
(PUT '|MOEBIUS;moebius;4F%;1| '|SPADreplace| 'VECTOR) 

(SDEFUN |MOEBIUS;moebius;4F%;1|
        ((|aa| (F)) (|bb| (F)) (|cc| (F)) (|dd| (F)) (% (%)))
        (VECTOR |aa| |bb| |cc| |dd|)) 

(PUT '|MOEBIUS;a| '|SPADreplace| '(XLAM (|t|) (QVELT |t| 0))) 

(SDEFUN |MOEBIUS;a| ((|t| (%)) (% (F))) (QVELT |t| 0)) 

(PUT '|MOEBIUS;b| '|SPADreplace| '(XLAM (|t|) (QVELT |t| 1))) 

(SDEFUN |MOEBIUS;b| ((|t| (%)) (% (F))) (QVELT |t| 1)) 

(PUT '|MOEBIUS;c| '|SPADreplace| '(XLAM (|t|) (QVELT |t| 2))) 

(SDEFUN |MOEBIUS;c| ((|t| (%)) (% (F))) (QVELT |t| 2)) 

(PUT '|MOEBIUS;d| '|SPADreplace| '(XLAM (|t|) (QVELT |t| 3))) 

(SDEFUN |MOEBIUS;d| ((|t| (%)) (% (F))) (QVELT |t| 3)) 

(SDEFUN |MOEBIUS;One;%;6| ((% (%)))
        (SPADCALL (|spadConstant| % 10) (|spadConstant| % 11)
                  (|spadConstant| % 11) (|spadConstant| % 10) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;*;3%;7| ((|t| (%)) (|s| (%)) (% (%)))
        (SPADCALL
         (SPADCALL
          (SPADCALL (|MOEBIUS;b| |t| %) (|MOEBIUS;c| |s| %) (QREFELT % 12))
          (SPADCALL (|MOEBIUS;a| |t| %) (|MOEBIUS;a| |s| %) (QREFELT % 12))
          (QREFELT % 13))
         (SPADCALL
          (SPADCALL (|MOEBIUS;b| |t| %) (|MOEBIUS;d| |s| %) (QREFELT % 12))
          (SPADCALL (|MOEBIUS;a| |t| %) (|MOEBIUS;b| |s| %) (QREFELT % 12))
          (QREFELT % 13))
         (SPADCALL
          (SPADCALL (|MOEBIUS;d| |t| %) (|MOEBIUS;c| |s| %) (QREFELT % 12))
          (SPADCALL (|MOEBIUS;c| |t| %) (|MOEBIUS;a| |s| %) (QREFELT % 12))
          (QREFELT % 13))
         (SPADCALL
          (SPADCALL (|MOEBIUS;d| |t| %) (|MOEBIUS;d| |s| %) (QREFELT % 12))
          (SPADCALL (|MOEBIUS;c| |t| %) (|MOEBIUS;b| |s| %) (QREFELT % 12))
          (QREFELT % 13))
         (QREFELT % 8))) 

