
(SDEFUN |HOMOL;homologyGroup;2M%;1|
        ((|AInt| (|Matrix| (|Integer|))) (|BInt| (|Matrix| (|Integer|)))
         (% (%)))
        (SPROG
         ((|kernelFree| (|List| (|Vector| (|Integer|))))
          (|v| (|Vector| (|Integer|))) (#1=#:G44 NIL) (|i| NIL)
          (|n_cols| #2=(|NonNegativeInteger|))
          (|n_rows| #3=(|NonNegativeInteger|))
          (|mFree| #4=(|Matrix| (|Integer|)))
          (|smitFree|
           #5=(|Record| (|:| |Smith| (|Matrix| (|Integer|)))
                        (|:| |leftEqMat| (|Matrix| (|Integer|)))
                        (|:| |rightEqMat| (|Matrix| (|Integer|)))))
          (|augmented| (|Matrix| (|Integer|)))
          (|res|
           (|List|
            (|Record| (|:| |vec| (|Vector| (|Integer|)))
                      (|:| |ord| (|Integer|)))))
          (|g|
           (|Record| (|:| |vec| (|Vector| (|Integer|)))
                     (|:| |ord| (|Integer|))))
          (#6=#:G42 NIL) (|order| (|Integer|)) (|r| (|Vector| (|Integer|)))
          (#7=#:G43 NIL) (|nr| NIL) (|mNCols| #2#) (|mNRows| #3#)
          (|leftNRows| #3#) (|m| #4#) (|left| (|Matrix| (|Integer|)))
          (|smit| #5#) (|zero| (|Matrix| (|Integer|))))
         (SEQ
          (COND
           ((SPADCALL (ANROWS |AInt|) (ANCOLS |BInt|) (QREFELT % 9))
            (SPADCALL
             (SPADCALL
              (SPADCALL
               (SPADCALL
                (SPADCALL "homologyGroup validation error - A rows : "
                          (QREFELT % 12))
                (SPADCALL (ANROWS |AInt|) (QREFELT % 13)) (QREFELT % 14))
               (SPADCALL "~= B cols : " (QREFELT % 12)) (QREFELT % 14))
              (SPADCALL (ANCOLS |BInt|) (QREFELT % 13)) (QREFELT % 14))
             (QREFELT % 16)))
           ('T
            (SEQ
             (LETT |zero|
                   (SPADCALL (ANROWS |BInt|) (ANCOLS |AInt|) (QREFELT % 18)))
             (EXIT
              (COND
               ((SPADCALL (SPADCALL |BInt| |AInt| (QREFELT % 19)) |zero|
                          (QREFELT % 20))
                (SPADCALL
                 (SPADCALL
                  (SPADCALL
                   (SPADCALL
                    (SPADCALL "homologyGroup validation error - B*A ~= 0 : "
                              (QREFELT % 12))
                    (SPADCALL (SPADCALL |BInt| |AInt| (QREFELT % 19))
                              (QREFELT % 21))
                    (QREFELT % 14))
                   (SPADCALL "  ~= 0 : " (QREFELT % 12)) (QREFELT % 14))
                  (SPADCALL |zero| (QREFELT % 21)) (QREFELT % 14))
                 (QREFELT % 16))))))))
          (LETT |res| NIL) (LETT |smit| (SPADCALL |AInt| (QREFELT % 24)))
          (LETT |left| (QVELT |smit| 1)) (LETT |m| (QVELT |smit| 0))
          (LETT |leftNRows| (ANROWS |left|)) (LETT |mNRows| (ANROWS |m|))
          (LETT |mNCols| (ANCOLS |m|))
          (SEQ (LETT |nr| 1) (LETT #7# |leftNRows|) G190
               (COND ((|greater_SI| |nr| #7#) (GO G191)))
               (SEQ
                (EXIT
                 (SEQ (LETT |r| (SPADCALL |left| |nr| (QREFELT % 27)))
                      (LETT |order| 1)
                      (COND
                       ((<= |nr| |mNRows|)
                        (COND
                         ((<= |nr| |mNCols|)
                          (LETT |order|
                                (SPADCALL |m| |nr| |nr| (QREFELT % 28)))))))
                      (EXIT
                       (COND
                        ((<= |order| 1)
                         (PROGN (LETT #6# |$NoValue|) (GO #8=#:G28)))
                        ('T
                         (SEQ (LETT |g| (CONS |r| |order|))
                              (EXIT
                               (LETT |res|
                                     (SPADCALL |res| |g|
                                               (QREFELT % 31))))))))))
                #8# (EXIT #6#))
               (LETT |nr| (|inc_SI| |nr|)) (GO G190) G191 (EXIT NIL))
          (LETT |augmented|
                (SPADCALL (SPADCALL |AInt| (QREFELT % 32)) |BInt|
                          (QREFELT % 33)))
          (LETT |smitFree| (SPADCALL |augmented| (QREFELT % 24)))
          (LETT |mFree| (QVELT |smitFree| 0)) (LETT |n_rows| (ANROWS |mFree|))
          (LETT |n_cols| (ANCOLS |mFree|)) (LETT |kernelFree| NIL)
          (SEQ (LETT |i| 1) (LETT #1# |n_cols|) G190
               (COND ((|greater_SI| |i| #1#) (GO G191)))
               (SEQ
                (EXIT
                 (COND
                  ((OR (> |i| |n_rows|)
                       (EQL (SPADCALL |mFree| |i| |i| (QREFELT % 28)) 0))
                   (SEQ (LETT |v| (MAKEARR1 |n_cols| 0))
                        (SPADCALL |v| |i| 1 (QREFELT % 34))
                        (EXIT
                         (LETT |kernelFree|
                               (CONS
                                (SPADCALL (QVELT |smitFree| 2) |v|
                                          (QREFELT % 35))
                                |kernelFree|))))))))
               (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
          (EXIT (CONS |res| (NREVERSE |kernelFree|)))))) 

