP;expa;%Im;3| ((|x| (%)) (% (|IntegerMod| |n|)))
        (QCAR (|DIHGRP;rep| |x| %))) 

(SDEFUN |DIHGRP;expb;%Im;4| ((|x| (%)) (% (|IntegerMod| 2)))
        (QCDR (|DIHGRP;rep| |x| %))) 

(SDEFUN |DIHGRP;exponenta;%I;5| ((|x| (%)) (% (|Integer|)))
        (SPADCALL (SPADCALL |x| (QREFELT % 11)) (QREFELT % 15))) 

(SDEFUN |DIHGRP;exponentb;%I;6| ((|x| (%)) (% (|Integer|)))
        (SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 17))) 

(SDEFUN |DIHGRP;One;%;7| ((% (%)))
        (|DIHGRP;per| (CONS (|spadConstant| % 19) (|spadConstant| % 20)) %)) 

(SDEFUN |DIHGRP;one?;%B;8| ((|x| (%)) (% (|Boolean|)))
        (COND
         ((SPADCALL (SPADCALL |x| (QREFELT % 11)) (QREFELT % 23))
          (SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 24)))
         ('T NIL))) 

(SDEFUN |DIHGRP;coerce;%Of;9| ((|y| (%)) (% (|OutputForm|)))
        (SPROG ((|aout| (|OutputForm|)))
               (SEQ
                (COND
                 ((SPADCALL |y| (QREFELT % 25)) (SPADCALL 1 (QREFELT % 27)))
                 ((SPADCALL (SPADCALL |y| (QREFELT % 11)) (QREFELT % 23))
                  (SPADCALL (QREFELT % 8) (QREFELT % 29)))
                 (#1='T
                  (SEQ
                   (COND
                    ((SPADCALL (SPADCALL |y| (QREFELT % 11)) (QREFELT % 30))
                     (LETT |aout| (SPADCALL (QREFELT % 7) (QREFELT % 29))))
                    (#1#
                     (LETT |aout|
                           (SPADCALL (SPADCALL (QREFELT % 7) (QREFELT % 29))
                                     (SPADCALL (SPADCALL |y| (QREFELT % 11))
                                               (QREFELT % 31))
                                     (QREFELT % 32)))))
                   (EXIT
                    (COND
                     ((SPADCALL (SPADCALL |y| (QREFELT % 13)) (QREFELT % 24))
                      |aout|)
                     (#1#
                      (SPADCALL |aout| (SPADCALL (QREFELT % 8) (QREFELT % 29))
                                (QREFELT % 33))))))))))) 

(SDEFUN |DIHGRP;generators;L;10| ((% (|List| %)))
        (LIST
         (|DIHGRP;per| (CONS (|spadConstant| % 35) (|spadConstant| % 20)) %)
         (|DIHGRP;per| (CONS (|spadConstant| % 19) (|spadConstant| % 36)) %))) 

(SDEFUN |DIHGRP;*;3%;11| ((|x| (%)) (|y| (%)) (% (%)))
        (COND
         ((SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 24))
          (|DIHGRP;per|
           (CONS
            (SPADCALL (SPADCALL |x| (QREFELT % 11))
                      (SPADCALL |y| (QREFELT % 11)) (QREFELT % 39))
            (SPADCALL |y| (QREFELT % 13)))
           %))
         ('T
          (|DIHGRP;per|
           (CONS
            (SPADCALL (SPADCALL |x| (QREFELT % 11))
                      (SPADCALL |y| (QREFELT % 11)) (QREFELT % 40))
            (SPADCALL (SPADCALL |x| (QREFELT % 13))
                      (SPADCALL |y| (QREFELT % 13)) (QREFELT % 41)))
           %)))) 

(SDEFUN |DIHGRP;inv;2%;12| ((|x| (%)) (% (%)))
        (COND
         ((SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 24))
          (|DIHGRP;per|
           (CONS (SPADCALL (SPADCALL |x| (QREFELT % 11)) (QREFELT % 43))
                 (|spadConstant| % 20))
           %))
         ('T |x|))) 

(SDEFUN |DIHGRP;order;%I;13| ((|x| (%)) (% (|Integer|)))
        (COND ((SPADCALL |x| (QREFELT % 25)) 0)
              ((SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 45)) 2)
              ('T
               (QUOTIENT2 (QREFELT % 6)
                          (GCD
                           (SPADCALL (SPADCALL |x| (QREFELT % 11))
                                     (QREFELT % 15))
                           (QREFELT % 6)))))) 

(SDEFUN |DIHGRP;=;2%B;14| ((|x| (%)) (|y| (%)) (% (|Boolean|)))
        (COND
         ((SPADCALL (SPADCALL |x| (QREFELT % 11)) (SPADCALL |y| (QREFELT % 11))
                    (QREFELT % 47))
          (SPADCALL (SPADCALL |x| (QREFELT % 13)) (SPADCALL |y| (QREFELT % 13))
                    (QREFELT % 48)))
         ('T NIL))) 

