
(/VERSIONCHECK 2) 

(DEFUN |LIE;*;3$;1| (|a| |b| $)
  (SPADCALL (SPADCALL |a| |b| (QREFELT $ 9))
      (SPADCALL |b| |a| (QREFELT $ 9)) (QREFELT $ 10))) 

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

(DEFUN |LIE;coerce;$A;2| (|a| $) |a|) 

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

(DEFUN |LIE;coerce;A$;3| (|a| $) |a|) 

(DEFUN |LIE;**;$Pi$;4| (|a| |n| $)
  (COND ((EQL |n| 1) |a|) ('T (|spadConstant| $ 15)))) 

(DEFUN |AssociatedLieAlgebra| (&REST #0=#:G1828)
  (PROG ()
    (RETURN
      (PROG (#1=#:G1829)
        (RETURN
          (COND
            ((LETT #1#
                   (|lassocShiftWithFunction| (|devaluateList| #0#)
                       (HGET |$ConstructorCache|
                             '|AssociatedLieAlgebra|)
                       '|domainEqualList|)
                   . #2=(|AssociatedLieAlgebra|))
             (|CDRwithIncrement| #1#))
            ('T
             (UNWIND-PROTECT
               (PROG1 (APPLY (|function| |AssociatedLieAlgebra;|) #0#)
                 (LETT #1# T . #2#))
               (COND
                 ((NOT #1#)
                  (HREM |$ConstructorCache| '|AssociatedLieAlgebra|))))))))))) 

(DEFUN |AssociatedLieAlgebra;| (|#1| |#2|)
  (PROG (DV$1 DV$2 |dv$| $ |pv$|)
    (RETURN
      (PROGN
        (LETT DV$1 (|devaluate| |#1|) . #0=(|AssociatedLieAlgebra|))
        (LETT DV$2 (|devaluate| |#2|) . #0#)
        (LETT |dv$| (LIST '|AssociatedLieAlgebra| DV$1 DV$2) . #0#)
        (LETT $ (GETREFV 35) . #0#)
        (QSETREFV $ 0 |dv$|)
        (QSETREFV $ 3
            (LETT |pv$|
                  (|buildPredVector| 0 0
                      (LIST (|HasCategory| |#2|
                                (LIST '|FramedNonAssociativeAlgebra|
                                      (|devaluate| |#1|)))
                            (AND (|HasCategory| |#1| '(|Field|))
                                 (|HasCategory| |#2|
                                     (LIST
                                      '|FramedNonAssociativeAlgebra|
                                      (|devaluate| |#1|))))
                            (|HasCategory| |#2|
                                (LIST '|FiniteRankNonAssociativeAlgebra|
                                      (|devaluate| |#1|)))
                            (OR (AND (|HasCategory| |#1|
                                      '(|IntegralDomain|))
                                     (|HasCategory| |#2|
                                      (LIST
                                       '|FiniteRankNonAssociativeAlgebra|
                                       (|devaluate| |#1|))))
                                (AND (|HasCategory| |#1|
                                      '(|IntegralDomain|))
                                     (|HasCategory| |#2|
                                      (LIST
                                       '|FramedNonAssociativeAlgebra|
                                       (|devaluate| |#1|)))))
                            (OR (|HasCategory| |#2|
                                    (LIST
                                     '|FiniteRankNonAssociativeAlgebra|
                                     (|devaluate| |#1|)))
                                (|HasCategory| |#2|
                                    (LIST
                                     '|FramedNonAssociativeAlgebra|
                                     (|devaluate| |#1|)))))) . #0#))
        (|haddProp| |$ConstructorCache| '|AssociatedLieAlgebra|
            (LIST DV$1 DV$2) (CONS 1 $))
        (|stuffDomainSlots| $)
        (QSETREFV $ 5 |#2|)
        (QSETREFV $ 6 |#1|)
        (QSETREFV $ 7 |#2|)
        (QSETREFV $ 8 |#2|)
        $)))) 