(SDEFUN |HOMOL;homology;LLL%;2|
        ((|torsionVec| (|List| (|List| (|Integer|))))
         (|torsionOrd| (|List| (|Integer|)))
         (|free1| (|List| (|List| (|Integer|)))) (% (%)))
        (SPROG
         ((|kernelFree| (|List| (|Vector| (|Integer|)))) (#1=#:G58 NIL)
          (|v| NIL) (#2=#:G57 NIL)
          (|res|
           (|List|
            (|Record| (|:| |vec| (|Vector| (|Integer|)))
                      (|:| |ord| (|Integer|)))))
          (|r3|
           (|Record| (|:| |vec| (|Vector| (|Integer|)))
                     (|:| |ord| (|Integer|))))
          (#3=#:G55 NIL) (|r1| NIL) (#4=#:G56 NIL) (|r2| NIL))
         (SEQ
          (COND
           ((SPADCALL (LENGTH |torsionVec|) (LENGTH |torsionOrd|)
                      (QREFELT % 37))
            (|error|
             "attempt to construct homology with #torsionVec ~= #torsionOrd")))
          (LETT |res| NIL)
          (SEQ (LETT |r2| NIL) (LETT #4# |torsionOrd|) (LETT |r1| NIL)
               (LETT #3# |torsionVec|) G190
               (COND
                ((OR (ATOM #3#) (PROGN (LETT |r1| (CAR #3#)) NIL) (ATOM #4#)
                     (PROGN (LETT |r2| (CAR #4#)) NIL))
                 (GO G191)))
               (SEQ (LETT |r3| (CONS (SPADCALL |r1| (QREFELT % 39)) |r2|))
                    (EXIT (LETT |res| (SPADCALL |res| |r3| (QREFELT % 31)))))
               (LETT #3# (PROG1 (CDR #3#) (LETT #4# (CDR #4#)))) (GO G190) G191
               (EXIT NIL))
          (LETT |kernelFree|
                (PROGN
                 (LETT #2# NIL)
                 (SEQ (LETT |v| NIL) (LETT #1# |free1|) G190
                      (COND
                       ((OR (ATOM #1#) (PROGN (LETT |v| (CAR #1#)) NIL))
                        (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #2# (CONS (SPADCALL |v| (QREFELT % 39)) #2#))))
                      (LETT #1# (CDR #1#)) (GO G190) G191
                      (EXIT (NREVERSE #2#)))))
          (EXIT (CONS |res| |kernelFree|))))) 