(SDEFUN |MOEBIUS;inv;2%;8| ((|t| (%)) (% (%)))
        (SPADCALL (|MOEBIUS;d| |t| %)
                  (SPADCALL (|MOEBIUS;b| |t| %) (QREFELT % 15))
                  (SPADCALL (|MOEBIUS;c| |t| %) (QREFELT % 15))
                  (|MOEBIUS;a| |t| %) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;shift;F%;9| ((|f| (F)) (% (%)))
        (SPADCALL (|spadConstant| % 10) |f| (|spadConstant| % 11)
                  (|spadConstant| % 10) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;scale;F%;10| ((|f| (F)) (% (%)))
        (SPADCALL |f| (|spadConstant| % 11) (|spadConstant| % 11)
                  (|spadConstant| % 10) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;recip;%;11| ((% (%)))
        (SPADCALL (|spadConstant| % 11) (|spadConstant| % 10)
                  (|spadConstant| % 10) (|spadConstant| % 11) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;shift;%F%;12| ((|t| (%)) (|f| (F)) (% (%)))
        (SPADCALL
         (SPADCALL (|MOEBIUS;a| |t| %)
                   (SPADCALL |f| (|MOEBIUS;c| |t| %) (QREFELT % 12))
                   (QREFELT % 13))
         (SPADCALL (|MOEBIUS;b| |t| %)
                   (SPADCALL |f| (|MOEBIUS;d| |t| %) (QREFELT % 12))
                   (QREFELT % 13))
         (|MOEBIUS;c| |t| %) (|MOEBIUS;d| |t| %) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;scale;%F%;13| ((|t| (%)) (|f| (F)) (% (%)))
        (SPADCALL (SPADCALL |f| (|MOEBIUS;a| |t| %) (QREFELT % 12))
                  (SPADCALL |f| (|MOEBIUS;b| |t| %) (QREFELT % 12))
                  (|MOEBIUS;c| |t| %) (|MOEBIUS;d| |t| %) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;recip;2%;14| ((|t| (%)) (% (%)))
        (SPADCALL (|MOEBIUS;c| |t| %) (|MOEBIUS;d| |t| %) (|MOEBIUS;a| |t| %)
                  (|MOEBIUS;b| |t| %) (QREFELT % 8))) 

(SDEFUN |MOEBIUS;eval;%2F;15| ((|t| (%)) (|f| (F)) (% (F)))
        (SPADCALL
         (SPADCALL (SPADCALL (|MOEBIUS;a| |t| %) |f| (QREFELT % 12))
                   (|MOEBIUS;b| |t| %) (QREFELT % 13))
         (SPADCALL (SPADCALL (|MOEBIUS;c| |t| %) |f| (QREFELT % 12))
                   (|MOEBIUS;d| |t| %) (QREFELT % 13))
         (QREFELT % 23))) 

(SDEFUN |MOEBIUS;eval;%2Opc;16|
        ((|t| (%)) (|f| (|OnePointCompletion| F)) (% (|OnePointCompletion| F)))
        (SPROG ((|den| (F)) (|fff| (F)) (|ff| (|Union| F "failed")))
               (SEQ (LETT |ff| (SPADCALL |f| (QREFELT % 27)))
                    (EXIT
                     (COND
                      ((QEQCAR |ff| 1)
                       (SPADCALL
                        (SPADCALL (|MOEBIUS;a| |t| %) (|MOEBIUS;c| |t| %)
                                  (QREFELT % 23))
                        (QREFELT % 28)))
                      ((SPADCALL
                        (LETT |den|
                              (SPADCALL
                               (SPADCALL (|MOEBIUS;c| |t| %)
                                         (LETT |fff| (QCDR |ff|))
                                         (QREFELT % 12))
                               (|MOEBIUS;d| |t| %) (QREFELT % 13)))
                        (QREFELT % 30))
                       (SPADCALL (QREFELT % 31)))
                      ('T
                       (SPADCALL
                        (SPADCALL
                         (SPADCALL
                          (SPADCALL (|MOEBIUS;a| |t| %) |fff| (QREFELT % 12))
                          (|MOEBIUS;b| |t| %) (QREFELT % 13))
                         |den| (QREFELT % 23))
                        (QREFELT % 28)))))))) 

(SDEFUN |MOEBIUS;coerce;%Of;17| ((|t| (%)) (% (|OutputForm|)))
        (SPROG ((|den| #1=(|OutputForm|)) (|num| #1#) (|var| (|OutputForm|)))
               (SEQ (LETT |var| (SPADCALL "%x" (QREFELT % 35)))
                    (LETT |num|
                          (SPADCALL
                           (SPADCALL
                            (SPADCALL (|MOEBIUS;a| |t| %) (QREFELT % 36)) |var|
                            (QREFELT % 37))
                           (SPADCALL (|MOEBIUS;b| |t| %) (QREFELT % 36))
                           (QREFELT % 38)))
                    (LETT |den|
                          (SPADCALL
                           (SPADCALL
                            (SPADCALL (|MOEBIUS;c| |t| %) (QREFELT % 36)) |var|
                            (QREFELT % 37))
                           (SPADCALL (|MOEBIUS;d| |t| %) (QREFELT % 36))
                           (QREFELT % 38)))
                    (EXIT
                     (SPADCALL |var| (SPADCALL |num| |den| (QREFELT % 39))
                               (QREFELT % 40)))))) 