(MAKEPROP '|AssociatedLieAlgebra| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL (|local| |#2|) (|local| |#1|)
             (|local| |#2|) '|Rep| (0 . *) (6 . -) |LIE;*;3$;1|
             |LIE;coerce;$A;2| |LIE;coerce;A$;3| (12 . |One|)
             (16 . |Zero|) (|PositiveInteger|) |LIE;**;$Pi$;4|
             (|SparseUnivariatePolynomial| (|Polynomial| 6))
             (|Union| $ '"failed") (|SparseUnivariatePolynomial| 6)
             (|List| 28)
             (|Record| (|:| |particular| $) (|:| |basis| (|List| $)))
             (|Union| 22 '"failed") (|Vector| $)
             (|List| (|Polynomial| 6)) (|Matrix| 6) (|Vector| 26)
             (|Vector| 6) (|Boolean|) (|Integer|)
             (|NonNegativeInteger|) (|SingleInteger|) (|String|)
             (|OutputForm|))
          '#(~= 20 |zero?| 26 |unit| 31 |subtractIfCan| 35
             |structuralConstants| 41 |someBasis| 50 |sample| 54
             |rightUnits| 58 |rightUnit| 62 |rightTraceMatrix| 66
             |rightTrace| 75 |rightRegularRepresentation| 80
             |rightRecip| 91 |rightRankPolynomial| 96 |rightPower| 100
             |rightNorm| 106 |rightMinimalPolynomial| 111
             |rightDiscriminant| 116 |rightCharacteristicPolynomial|
             125 |rightAlternative?| 130 |represents| 134 |recip| 145
             |rank| 150 |powerAssociative?| 154 |plenaryPower| 158
             |noncommutativeJordanAlgebra?| 164 |lieAlgebra?| 168
             |lieAdmissible?| 172 |leftUnits| 176 |leftUnit| 180
             |leftTraceMatrix| 184 |leftTrace| 193
             |leftRegularRepresentation| 198 |leftRecip| 209
             |leftRankPolynomial| 214 |leftPower| 218 |leftNorm| 224
             |leftMinimalPolynomial| 229 |leftDiscriminant| 234
             |leftCharacteristicPolynomial| 243 |leftAlternative?| 248
             |latex| 252 |jordanAlgebra?| 257 |jordanAdmissible?| 261
             |jacobiIdentity?| 265 |hash| 269 |flexible?| 274 |elt| 278
             |coordinates| 284 |convert| 306 |conditionsForIdempotents|
             316 |commutator| 325 |commutative?| 331 |coerce| 335
             |basis| 350 |associatorDependence| 354 |associator| 358
             |associative?| 365 |apply| 369 |antiCommutator| 375
             |antiCommutative?| 381 |antiAssociative?| 385
             |alternative?| 389 |Zero| 393 = 397 - 403 + 414 ** 420 *
             426)
          'NIL
          (CONS (|makeByteWordVec2| 5
                    '(1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4))
                (CONS '#(|FramedNonAssociativeAlgebra&|
                         |FiniteRankNonAssociativeAlgebra&|
                         |NonAssociativeAlgebra&| |Module&| NIL
                         |NonAssociativeRng&| NIL NIL |AbelianGroup&|
                         NIL |AbelianMonoid&| |AbelianSemiGroup&|
                         |Monad&| |SetCategory&| NIL |BasicType&| NIL
                         NIL)
                      (CONS '#((|FramedNonAssociativeAlgebra| 6)
                               (|FiniteRankNonAssociativeAlgebra| 6)
                               (|NonAssociativeAlgebra| 6) (|Module| 6)
                               (|BiModule| 6 6) (|NonAssociativeRng|)
                               (|RightModule| 6) (|LeftModule| 6)
                               (|AbelianGroup|)
                               (|CancellationAbelianMonoid|)
                               (|AbelianMonoid|) (|AbelianSemiGroup|)
                               (|Monad|) (|SetCategory|)
                               (|CoercibleTo| 7) (|BasicType|)
                               (|CoercibleTo| 34) (|unitsKnown|))
                            (|makeByteWordVec2| 34
                                '(2 8 0 0 0 9 2 8 0 0 0 10 0 6 0 14 0 0
                                  0 15 2 0 29 0 0 1 1 0 29 0 1 0 4 19 1
                                  2 0 19 0 0 1 1 3 27 24 1 0 1 27 1 0 3
                                  24 1 0 0 0 1 0 4 23 1 0 4 19 1 1 3 26
                                  24 1 0 1 26 1 1 3 6 0 1 2 3 26 0 24 1
                                  1 1 26 0 1 1 4 19 0 1 0 2 18 1 2 0 0
                                  0 16 1 1 3 6 0 1 1 4 20 0 1 1 3 6 24
                                  1 0 1 6 1 1 3 20 0 1 0 3 29 1 2 3 0
                                  28 24 1 1 1 0 28 1 1 4 19 0 1 0 3 16
                                  1 0 3 29 1 2 0 0 0 16 1 0 3 29 1 0 3
                                  29 1 0 3 29 1 0 4 23 1 0 4 19 1 1 3
                                  26 24 1 0 1 26 1 1 3 6 0 1 2 3 26 0
                                  24 1 1 1 26 0 1 1 4 19 0 1 0 2 18 1 2
                                  0 0 0 16 1 1 3 6 0 1 1 4 20 0 1 1 3 6
                                  24 1 0 1 6 1 1 3 20 0 1 0 3 29 1 1 0
                                  33 0 1 0 3 29 1 0 3 29 1 0 3 29 1 1 0
                                  32 0 1 0 3 29 1 2 1 6 0 30 1 2 3 28 0
                                  24 1 2 3 26 24 24 1 1 1 28 0 1 1 1 26
                                  24 1 1 1 28 0 1 1 1 0 28 1 1 3 25 24
                                  1 0 1 25 1 2 0 0 0 0 1 0 3 29 1 1 0 0
                                  5 13 1 0 5 0 12 1 0 34 0 1 0 1 24 1 0
                                  4 21 1 3 0 0 0 0 0 1 0 3 29 1 2 1 0
                                  26 0 1 2 0 0 0 0 1 0 3 29 1 0 3 29 1
                                  0 3 29 1 0 0 0 15 2 0 29 0 0 1 1 0 0
                                  0 1 2 0 0 0 0 1 2 0 0 0 0 1 2 0 0 0
                                  16 17 2 0 0 6 0 1 2 0 0 0 6 1 2 0 0 0
                                  0 11 2 0 0 30 0 1 2 0 0 31 0 1 2 0 0
                                  16 0 1)))))
          '|lookupComplete|)) 
