
(SDEFUN |QFORM;quadraticForm;Sm%;1| ((|m| (|SquareMatrix| |n| K)) (% (%)))
        (COND
         ((NULL (SPADCALL |m| (QREFELT % 10)))
          (|error| "quadraticForm requires a symmetric matrix"))
         ('T |m|))) 

(PUT '|QFORM;matrix;%Sm;2| '|SPADreplace| '(XLAM (|q|) |q|)) 

(SDEFUN |QFORM;matrix;%Sm;2| ((|q| (%)) (% (|SquareMatrix| |n| K))) |q|) 

(SDEFUN |QFORM;elt;%DpK;3| ((|q| (%)) (|v| (|DirectProduct| |n| K)) (% (K)))
        (SPADCALL |v|
                  (SPADCALL (SPADCALL |q| (QREFELT % 12)) |v| (QREFELT % 14))
                  (QREFELT % 15))) 

(SDEFUN |QFORM;convert;%If;4| ((|q| (%)) (% (|InputForm|)))
        (SPROG ((|qf| (|InputForm|)) (|mif| (|InputForm|)))
               (SEQ
                (LETT |mif|
                      (SPADCALL (SPADCALL |q| (QREFELT % 12)) (QREFELT % 18)))
                (LETT |qf|
                      (SPADCALL (SPADCALL '|quadraticForm| (QREFELT % 21))
                                (QREFELT % 22)))
                (EXIT (SPADCALL (LIST |qf| |mif|) (QREFELT % 24)))))) 

(DECLAIM (NOTINLINE |QuadraticForm;|)) 

(DEFUN |QuadraticForm;| (|#1| |#2|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 |#1|)
          (LETT DV$2 (|devaluate| |#2|))
          (LETT |dv$| (LIST '|QuadraticForm| DV$1 DV$2))
          (LETT % (GETREFV 32))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3
                    (LETT |pv$|
                          (|buildPredVector| 0 0
                                             (LIST
                                              (|HasCategory|
                                               (|SquareMatrix| |#1| |#2|)
                                               '(|ConvertibleTo|
                                                 (|InputForm|)))))))
          (|haddProp| |$ConstructorCache| '|QuadraticForm| (LIST DV$1 DV$2)
                      (CONS 1 %))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (QSETREFV % 7 |#2|)
          (SETF |pv$| (QREFELT % 3))
          (QSETREFV % 8 (|SquareMatrix| |#1| |#2|))
          (COND
           ((|testBitVector| |pv$| 1)
            (QSETREFV % 25
                      (CONS (|dispatchFunction| |QFORM;convert;%If;4|) %))))
          %))) 

(DEFUN |QuadraticForm| (&REST #1=#:G11)
  (SPROG NIL
         (PROG (#2=#:G12)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluate_sig| #1# '(NIL T))
                                               (HGET |$ConstructorCache|
                                                     '|QuadraticForm|)
                                               '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |QuadraticForm;|) #1#)
                    (LETT #2# T))
                (COND
                 ((NOT #2#) (HREM |$ConstructorCache| '|QuadraticForm|)))))))))) 

(MAKEPROP '|QuadraticForm| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL (|SquareMatrix| (NRTEVAL (QREFELT % 6)) 7)
              (|local| |#1|) (|local| |#2|) '|Rep| (|Boolean|)
              (0 . |symmetric?|) |QFORM;quadraticForm;Sm%;1|
              |QFORM;matrix;%Sm;2| (|DirectProduct| (NRTEVAL (QREFELT % 6)) 7)
              (5 . *) (11 . |dot|) |QFORM;elt;%DpK;3| (|InputForm|)
              (17 . |convert|) (|Symbol|) (|SExpression|) (22 . |convert|)
              (27 . |convert|) (|List| %) (32 . |convert|) (37 . |convert|)
              (|OutputForm|) (|String|) (|PositiveInteger|)
              (|NonNegativeInteger|) (|Union| % '"failed") (|Integer|))
           '#(~= 42 |zero?| 48 |subtractIfCan| 53 |sample| 59 |quadraticForm|
              63 |opposite?| 68 |matrix| 74 |latex| 79 |elt| 84 |convert| 90
              |coerce| 95 |Zero| 100 = 104 - 110 + 121 * 127)
           'NIL
           (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 1 0 0))
                 (CONS
                  '#(|AbelianGroup&| NIL |AbelianMonoid&| |AbelianSemiGroup&|
                     |SetCategory&| NIL NIL |BasicType&|)
                  (CONS
                   '#((|AbelianGroup|) (|CancellationAbelianMonoid|)
                      (|AbelianMonoid|) (|AbelianSemiGroup|) (|SetCategory|)
                      (|ConvertibleTo| 17) (|CoercibleTo| 26) (|BasicType|))
                   (|makeByteWordVec2| 31
                                       '(1 8 9 0 10 2 8 13 0 13 14 2 13 7 0 0
                                         15 1 5 17 0 18 1 20 0 19 21 1 17 0 20
                                         22 1 17 0 23 24 1 0 17 0 25 2 0 9 0 0
                                         1 1 0 9 0 1 2 0 30 0 0 1 0 0 0 1 1 0 0
                                         5 11 2 0 9 0 0 1 1 0 5 0 12 1 0 27 0 1
                                         2 0 7 0 13 16 1 1 17 0 25 1 0 26 0 1 0
                                         0 0 1 2 0 9 0 0 1 1 0 0 0 1 2 0 0 0 0
                                         1 2 0 0 0 0 1 2 0 0 28 0 1 2 0 0 29 0
                                         1 2 0 0 31 0 1)))))
           '|lookupComplete|)) 
