
(SDEFUN |JORDAN;*;3$;1| ((|a| $) (|b| $) ($ $))
        (COND
         ((SPADCALL (QREFELT $ 11) (QREFELT $ 16))
          (|error|
           "constructor must no be called with Ring of characteristic 2"))
         ('T
          (SPADCALL
           (SPADCALL (SPADCALL |a| |b| (QREFELT $ 17))
                     (SPADCALL |b| |a| (QREFELT $ 17)) (QREFELT $ 18))
           (QREFELT $ 14) (QREFELT $ 19))))) 

(PUT '|JORDAN;coerce;$A;2| '|SPADreplace| '(XLAM (|a|) |a|)) 

(SDEFUN |JORDAN;coerce;$A;2| ((|a| $) ($ A)) |a|) 

(PUT '|JORDAN;coerce;A$;3| '|SPADreplace| '(XLAM (|a|) |a|)) 

(SDEFUN |JORDAN;coerce;A$;3| ((|a| A) ($ $)) |a|) 

(PUT '|JORDAN;^;$Pi$;4| '|SPADreplace| '(XLAM (|a| |n|) |a|)) 

(SDEFUN |JORDAN;^;$Pi$;4| ((|a| $) (|n| |PositiveInteger|) ($ $)) |a|) 

(DECLAIM (NOTINLINE |AssociatedJordanAlgebra;|)) 

(DEFUN |AssociatedJordanAlgebra| (&REST #1=#:G720)
  (SPROG NIL
         (PROG (#2=#:G721)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluateList| #1#)
                                               (HGET |$ConstructorCache|
                                                     '|AssociatedJordanAlgebra|)
                                               '|domainEqualList|)
                    . #3=(|AssociatedJordanAlgebra|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |AssociatedJordanAlgebra;|) #1#)
                    (LETT #2# T . #3#))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache| '|AssociatedJordanAlgebra|)))))))))) 

(DEFUN |AssociatedJordanAlgebra;| (|#1| |#2|)
  (SPROG
   ((#1=#:G692 NIL) (|pv$| NIL) ($ NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
   (PROGN
    (LETT DV$1 (|devaluate| |#1|) . #2=(|AssociatedJordanAlgebra|))
    (LETT DV$2 (|devaluate| |#2|) . #2#)
    (LETT |dv$| (LIST '|AssociatedJordanAlgebra| DV$1 DV$2) . #2#)
    (LETT $ (GETREFV 43) . #2#)
    (QSETREFV $ 0 |dv$|)
    (QSETREFV $ 3
              (LETT |pv$|
                    (|buildPredVector| 0 0
                                       (LIST
                                        (|HasCategory| |#2|
                                                       (LIST
                                                        '|FramedNonAssociativeAlgebra|
                                                        (|devaluate| |#1|)))
                                        (AND (|HasCategory| |#1| '(|Finite|))
                                             (|HasCategory| |#2|
                                                            (LIST
                                                             '|FramedNonAssociativeAlgebra|
                                                             (|devaluate|
                                                              |#1|))))
                                        (|HasCategory| |#2|
                                                       (LIST
                                                        '|FiniteRankNonAssociativeAlgebra|
                                                        (|devaluate| |#1|)))
                                        (OR
                                         (AND
                                          (|HasCategory| |#1|
                                                         '(|IntegralDomain|))
                                          (|HasCategory| |#2|
                                                         (LIST
                                                          '|FiniteRankNonAssociativeAlgebra|
                                                          (|devaluate| |#1|))))
                                         (AND
                                          (|HasCategory| |#1|
                                                         '(|IntegralDomain|))
                                          (|HasCategory| |#2|
                                                         (LIST
                                                          '|FramedNonAssociativeAlgebra|
                                                          (|devaluate|
                                                           |#1|)))))
                                        (OR
                                         (|HasCategory| |#2|
                                                        (LIST
                                                         '|FiniteRankNonAssociativeAlgebra|
                                                         (|devaluate| |#1|)))
                                         (|HasCategory| |#2|
                                                        (LIST
                                                         '|FramedNonAssociativeAlgebra|
                                                         (|devaluate| |#1|))))
                                        (AND (|HasCategory| |#1| '(|Field|))
                                             (|HasCategory| |#2|
                                                            (LIST
                                                             '|FramedNonAssociativeAlgebra|
                                                             (|devaluate|
                                                              |#1|))))))
                    . #2#))
    (|haddProp| |$ConstructorCache| '|AssociatedJordanAlgebra| (LIST DV$1 DV$2)
                (CONS 1 $))
    (|stuffDomainSlots| $)
    (QSETREFV $ 5 |#2|)
    (QSETREFV $ 6 |#1|)
    (QSETREFV $ 7 |#2|)
    (SETF |pv$| (QREFELT $ 3))
    (QSETREFV $ 8 |#2|)
    (QSETREFV $ 11
              (SPADCALL (|spadConstant| $ 9) (|spadConstant| $ 9)
                        (QREFELT $ 10)))
    (QSETREFV $ 14
              (PROG2
                  (LETT #1# #3=(SPADCALL (QREFELT $ 11) (QREFELT $ 13)) . #2#)
                  (QCDR #1#)
                (|check_union2| (QEQCAR #1# 0) #3# (|Union| #3# "failed")
                                #1#)))
    $))) 