(SDEFUN |HOMOL;homology0;%;3| ((% (%))) (SPADCALL NIL NIL NIL (QREFELT % 41))) 

(SDEFUN |HOMOL;homologyz;%;4| ((% (%)))
        (SPADCALL NIL NIL (LIST (LIST 1)) (QREFELT % 41))) 

(SDEFUN |HOMOL;homologyzz;%;5| ((% (%)))
        (SPADCALL NIL NIL (LIST (LIST 1 0) (LIST 0 1)) (QREFELT % 41))) 

(SDEFUN |HOMOL;homologyc2;%;6| ((% (%)))
        (SPADCALL (LIST (LIST 1)) (LIST 2) NIL (QREFELT % 41))) 

(SDEFUN |HOMOL;homologyzc2;%;7| ((% (%)))
        (SPADCALL (LIST (LIST 1 0)) (LIST 2) (LIST (LIST 0 1)) (QREFELT % 41))) 

(SDEFUN |HOMOL;dispGenerators;%Of;8| ((|s| (%)) (% (|OutputForm|)))
        (SPROG
         ((|res| (|OutputForm|)) (|ln2| #1=(|OutputForm|)) (|ln| #1#)
          (#2=#:G70 NIL) (|g| NIL) (|s1| (|Rep|)))
         (SEQ (LETT |res| (SPADCALL (QREFELT % 47))) (LETT |s1| |s|)
              (SEQ (LETT |g| NIL) (LETT #2# (QCAR |s1|)) G190
                   (COND
                    ((OR (ATOM #2#) (PROGN (LETT |g| (CAR #2#)) NIL))
                     (GO G191)))
                   (SEQ
                    (LETT |ln|
                          (SPADCALL
                           (LIST (SPADCALL "gen=" (QREFELT % 12))
                                 (SPADCALL (QCAR |g|) (QREFELT % 48))
                                 (SPADCALL " ord=" (QREFELT % 12))
                                 (SPADCALL (QCDR |g|) (QREFELT % 49)))
                           (QREFELT % 51)))
                    (EXIT (LETT |res| (SPADCALL |res| |ln| (QREFELT % 52)))))
                   (LETT #2# (CDR #2#)) (GO G190) G191 (EXIT NIL))
              (LETT |ln2|
                    (SPADCALL
                     (LIST (SPADCALL " free part=" (QREFELT % 12))
                           (SPADCALL (QCDR |s1|) (QREFELT % 54)))
                     (QREFELT % 51)))
              (LETT |res| (SPADCALL |res| |ln2| (QREFELT % 52))) (EXIT |res|)))) 

(SDEFUN |HOMOL;=;2%B;9| ((|a| (%)) (|b| (%)) (% (|Boolean|)))
        (SPROG
         ((#1=#:G84 NIL) (|noTorsionB| #2=(|Boolean|)) (#3=#:G86 NIL)
          (|tb| NIL) (|noTorsionA| #2#) (#4=#:G85 NIL) (|ta| NIL)
          (|torb|
           #5=(|List|
               (|Record| (|:| |vec| (|Vector| (|Integer|)))
                         (|:| |ord| (|Integer|)))))
          (|tora| #5#))
         (SEQ
          (EXIT
           (SEQ (LETT |tora| (QCAR |a|)) (LETT |torb| (QCAR |b|))
                (LETT |noTorsionA| 'T) (LETT |noTorsionB| 'T)
                (SEQ (LETT |ta| NIL) (LETT #4# |tora|) G190
                     (COND
                      ((OR (ATOM #4#) (PROGN (LETT |ta| (CAR #4#)) NIL))
                       (GO G191)))
                     (SEQ
                      (EXIT
                       (COND
                        ((SPADCALL (QCDR |ta|) 0 (QREFELT % 37))
                         (COND
                          ((SPADCALL (QCDR |ta|) 1 (QREFELT % 37))
                           (LETT |noTorsionA| NIL)))))))
                     (LETT #4# (CDR #4#)) (GO G190) G191 (EXIT NIL))
                (SEQ (LETT |tb| NIL) (LETT #3# |torb|) G190
                     (COND
                      ((OR (ATOM #3#) (PROGN (LETT |tb| (CAR #3#)) NIL))
                       (GO G191)))
                     (SEQ
                      (EXIT
                       (COND
                        ((SPADCALL (QCDR |tb|) 0 (QREFELT % 37))
                         (COND
                          ((SPADCALL (QCDR |tb|) 1 (QREFELT % 37))
                           (LETT |noTorsionB| NIL)))))))
                     (LETT #3# (CDR #3#)) (GO G190) G191 (EXIT NIL))
                (COND
                 ((SPADCALL |noTorsionA| |noTorsionA| (QREFELT % 56))
                  (PROGN (LETT #1# NIL) (GO #6=#:G83))))
                (EXIT (EQL (LENGTH (QCDR |a|)) (LENGTH (QCDR |b|))))))
          #6# (EXIT #1#)))) 

