
(SDEFUN |FRAMALG-;traceMatrix;M;1| (($ |Matrix| R))
        (SPADCALL (SPADCALL (QREFELT $ 10)) (QREFELT $ 12))) 

(SDEFUN |FRAMALG-;discriminant;R;2| (($ R))
        (SPADCALL (SPADCALL (QREFELT $ 10)) (QREFELT $ 14))) 

(SDEFUN |FRAMALG-;regularRepresentation;SM;3| ((|x| S) ($ |Matrix| R))
        (SPADCALL |x| (SPADCALL (QREFELT $ 10)) (QREFELT $ 16))) 

(SDEFUN |FRAMALG-;coordinates;SV;4| ((|x| S) ($ |Vector| R))
        (SPADCALL |x| (SPADCALL (QREFELT $ 10)) (QREFELT $ 19))) 

(SDEFUN |FRAMALG-;represents;VS;5| ((|x| |Vector| R) ($ S))
        (SPADCALL |x| (SPADCALL (QREFELT $ 10)) (QREFELT $ 21))) 

(SDEFUN |FRAMALG-;regularRepresentation;SM;6| ((|x| S) ($ |Matrix| R))
        (SPROG
         ((#1=#:G716 NIL) (|i| NIL) (|j| NIL) (|b| (|Vector| S))
          (|m| (|Matrix| R)) (|n| (|NonNegativeInteger|)))
         (SEQ
          (LETT |m|
                (MAKE_MATRIX1
                 (LETT |n| (SPADCALL (QREFELT $ 24))
                       . #2=(|FRAMALG-;regularRepresentation;SM;6|))
                 |n| (|spadConstant| $ 25))
                . #2#)
          (LETT |b| (SPADCALL (QREFELT $ 10)) . #2#)
          (SEQ (LETT |j| 1 . #2#)
               (LETT |i| (SPADCALL |b| (QREFELT $ 28)) . #2#)
               (LETT #1# (QVSIZE |b|) . #2#) G190
               (COND ((> |i| #1#) (GO G191)))
               (SEQ
                (EXIT
                 (SPADCALL |m| |j|
                           (SPADCALL
                            (SPADCALL |x| (QAREF1O |b| |i| 1) (QREFELT $ 29))
                            (QREFELT $ 30))
                           (QREFELT $ 31))))
               (LETT |i| (PROG1 (+ |i| 1) (LETT |j| (|inc_SI| |j|) . #2#))
                     . #2#)
               (GO G190) G191 (EXIT NIL))
          (EXIT (SPADCALL |m| (QREFELT $ 32)))))) 

(SDEFUN |FRAMALG-;characteristicPolynomial;SUP;7| ((|x| S) ($ UP))
        (SPROG
         ((|mat1| (|Matrix| UP)) (|mat0| (|Matrix| UP)) (|mat00| (|Matrix| R)))
         (SEQ
          (LETT |mat00| (SPADCALL |x| (QREFELT $ 33))
                . #1=(|FRAMALG-;characteristicPolynomial;SUP;7|))
          (LETT |mat0| (SPADCALL (ELT $ 34) |mat00| (QREFELT $ 38)) . #1#)
          (LETT |mat1|
                (SPADCALL (SPADCALL (QREFELT $ 24))
                          (SPADCALL (|spadConstant| $ 40) 1 (QREFELT $ 42))
                          (QREFELT $ 43))
                . #1#)
          (EXIT
           (SPADCALL (SPADCALL |mat1| |mat0| (QREFELT $ 44)) (QREFELT $ 45)))))) 

(SDEFUN |FRAMALG-;minimalPolynomial;SUP;8| ((|x| S) ($ UP))
        (SPROG
         ((#1=#:G731 NIL) (#2=#:G730 (UP)) (#3=#:G732 (UP)) (#4=#:G736 NIL)
          (|i| NIL) (|v| (|Vector| R)) (|y| (S)) (#5=#:G735 NIL)
          (|m| (|Matrix| R)) (|n| (|PositiveInteger|)))
         (SEQ
          (LETT |y| (|spadConstant| $ 39)
                . #6=(|FRAMALG-;minimalPolynomial;SUP;8|))
          (LETT |n| (SPADCALL (QREFELT $ 24)) . #6#)
          (LETT |m| (SPADCALL |n| (+ |n| 1) (QREFELT $ 47)) . #6#)
          (SEQ (LETT |i| 1 . #6#) (LETT #5# (+ |n| 1) . #6#) G190
               (COND ((|greater_SI| |i| #5#) (GO G191)))
               (SEQ
                (SPADCALL |m| |i| (SPADCALL |y| (QREFELT $ 30)) (QREFELT $ 48))
                (EXIT (LETT |y| (SPADCALL |y| |x| (QREFELT $ 29)) . #6#)))
               (LETT |i| (|inc_SI| |i|) . #6#) (GO G190) G191 (EXIT NIL))
          (LETT |v| (|SPADfirst| (SPADCALL |m| (QREFELT $ 50))) . #6#)
          (EXIT
           (PROGN
            (LETT #1# NIL . #6#)
            (SEQ (LETT |i| 0 . #6#) (LETT #4# (- (QVSIZE |v|) 1) . #6#) G190
                 (COND ((|greater_SI| |i| #4#) (GO G191)))
                 (SEQ
                  (EXIT
                   (PROGN
                    (LETT #3#
                          (SPADCALL (SPADCALL |v| (+ |i| 1) (QREFELT $ 51)) |i|
                                    (QREFELT $ 42))
                          . #6#)
                    (COND
                     (#1# (LETT #2# (SPADCALL #2# #3# (QREFELT $ 52)) . #6#))
                     ('T (PROGN (LETT #2# #3# . #6#) (LETT #1# 'T . #6#)))))))
                 (LETT |i| (|inc_SI| |i|) . #6#) (GO G190) G191 (EXIT NIL))
            (COND (#1# #2#) ('T (|spadConstant| $ 53)))))))) 