(MAKEPROP '|AssociatedJordanAlgebra| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL (|local| |#2|) (|local| |#1|) (|local| |#2|)
              '|Rep| (0 . |One|) (4 . +) '|two| (|Union| $ '"failed")
              (10 . |recip|) '|oneHalf| (|Boolean|) (15 . |zero?|) (20 . *)
              (26 . +) (32 . *) |JORDAN;*;3$;1| |JORDAN;coerce;$A;2|
              |JORDAN;coerce;A$;3| (|PositiveInteger|) |JORDAN;^;$Pi$;4|
              (|SparseUnivariatePolynomial| (|Polynomial| 6)) (|List| $)
              (|NonNegativeInteger|) (|InputForm|)
              (|Record| (|:| |particular| $) (|:| |basis| 26))
              (|Union| 29 '"failed") (|SparseUnivariatePolynomial| 6)
              (|List| 35) (|Matrix| 6) (|Vector| $) (|Vector| 6) (|Vector| 33)
              (|List| (|Polynomial| 6)) (|Integer|) (|HashState|) (|String|)
              (|OutputForm|) (|SingleInteger|))
           '#(~= 38 |zero?| 44 |unit| 49 |subtractIfCan| 53
              |structuralConstants| 59 |someBasis| 68 |smaller?| 72 |size| 78
              |sample| 82 |rightUnits| 86 |rightUnit| 90 |rightTraceMatrix| 94
              |rightTrace| 103 |rightRegularRepresentation| 108 |rightRecip|
              119 |rightRankPolynomial| 124 |rightPower| 128 |rightNorm| 134
              |rightMinimalPolynomial| 139 |rightDiscriminant| 144
              |rightCharacteristicPolynomial| 153 |rightAlternative?| 158
              |represents| 162 |recip| 173 |rank| 178 |random| 182
              |powerAssociative?| 186 |plenaryPower| 190 |opposite?| 196
              |noncommutativeJordanAlgebra?| 202 |lookup| 206 |lieAlgebra?| 211
              |lieAdmissible?| 215 |leftUnits| 219 |leftUnit| 223
              |leftTraceMatrix| 227 |leftTrace| 236 |leftRegularRepresentation|
              241 |leftRecip| 252 |leftRankPolynomial| 257 |leftPower| 261
              |leftNorm| 267 |leftMinimalPolynomial| 272 |leftDiscriminant| 277
              |leftCharacteristicPolynomial| 286 |leftAlternative?| 291 |latex|
              295 |jordanAlgebra?| 300 |jordanAdmissible?| 304
              |jacobiIdentity?| 308 |index| 312 |hashUpdate!| 317 |hash| 323
              |flexible?| 328 |enumerate| 332 |elt| 336 |coordinates| 342
              |convert| 364 |conditionsForIdempotents| 379 |commutator| 388
              |commutative?| 394 |coerce| 398 |basis| 413
              |associatorDependence| 417 |associator| 421 |associative?| 428
              |apply| 432 |antiCommutator| 438 |antiCommutative?| 444
              |antiAssociative?| 448 |alternative?| 452 ^ 456 |Zero| 462 = 466
              - 472 + 483 * 489)
           'NIL
           (CONS
            (|makeByteWordVec2| 5
                                '(1 5 0 0 0 1 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 4
                                  2))
            (CONS
             '#(|FramedNonAssociativeAlgebra&|
                |FiniteRankNonAssociativeAlgebra&| |NonAssociativeAlgebra&|
                |Module&| NIL |FramedModule&| |NonAssociativeRng&| NIL NIL