(SDEFUN |MOEBIUS;proportional?|
        ((|list1| (|List| F)) (|list2| (|List| F)) (% (|Boolean|)))
        (SPROG ((|x2| (F)) (|x1| (F)))
               (COND ((NULL |list1|) (NULL |list2|)) ((NULL |list2|) NIL)
                     ((SPADCALL (LETT |x1| (|SPADfirst| |list1|))
                                (QREFELT % 30))
                      (COND
                       ((SPADCALL (|SPADfirst| |list2|) (QREFELT % 30))
                        (|MOEBIUS;proportional?| (CDR |list1|) (CDR |list2|)
                         %))
                       (#1='T NIL)))
                     ((SPADCALL (LETT |x2| (|SPADfirst| |list2|))
                                (QREFELT % 30))
                      NIL)
                     (#1#
                      (SPADCALL
                       (SPADCALL
                        (CONS #'|MOEBIUS;proportional?!0| (VECTOR % |x1|))
                        |list1| (QREFELT % 44))
                       (SPADCALL
                        (CONS #'|MOEBIUS;proportional?!1| (VECTOR % |x2|))
                        |list2| (QREFELT % 44))
                       (QREFELT % 45)))))) 

(SDEFUN |MOEBIUS;proportional?!1| ((|f1| NIL) ($$ NIL))
        (PROG (|x2| %)
          (LETT |x2| (QREFELT $$ 1))
          (LETT % (QREFELT $$ 0))
          (RETURN (PROGN (SPADCALL |f1| |x2| (QREFELT % 23)))))) 

(SDEFUN |MOEBIUS;proportional?!0| ((|f1| NIL) ($$ NIL))
        (PROG (|x1| %)
          (LETT |x1| (QREFELT $$ 1))
          (LETT % (QREFELT $$ 0))
          (RETURN (PROGN (SPADCALL |f1| |x1| (QREFELT % 23)))))) 

(SDEFUN |MOEBIUS;=;2%B;19| ((|t| (%)) (|s| (%)) (% (|Boolean|)))
        (SPROG ((|list2| (|List| F)) (|list1| (|List| F)))
               (SEQ
                (LETT |list1|
                      (LIST (|MOEBIUS;a| |t| %) (|MOEBIUS;b| |t| %)
                            (|MOEBIUS;c| |t| %) (|MOEBIUS;d| |t| %)))
                (LETT |list2|
                      (LIST (|MOEBIUS;a| |s| %) (|MOEBIUS;b| |s| %)
                            (|MOEBIUS;c| |s| %) (|MOEBIUS;d| |s| %)))
                (EXIT (|MOEBIUS;proportional?| |list1| |list2| %))))) 

(DECLAIM (NOTINLINE |MoebiusTransform;|)) 

(DEFUN |MoebiusTransform;| (|#1|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|))
          (LETT |dv$| (LIST '|MoebiusTransform| DV$1))
          (LETT % (GETREFV 51))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3 (LETT |pv$| (|buildPredVector| 0 0 NIL)))
          (|haddProp| |$ConstructorCache| '|MoebiusTransform| (LIST DV$1)
                      (CONS 1 %))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (SETF |pv$| (QREFELT % 3))
          (QSETREFV % 7
                    (|Record| (|:| |a| |#1|) (|:| |b| |#1|) (|:| |c| |#1|)
                              (|:| |d| |#1|)))
          %))) 

(DEFUN |MoebiusTransform| (#1=#:G53)
  (SPROG NIL
         (PROG (#2=#:G54)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (LIST (|devaluate| #1#))
                                               (HGET |$ConstructorCache|
                                                     '|MoebiusTransform|)
                                               '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT (PROG1 (|MoebiusTransform;| #1#) (LETT #2# T))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache| '|MoebiusTransform|)))))))))) 

