
(SDEFUN |FINRALG-;discriminant;VR;1| ((|v| (|Vector| S)) (% (R)))
        (SPADCALL (SPADCALL |v| (QREFELT % 11)) (QREFELT % 12))) 

(SDEFUN |FINRALG-;coordinates;2VM;2|
        ((|v| (|Vector| S)) (|b| (|Vector| S)) (% (|Matrix| R)))
        (SPROG ((#1=#:G24 NIL) (|i| NIL) (|j| NIL) (|m| (|Matrix| R)))
               (SEQ
                (LETT |m|
                      (MAKE_MATRIX1 (QVSIZE |v|) (QVSIZE |b|)
                                    (|spadConstant| % 14)))
                (SEQ (LETT |j| (PROGN |m| 1))
                     (LETT |i| (SPADCALL |v| (QREFELT % 17)))
                     (LETT #1# (QVSIZE |v|)) G190
                     (COND ((> |i| #1#) (GO G191)))
                     (SEQ
                      (EXIT
                       (SPADCALL |m| |j|
                                 (SPADCALL (QAREF1O |v| |i| 1) |b|
                                           (QREFELT % 19))
                                 (QREFELT % 20))))
                     (LETT |i| (PROG1 (+ |i| 1) (LETT |j| (+ |j| 1))))
                     (GO G190) G191 (EXIT NIL))
                (EXIT |m|)))) 

(SDEFUN |FINRALG-;represents;VVS;3|
        ((|v| (|Vector| R)) (|b| (|Vector| S)) (% (S)))
        (SPROG
         ((#1=#:G27 NIL) (#2=#:G26 (S)) (#3=#:G28 (S)) (#4=#:G31 NIL) (|i| NIL)
          (|m| (|Integer|)))
         (SEQ (LETT |m| (- (SPADCALL |v| (QREFELT % 22)) 1))
              (EXIT
               (PROGN
                (LETT #1# NIL)
                (SEQ (LETT |i| 1) (LETT #4# (SPADCALL (QREFELT % 24))) G190
                     (COND ((|greater_SI| |i| #4#) (GO G191)))
                     (SEQ
                      (EXIT
                       (PROGN
                        (LETT #3#
                              (SPADCALL
                               (SPADCALL |v| (+ |i| |m|) (QREFELT % 25))
                               (SPADCALL |b| (+ |i| |m|) (QREFELT % 26))
                               (QREFELT % 27)))
                        (COND
                         (#1# (LETT #2# (SPADCALL #2# #3# (QREFELT % 28))))
                         ('T (PROGN (LETT #2# #3#) (LETT #1# 'T)))))))
                     (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                (COND (#1# #2#) ('T (|spadConstant| % 29)))))))) 

(SDEFUN |FINRALG-;traceMatrix;VM;4| ((|v| (|Vector| S)) (% (|Matrix| R)))
        (SPROG
         ((#1=#:G44 NIL) (|j| NIL) (#2=#:G43 NIL) (#3=#:G42 NIL) (|i| NIL)
          (#4=#:G41 NIL))
         (SEQ
          (SPADCALL
           (PROGN
            (LETT #4# NIL)
            (SEQ (LETT |i| (SPADCALL |v| (QREFELT % 17)))
                 (LETT #3# (QVSIZE |v|)) G190 (COND ((> |i| #3#) (GO G191)))
                 (SEQ
                  (EXIT
                   (LETT #4#
                         (CONS
                          (PROGN
                           (LETT #2# NIL)
                           (SEQ (LETT |j| (SPADCALL |v| (QREFELT % 17)))
                                (LETT #1# (QVSIZE |v|)) G190
                                (COND ((> |j| #1#) (GO G191)))
                                (SEQ
                                 (EXIT
                                  (LETT #2#
                                        (CONS
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |v| |i| (QREFELT % 26))
                                           (SPADCALL |v| |j| (QREFELT % 26))
                                           (QREFELT % 31))
                                          (QREFELT % 32))
                                         #2#))))
                                (LETT |j| (+ |j| 1)) (GO G190) G191
                                (EXIT (NREVERSE #2#))))
                          #4#))))
                 (LETT |i| (+ |i| 1)) (GO G190) G191 (EXIT (NREVERSE #4#))))
           (QREFELT % 34))))) 