(SDEFUN |HOMOL;coerce;%Of;10| ((|s| (%)) (% (|OutputForm|)))
        (SPROG
         ((|res| (|OutputForm|)) (|firstTermRead| (|Boolean|))
          (|ln2| (|OutputForm|)) (#1=#:G97 NIL) (|t| NIL)
          (|nFree| (|NonNegativeInteger|)) (|s1| (|Rep|)))
         (SEQ (LETT |res| (SPADCALL (QREFELT % 47))) (LETT |firstTermRead| NIL)
              (LETT |s1| |s|) (LETT |nFree| (LENGTH (QCDR |s1|)))
              (COND
               ((> |nFree| 0)
                (SEQ
                 (LETT |res|
                       (SPADCALL |res| (SPADCALL "Z" (QREFELT % 12))
                                 (QREFELT % 14)))
                 (COND
                  ((> |nFree| 1)
                   (LETT |res|
                         (SPADCALL
                          (LIST |res| (SPADCALL "*" (QREFELT % 12))
                                (SPADCALL |nFree| (QREFELT % 13)))
                          (QREFELT % 51)))))
                 (EXIT (LETT |firstTermRead| 'T)))))
              (SEQ (LETT |t| NIL) (LETT #1# (QCAR |s1|)) G190
                   (COND
                    ((OR (ATOM #1#) (PROGN (LETT |t| (CAR #1#)) NIL))
                     (GO G191)))
                   (SEQ
                    (EXIT
                     (COND
                      ((NULL (EQL (QCDR |t|) 0))
                       (COND
                        ((NULL (EQL (QCDR |t|) 1))
                         (SEQ
                          (COND
                           (|firstTermRead|
                            (LETT |res|
                                  (SPADCALL |res| (SPADCALL "+" (QREFELT % 12))
                                            (QREFELT % 14)))))
                          (LETT |ln2|
                                (SPADCALL
                                 (LIST (SPADCALL "C" (QREFELT % 12))
                                       (SPADCALL (QCDR |t|) (QREFELT % 49)))
                                 (QREFELT % 51)))
                          (LETT |res| (SPADCALL |res| |ln2| (QREFELT % 14)))
                          (EXIT (LETT |firstTermRead| 'T)))))))))
                   (LETT #1# (CDR #1#)) (GO G190) G191 (EXIT NIL))
              (COND
               ((NULL |firstTermRead|)
                (LETT |res|
                      (SPADCALL |res| (SPADCALL "0" (QREFELT % 12))
                                (QREFELT % 14)))))
              (EXIT |res|)))) 

(DECLAIM (NOTINLINE |Homology;|)) 

(DEFUN |Homology| ()
  (SPROG NIL
         (PROG (#1=#:G99)
           (RETURN
            (COND
             ((LETT #1# (HGET |$ConstructorCache| '|Homology|))
              (|CDRwithIncrement| (CDAR #1#)))
             ('T
              (UNWIND-PROTECT
                  (PROG1
                      (CDDAR
                       (HPUT |$ConstructorCache| '|Homology|
                             (LIST (CONS NIL (CONS 1 (|Homology;|))))))
                    (LETT #1# T))
                (COND ((NOT #1#) (HREM |$ConstructorCache| '|Homology|)))))))))) 