(DECLAIM (NOTINLINE |FramedAlgebra&;|)) 

(DEFUN |FramedAlgebra&| (|#1| |#2| |#3|)
  (SPROG ((|pv$| NIL) ($ NIL) (|dv$| NIL) (DV$3 NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|) . #1=(|FramedAlgebra&|))
          (LETT DV$2 (|devaluate| |#2|) . #1#)
          (LETT DV$3 (|devaluate| |#3|) . #1#)
          (LETT |dv$| (LIST '|FramedAlgebra&| DV$1 DV$2 DV$3) . #1#)
          (LETT $ (GETREFV 55) . #1#)
          (QSETREFV $ 0 |dv$|)
          (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
          (|stuffDomainSlots| $)
          (QSETREFV $ 6 |#1|)
          (QSETREFV $ 7 |#2|)
          (QSETREFV $ 8 |#3|)
          (SETF |pv$| (QREFELT $ 3))
          (COND
           ((|HasCategory| |#3| '(|CommutativeRing|))
            (QSETREFV $ 46
                      (CONS
                       (|dispatchFunction|
                        |FRAMALG-;characteristicPolynomial;SUP;7|)
                       $))))
          (COND
           ((|HasCategory| |#2| '(|Field|))
            (PROGN
             (QSETREFV $ 54
                       (CONS
                        (|dispatchFunction| |FRAMALG-;minimalPolynomial;SUP;8|)
                        $)))))
          $))) 

(MAKEPROP '|FramedAlgebra&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|local| |#3|) (|Vector| $) (0 . |basis|) (|Matrix| 7)
              (4 . |traceMatrix|) |FRAMALG-;traceMatrix;M;1|
              (9 . |discriminant|) |FRAMALG-;discriminant;R;2|
              (14 . |regularRepresentation|)
              |FRAMALG-;regularRepresentation;SM;6| (|Vector| 7)
              (20 . |coordinates|) |FRAMALG-;coordinates;SV;4|
              (26 . |represents|) |FRAMALG-;represents;VS;5|
              (|PositiveInteger|) (32 . |rank|) (36 . |Zero|) (|Integer|)
              (|Vector| 6) (40 . |minIndex|) (45 . *) (51 . |coordinates|)
              (56 . |setRow!|) (63 . |transpose|)
              (68 . |regularRepresentation|) (73 . |coerce|) (|Matrix| 8)
              (|Mapping| 8 7)
              (|MatrixCategoryFunctions2| 7 18 18 11 8 (|Vector| 8)
                                          (|Vector| 8) 35)
              (78 . |map|) (84 . |One|) (88 . |One|) (|NonNegativeInteger|)
              (92 . |monomial|) (98 . |scalarMatrix|) (104 . -)
              (110 . |determinant|) (115 . |characteristicPolynomial|)
              (120 . |zero|) (126 . |setColumn!|) (|List| 18)
              (133 . |nullSpace|) (138 . |elt|) (144 . +) (150 . |Zero|)
              (154 . |minimalPolynomial|))
           '#(|traceMatrix| 159 |represents| 163 |regularRepresentation| 168
              |minimalPolynomial| 173 |discriminant| 178 |coordinates| 182
              |characteristicPolynomial| 187)
           'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 54
                                                 '(0 6 9 10 1 6 11 9 12 1 6 7 9
                                                   14 2 6 11 0 9 16 2 6 18 0 9
                                                   19 2 6 0 18 9 21 0 6 23 24 0
                                                   7 0 25 1 27 26 0 28 2 6 0 0
                                                   0 29 1 6 18 0 30 3 11 0 0 26
                                                   18 31 1 11 0 0 32 1 6 11 0
                                                   33 1 8 0 7 34 2 37 35 36 11
                                                   38 0 6 0 39 0 7 0 40 2 8 0 7
                                                   41 42 2 35 0 41 8 43 2 35 0
                                                   0 0 44 1 35 8 0 45 1 0 8 0
                                                   46 2 11 0 41 41 47 3 11 0 0
                                                   26 18 48 1 11 49 0 50 2 18 7
                                                   0 26 51 2 8 0 0 0 52 0 8 0
                                                   53 1 0 8 0 54 0 0 11 13 1 0
                                                   0 18 22 1 0 11 0 17 1 0 8 0
                                                   54 0 0 7 15 1 0 18 0 20 1 0
                                                   8 0 46)))))
           '|lookupComplete|)) 