(SDEFUN |FINRALG-;regularRepresentation;SVM;5|
        ((|x| (S)) (|b| (|Vector| S)) (% (|Matrix| R)))
        (SPROG ((#1=#:G52 NIL) (|i| NIL) (#2=#:G51 NIL) (|m| (|Integer|)))
               (SEQ (LETT |m| (- (SPADCALL |b| (QREFELT % 17)) 1))
                    (EXIT
                     (SPADCALL
                      (SPADCALL
                       (PROGN
                        (LETT #2# NIL)
                        (SEQ (LETT |i| 1) (LETT #1# (SPADCALL (QREFELT % 24)))
                             G190 (COND ((|greater_SI| |i| #1#) (GO G191)))
                             (SEQ
                              (EXIT
                               (LETT #2#
                                     (CONS
                                      (SPADCALL
                                       (SPADCALL
                                        (SPADCALL |x|
                                                  (SPADCALL |b| (+ |i| |m|)
                                                            (QREFELT % 26))
                                                  (QREFELT % 31))
                                        |b| (QREFELT % 19))
                                       (QREFELT % 37))
                                      #2#))))
                             (LETT |i| (|inc_SI| |i|)) (GO G190) G191
                             (EXIT (NREVERSE #2#))))
                       (QREFELT % 34))
                      (QREFELT % 38)))))) 

(DECLAIM (NOTINLINE |FiniteRankAlgebra&;|)) 

(DEFUN |FiniteRankAlgebra&| (|#1| |#2| |#3|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$3 NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|))
          (LETT DV$2 (|devaluate| |#2|))
          (LETT DV$3 (|devaluate| |#3|))
          (LETT |dv$| (LIST '|FiniteRankAlgebra&| DV$1 DV$2 DV$3))
          (LETT % (GETREFV 40))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3
                    (LETT |pv$|
                          (|buildPredVector| 0 0
                                             (LIST
                                              (|HasCategory| |#2|
                                                             '(|CharacteristicNonZero|))
                                              (|HasCategory| |#2|
                                                             '(|CharacteristicZero|))
                                              (|HasCategory| |#2|
                                                             '(|Field|))))))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (QSETREFV % 7 |#2|)
          (QSETREFV % 8 |#3|)
          (SETF |pv$| (QREFELT % 3))
          %))) 

(MAKEPROP '|FiniteRankAlgebra&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|local| |#3|) (|Matrix| 7) (|Vector| %) (0 . |traceMatrix|)
              (5 . |determinant|) |FINRALG-;discriminant;VR;1| (10 . |Zero|)
              (|Integer|) (|Vector| 6) (14 . |minIndex|) (|Vector| 7)
              (19 . |coordinates|) (25 . |setRow!|)
              |FINRALG-;coordinates;2VM;2| (32 . |minIndex|)
              (|PositiveInteger|) (37 . |rank|) (41 . |elt|) (47 . |elt|)
              (53 . *) (59 . +) (65 . |Zero|) |FINRALG-;represents;VVS;3|
              (69 . *) (75 . |trace|) (|List| 36) (80 . |matrix|)
              |FINRALG-;traceMatrix;VM;4| (|List| 7) (85 . |parts|)
              (90 . |transpose|) |FINRALG-;regularRepresentation;SVM;5|)
           '#(|traceMatrix| 95 |represents| 100 |regularRepresentation| 106
              |discriminant| 112 |coordinates| 117)
           'NIL
           (CONS (|makeByteWordVec2| 1 '(0))
                 (CONS '#(NIL)
                       (CONS
                        '#((|Join|
                            (|mkCategory|
                             (LIST
                              '((|traceMatrix|
                                 ((|Matrix| |#2|) (|Vector| |#1|)))
                                T)
                              '((|discriminant| (|#2| (|Vector| |#1|))) T)
                              '((|represents|
                                 (|#1| (|Vector| |#2|) (|Vector| |#1|)))
                                T)
                              '((|coordinates|
                                 ((|Matrix| |#2|) (|Vector| |#1|)
                                  (|Vector| |#1|)))
                                T)
                              '((|coordinates|
                                 ((|Vector| |#2|) |#1| (|Vector| |#1|)))
                                T)
                              '((|regularRepresentation|
                                 ((|Matrix| |#2|) |#1| (|Vector| |#1|)))
                                T))
                             (LIST) NIL NIL)))
                        (|makeByteWordVec2| 39
                                            '(1 6 9 10 11 1 9 7 0 12 0 7 0 14 1
                                              16 15 0 17 2 6 18 0 10 19 3 9 0 0
                                              15 18 20 1 18 15 0 22 0 6 23 24 2
                                              18 7 0 15 25 2 16 6 0 15 26 2 6 0
                                              7 0 27 2 6 0 0 0 28 0 6 0 29 2 6
                                              0 0 0 31 1 6 7 0 32 1 9 0 33 34 1
                                              18 36 0 37 1 9 0 0 38 1 0 9 10 35
                                              2 0 0 18 10 30 2 0 9 0 10 39 1 0
                                              7 10 13 2 0 9 10 10 21)))))
           '|lookupComplete|)) 