(DEFUN |Homology;| ()
  (SPROG ((|dv$| NIL) (% NIL) (|pv$| NIL))
         (PROGN
          (LETT |dv$| '(|Homology|))
          (LETT % (GETREFV 59))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3 (LETT |pv$| (|buildPredVector| 0 0 NIL)))
          (|haddProp| |$ConstructorCache| '|Homology| NIL (CONS 1 %))
          (|stuffDomainSlots| %)
          (SETF |pv$| (QREFELT % 3))
          (QSETREFV % 6
                    (|Record|
                     (|:| |torsionPart|
                          (|List|
                           (|Record| (|:| |vec| (|Vector| (|Integer|)))
                                     (|:| |ord| (|Integer|)))))
                     (|:| |freePart| (|List| (|Vector| (|Integer|))))))
          %))) 

(MAKEPROP '|Homology| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL '|Rep| (|Boolean|) (|NonNegativeInteger|)
              (0 . ~=) (|String|) (|OutputForm|) (6 . |message|)
              (11 . |coerce|) (16 . |hconcat|) (|Void|) (22 . |print|)
              (|Matrix| 26) (27 . |zero|) (33 . *) (39 . ~=) (45 . |coerce|)
              (|Record| (|:| |Smith| 17) (|:| |leftEqMat| 17)
                        (|:| |rightEqMat| 17))
              (|SmithNormalForm| 26 25 25 17) (50 . |completeSmith|)
              (|Vector| 26) (|Integer|) (55 . |row|) (61 . |elt|)
              (|Record| (|:| |vec| 25) (|:| |ord| 26)) (|List| 29)
              (68 . |concat|) (74 . |transpose|) (79 . |vertConcat|)
              (85 . |setelt!|) (92 . *) |HOMOL;homologyGroup;2M%;1| (98 . ~=)
              (|List| 26) (104 . |vector|) (|List| 38) |HOMOL;homology;LLL%;2|
              |HOMOL;homology0;%;3| |HOMOL;homologyz;%;4|
              |HOMOL;homologyzz;%;5| |HOMOL;homologyc2;%;6|
              |HOMOL;homologyzc2;%;7| (109 . |empty|) (113 . |coerce|)
              (118 . |coerce|) (|List| %) (123 . |hconcat|) (128 . |vconcat|)
              (|List| 25) (134 . |coerce|) |HOMOL;dispGenerators;%Of;8|
              (139 . ~=) |HOMOL;=;2%B;9| |HOMOL;coerce;%Of;10|)
           '#(~= 145 |latex| 151 |homologyzz| 156 |homologyzc2| 160 |homologyz|
              164 |homologyc2| 168 |homologyGroup| 172 |homology0| 178
              |homology| 182 |dispGenerators| 189 |coerce| 194 = 199)
           'NIL
           (CONS (|makeByteWordVec2| 1 '(0 0 0))
                 (CONS '#(|SetCategory&| NIL |BasicType&|)
                       (CONS
                        '#((|SetCategory|) (|CoercibleTo| 11) (|BasicType|))
                        (|makeByteWordVec2| 58
                                            '(2 8 7 0 0 9 1 11 0 10 12 1 8 11 0
                                              13 2 11 0 0 0 14 1 11 15 0 16 2
                                              17 0 8 8 18 2 17 0 0 0 19 2 17 7
                                              0 0 20 1 17 11 0 21 1 23 22 17 24
                                              2 17 25 0 26 27 3 17 26 0 26 26
                                              28 2 30 0 0 29 31 1 17 0 0 32 2
                                              17 0 0 0 33 3 25 26 0 26 26 34 2
                                              17 25 0 25 35 2 26 7 0 0 37 1 25
                                              0 38 39 0 11 0 47 1 25 11 0 48 1
                                              26 11 0 49 1 11 0 50 51 2 11 0 0
                                              0 52 1 53 11 0 54 2 7 7 0 0 56 2
                                              0 7 0 0 1 1 0 10 0 1 0 0 0 44 0 0
                                              0 46 0 0 0 43 0 0 0 45 2 0 0 17
                                              17 36 0 0 0 42 3 0 0 40 38 40 41
                                              1 0 11 0 55 1 0 11 0 58 2 0 7 0 0
                                              57)))))
           '|lookupComplete|)) 