(SDEFUN |DIHGRP;smaller?;2%B;15| ((|x| (%)) (|y| (%)) (% (|Boolean|)))
        (COND
         ((< (SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 17))
             (SPADCALL (SPADCALL |y| (QREFELT % 13)) (QREFELT % 17)))
          'T)
         ('T
          (NULL
           (OR
            (> (SPADCALL (SPADCALL |x| (QREFELT % 13)) (QREFELT % 17))
               (SPADCALL (SPADCALL |y| (QREFELT % 13)) (QREFELT % 17)))
            (NULL
             (< (SPADCALL (SPADCALL |x| (QREFELT % 11)) (QREFELT % 15))
                (SPADCALL (SPADCALL |y| (QREFELT % 11)) (QREFELT % 15))))))))) 

(SDEFUN |DIHGRP;size;Nni;16| ((% (|NonNegativeInteger|))) (* 2 (QREFELT % 6))) 

(SDEFUN |DIHGRP;index;Pi%;17| ((|i| (|PositiveInteger|)) (% (%)))
        (SPROG ((|imodn| (|IntegerMod| |n|)))
               (SEQ
                (COND ((> |i| (* 2 (QREFELT % 6))) (|error| "out of range"))
                      (#1='T
                       (SEQ (LETT |imodn| (SPADCALL (- |i| 1) (QREFELT % 53)))
                            (EXIT
                             (COND
                              ((> |i| (QREFELT % 6))
                               (|DIHGRP;per|
                                (CONS |imodn| (|spadConstant| % 36)) %))
                              (#1#
                               (|DIHGRP;per|
                                (CONS |imodn| (|spadConstant| % 20)) %)))))))))) 

(SDEFUN |DIHGRP;lookup;%Pi;18| ((|x| (%)) (% (|PositiveInteger|)))
        (SPROG ((|xa| (|PositiveInteger|)))
               (LETT |xa|
                     (+
                      (+
                       (SPADCALL (SPADCALL |x| (QREFELT % 11)) (QREFELT % 15))
                       1)
                      (* (QREFELT % 6)
                         (SPADCALL (SPADCALL |x| (QREFELT % 13))
                                   (QREFELT % 17))))))) 

(SDEFUN |DIHGRP;enumerate;L;19| ((% (|List| %)))
        (SPROG
         ((#1=#:G69 NIL) (|k| NIL) (#2=#:G68 NIL) (#3=#:G67 NIL)
          (#4=#:G66 NIL))
         (SEQ
          (SPADCALL
           (PROGN
            (LETT #4# NIL)
            (SEQ (LETT |k| 0) (LETT #3# (- (QREFELT % 6) 1)) G190
                 (COND ((|greater_SI| |k| #3#) (GO G191)))
                 (SEQ
                  (EXIT
                   (LETT #4#
                         (CONS
                          (|DIHGRP;per|
                           (CONS (SPADCALL |k| (QREFELT % 53))
                                 (|spadConstant| % 20))
                           %)
                          #4#))))
                 (LETT |k| (|inc_SI| |k|)) (GO G190) G191
                 (EXIT (NREVERSE #4#))))
           (PROGN
            (LETT #2# NIL)
            (SEQ (LETT |k| 0) (LETT #1# (- (QREFELT % 6) 1)) G190
                 (COND ((|greater_SI| |k| #1#) (GO G191)))
                 (SEQ
                  (EXIT
                   (LETT #2#
                         (CONS
                          (|DIHGRP;per|
                           (CONS (SPADCALL |k| (QREFELT % 53))
                                 (|spadConstant| % 36))
                           %)
                          #2#))))
                 (LETT |k| (|inc_SI| |k|)) (GO G190) G191
                 (EXIT (NREVERSE #2#))))
           (QREFELT % 58))))) 

(DECLAIM (NOTINLINE |DihedralGroup;|)) 

(DEFUN |DihedralGroup;| (|#1| |#2| |#3|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$3 NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 |#1|)
          (LETT DV$2 |#2|)
          (LETT DV$3 |#3|)
          (LETT |dv$| (LIST '|DihedralGroup| DV$1 DV$2 DV$3))
          (LETT % (GETREFV 65))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3 (LETT |pv$| (|buildPredVector| 0 0 NIL)))
          (|haddProp| |$ConstructorCache| '|DihedralGroup|
                      (LIST DV$1 DV$2 DV$3) (CONS 1 %))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (QSETREFV % 7 |#2|)
          (QSETREFV % 8 |#3|)
          (SETF |pv$| (QREFELT % 3))
          (QSETREFV % 9
                    (|Record| (|:| |expa| (|IntegerMod| |#1|))
                              (|:| |expb| (|IntegerMod| 2))))
          %))) 

(DEFUN |DihedralGroup| (&REST #1=#:G73)
  (SPROG NIL
         (PROG (#2=#:G74)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction|
                     (|devaluate_sig| #1# '(NIL NIL NIL))
                     (HGET |$ConstructorCache| '|DihedralGroup|)
                     '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |DihedralGroup;|) #1#)
                    (LETT #2# T))
                (COND
                 ((NOT #2#) (HREM |$ConstructorCache| '|DihedralGroup|)))))))))) 