                |AbelianGroup&| NIL |NonAssociativeSemiRng&| |AbelianMonoid&|
                |Finite&| |AbelianSemiGroup&| |Magma&| NIL |SetCategory&| NIL
                |BasicType&| NIL NIL NIL)
             (CONS
              '#((|FramedNonAssociativeAlgebra| 6)
                 (|FiniteRankNonAssociativeAlgebra| 6)
                 (|NonAssociativeAlgebra| 6) (|Module| 6) (|BiModule| 6 6)
                 (|FramedModule| 6) (|NonAssociativeRng|) (|RightModule| 6)
                 (|LeftModule| 6) (|AbelianGroup|)
                 (|CancellationAbelianMonoid|) (|NonAssociativeSemiRng|)
                 (|AbelianMonoid|) (|Finite|) (|AbelianSemiGroup|) (|Magma|)
                 (|Comparable|) (|SetCategory|) (|CoercibleTo| 7) (|BasicType|)
                 (|CoercibleTo| 41) (|unitsKnown|) (|ConvertibleTo| 28))
              (|makeByteWordVec2| 42
                                  '(0 6 0 9 2 6 0 0 0 10 1 6 12 0 13 1 6 15 0
                                    16 2 8 0 0 0 17 2 8 0 0 0 18 2 0 0 0 6 19 2
                                    0 15 0 0 1 1 0 15 0 1 0 4 12 1 2 0 12 0 0 1
                                    1 3 36 34 1 0 1 36 1 0 3 34 1 2 2 15 0 0 1
                                    0 2 27 1 0 0 0 1 0 4 30 1 0 4 12 1 1 3 33
                                    34 1 0 1 33 1 1 3 6 0 1 2 3 33 0 34 1 1 1
                                    33 0 1 1 4 12 0 1 0 6 25 1 2 0 0 0 23 1 1 3
                                    6 0 1 1 4 31 0 1 1 3 6 34 1 0 1 6 1 1 3 31
                                    0 1 0 3 15 1 2 3 0 35 34 1 1 1 0 35 1 1 4
                                    12 0 1 0 3 23 1 0 2 0 1 0 3 15 1 2 0 0 0 23
                                    1 2 0 15 0 0 1 0 3 15 1 1 2 23 0 1 0 3 15 1
                                    0 3 15 1 0 4 30 1 0 4 12 1 1 3 33 34 1 0 1
                                    33 1 1 3 6 0 1 2 3 33 0 34 1 1 1 33 0 1 1 4
                                    12 0 1 0 6 25 1 2 0 0 0 23 1 1 3 6 0 1 1 4
                                    31 0 1 1 3 6 34 1 0 1 6 1 1 3 31 0 1 0 3 15
                                    1 1 0 40 0 1 0 3 15 1 0 3 15 1 0 3 15 1 1 2
                                    0 23 1 2 0 39 39 0 1 1 0 42 0 1 0 3 15 1 0
                                    2 26 1 2 1 6 0 38 1 2 3 35 0 34 1 2 3 33 34
                                    34 1 1 1 35 0 1 1 1 33 34 1 1 2 28 0 1 1 1
                                    35 0 1 1 1 0 35 1 1 3 37 34 1 0 1 37 1 2 0
                                    0 0 0 1 0 3 15 1 1 0 0 5 22 1 0 5 0 21 1 0
                                    41 0 1 0 1 34 1 0 4 32 1 3 0 0 0 0 0 1 0 3
                                    15 1 2 1 0 33 0 1 2 0 0 0 0 1 0 3 15 1 0 3
                                    15 1 0 3 15 1 2 0 0 0 23 24 0 0 0 1 2 0 15
                                    0 0 1 1 0 0 0 1 2 0 0 0 0 1 2 0 0 0 0 1 2 0
                                    0 6 0 1 2 0 0 0 6 19 2 0 0 27 0 1 2 0 0 38
                                    0 1 2 0 0 0 0 20 2 0 0 23 0 1)))))
           '|lookupComplete|)) 