(MAKEPROP '|MoebiusTransform| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) '|Rep|
              |MOEBIUS;moebius;4F%;1|
              (CONS IDENTITY
                    (FUNCALL (|dispatchFunction| |MOEBIUS;One;%;6|) %))
              (0 . |One|) (4 . |Zero|) (8 . *) (14 . +) |MOEBIUS;*;3%;7|
              (20 . -) |MOEBIUS;inv;2%;8| |MOEBIUS;shift;F%;9|
              |MOEBIUS;scale;F%;10| |MOEBIUS;recip;%;11| |MOEBIUS;shift;%F%;12|
              |MOEBIUS;scale;%F%;13| |MOEBIUS;recip;2%;14| (25 . /)
              |MOEBIUS;eval;%2F;15| (|Union| 6 '"failed")
              (|OnePointCompletion| 6) (31 . |retractIfCan|) (36 . |coerce|)
              (|Boolean|) (41 . |zero?|) (46 . |infinity|)
              |MOEBIUS;eval;%2Opc;16| (|String|) (|OutputForm|)
              (50 . |message|) (55 . |coerce|) (60 . *) (66 . +) (72 . /)
              (78 . |rarrow|) |MOEBIUS;coerce;%Of;17| (|Mapping| 6 6)
              (|List| 6) (84 . |map|) (90 . =) |MOEBIUS;=;2%B;19|
              (|PositiveInteger|) (|Union| % '"failed") (|NonNegativeInteger|)
              (|Integer|))
           '#(~= 96 |shift| 102 |scale| 113 |sample| 124 |rightRecip| 128
              |rightPower| 133 |recip| 145 |one?| 159 |moebius| 164 |leftRecip|
              172 |leftPower| 177 |latex| 189 |inv| 194 |eval| 199 |conjugate|
              211 |commutator| 217 |coerce| 223 ^ 228 |One| 246 = 250 / 256 *
              262)
           'NIL
           (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0))
                 (CONS
                  '#(|Group&| NIL |MagmaWithUnit&| NIL |Magma&| |SetCategory&|
                     NIL |BasicType&| NIL NIL)
                  (CONS
                   '#((|Group|) (|Monoid|) (|MagmaWithUnit|) (|SemiGroup|)
                      (|Magma|) (|SetCategory|) (|CoercibleTo| 34)
                      (|BasicType|) (|TwoSidedRecip|) (|unitsKnown|))
                   (|makeByteWordVec2| 50
                                       '(0 6 0 10 0 6 0 11 2 6 0 0 0 12 2 6 0 0
                                         0 13 1 6 0 0 15 2 6 0 0 0 23 1 26 25 0
                                         27 1 26 0 6 28 1 6 29 0 30 0 26 0 31 1
                                         34 0 33 35 1 6 34 0 36 2 34 0 0 0 37 2
                                         34 0 0 0 38 2 34 0 0 0 39 2 34 0 0 0
                                         40 2 43 0 42 0 44 2 43 29 0 0 45 2 0
                                         29 0 0 1 1 0 0 6 17 2 0 0 0 6 20 1 0 0
                                         6 18 2 0 0 0 6 21 0 0 0 1 1 0 48 0 1 2
                                         0 0 0 47 1 2 0 0 0 49 1 1 0 48 0 1 0 0
                                         0 19 1 0 0 0 22 1 0 29 0 1 4 0 0 6 6 6
                                         6 8 1 0 48 0 1 2 0 0 0 47 1 2 0 0 0 49
                                         1 1 0 33 0 1 1 0 0 0 16 2 0 6 0 6 24 2
                                         0 26 0 26 32 2 0 0 0 0 1 2 0 0 0 0 1 1
                                         0 34 0 41 2 0 0 0 47 1 2 0 0 0 49 1 2
                                         0 0 0 50 1 0 0 0 9 2 0 29 0 0 46 2 0 0
                                         0 0 1 2 0 0 0 0 14)))))
           '|lookupComplete|)) 