(MAKEPROP '|DihedralGroup| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|local| |#3|) '|Rep| (|IntegerMod| (NRTEVAL (QREFELT % 6)))
              |DIHGRP;expa;%Im;3| (|IntegerMod| '2) |DIHGRP;expb;%Im;4|
              (|Integer|) (0 . |convert|) |DIHGRP;exponenta;%I;5|
              (5 . |convert|) |DIHGRP;exponentb;%I;6| (10 . |Zero|)
              (14 . |Zero|)
              (CONS IDENTITY (FUNCALL (|dispatchFunction| |DIHGRP;One;%;7|) %))
              (|Boolean|) (18 . |zero?|) (23 . |zero?|) |DIHGRP;one?;%B;8|
              (|OutputForm|) (28 . |coerce|) (|Symbol|) (33 . |coerce|)
              (38 . |one?|) (43 . |coerce|) (48 . ^) (54 . *)
              |DIHGRP;coerce;%Of;9| (60 . |One|) (64 . |One|) (|List| %)
              |DIHGRP;generators;L;10| (68 . +) (74 . -) (80 . +)
              |DIHGRP;*;3%;11| (86 . -) |DIHGRP;inv;2%;12| (91 . |one?|)
              |DIHGRP;order;%I;13| (96 . =) (102 . =) |DIHGRP;=;2%B;14|
              |DIHGRP;smaller?;2%B;15| (|NonNegativeInteger|)
              |DIHGRP;size;Nni;16| (108 . |coerce|) (|PositiveInteger|)
              |DIHGRP;index;Pi%;17| |DIHGRP;lookup;%Pi;18| (|List| $$)
              (113 . |concat|) |DIHGRP;enumerate;L;19| (|String|)
              (|Union| % '"failed") (|SingleInteger|) (|HashState|)
              (|InputForm|))
           '#(~= 119 |smaller?| 125 |size| 131 |sample| 135 |rightRecip| 139
              |rightPower| 144 |recip| 156 |random| 161 |order| 165 |one?| 170
              |lookup| 175 |leftRecip| 180 |leftPower| 185 |latex| 197 |inv|
              202 |index| 207 |hashUpdate!| 212 |hash| 218 |generators| 223
              |exponentb| 227 |exponenta| 232 |expb| 237 |expa| 242 |enumerate|
              247 |convert| 251 |conjugate| 256 |commutator| 262 |coerce| 268 ^
              273 |One| 291 = 295 / 301 * 307)
           'NIL
           (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
                 (CONS
                  '#(|FiniteGroup&| |Group&| NIL |MagmaWithUnit&| |Finite&| NIL
                     |Magma&| NIL |SetCategory&| |Hashable&| NIL |BasicType&|
                     NIL NIL NIL NIL)
                  (CONS
                   '#((|FiniteGroup|) (|Group|) (|Monoid|) (|MagmaWithUnit|)
                      (|Finite|) (|SemiGroup|) (|Magma|) (|Comparable|)
                      (|SetCategory|) (|Hashable|) (|CoercibleTo| 26)
                      (|BasicType|) (|TwoSidedRecip|) (|unitsKnown|)
                      (|ConvertibleTo| 64) (|FinitelyGenerated|))
                   (|makeByteWordVec2| 64
                                       '(1 10 14 0 15 1 12 14 0 17 0 10 0 19 0
                                         12 0 20 1 10 22 0 23 1 12 22 0 24 1 14
                                         26 0 27 1 28 26 0 29 1 10 22 0 30 1 10
                                         26 0 31 2 26 0 0 0 32 2 26 0 0 0 33 0
                                         10 0 35 0 12 0 36 2 10 0 0 0 39 2 10 0
                                         0 0 40 2 12 0 0 0 41 1 10 0 0 43 1 12
                                         22 0 45 2 10 22 0 0 47 2 12 22 0 0 48
                                         1 10 0 14 53 2 57 0 0 0 58 2 0 22 0 0
                                         1 2 0 22 0 0 50 0 0 51 52 0 0 0 1 1 0
                                         61 0 1 2 0 0 0 54 1 2 0 0 0 51 1 1 0
                                         61 0 1 0 0 0 1 1 0 14 0 46 1 0 22 0 25
                                         1 0 54 0 56 1 0 61 0 1 2 0 0 0 54 1 2
                                         0 0 0 51 1 1 0 60 0 1 1 0 0 0 44 1 0 0
                                         54 55 2 0 63 63 0 1 1 0 62 0 1 0 0 37
                                         38 1 0 14 0 18 1 0 14 0 16 1 0 12 0 13
                                         1 0 10 0 11 0 0 37 59 1 0 64 0 1 2 0 0
                                         0 0 1 2 0 0 0 0 1 1 0 26 0 34 2 0 0 0
                                         54 1 2 0 0 0 51 1 2 0 0 0 14 1 0 0 0
                                         21 2 0 22 0 0 49 2 0 0 0 0 1 2 0 0 0 0
                                         42)))))
           '|lookupComplete|)) 
