
(/VERSIONCHECK 2) 

(DEFUN |LSQM;conv| (|v| $)
  (PROG (|z| #1=#:G668 |j| #2=#:G667 |i| |cond|)
    (RETURN
     (SEQ
      (LETT |cond|
            (SPADCALL (QREFELT $ 6) (QREFELT $ 6) (|spadConstant| $ 10)
                      (QREFELT $ 13))
            . #3=(|LSQM;conv|))
      (LETT |z| 0 . #3#)
      (SEQ (LETT |i| 1 . #3#) (LETT #2# (QREFELT $ 6) . #3#) G190
           (COND ((QSGREATERP |i| #2#) #4=(GO G191)))
           (SEQ
            (EXIT
             (SEQ (LETT |j| 1 . #3#) (LETT #1# (QREFELT $ 6) . #3#) G190
                  (COND ((QSGREATERP |j| #1#) #4#))
                  (SEQ (LETT |z| (+ |z| 1) . #3#)
                       (EXIT
                        (SPADCALL |cond| |i| |j|
                                  (SPADCALL |v| |z| (QREFELT $ 16))
                                  (QREFELT $ 17))))
                  (LETT |j| (QSADD1 |j|) . #3#) #5=(GO G190) G191 (EXIT NIL))))
           (LETT |i| (QSADD1 |i|) . #3#) #5# G191 (EXIT NIL))
      (EXIT (SPADCALL |cond| (QREFELT $ 19))))))) 

(DEFUN |LSQM;coordinates;$VV;2| (|a| |b| $)
  (PROG (|z| #1=#:G675 |j| #2=#:G674 |i| |res|)
    (RETURN
     (SEQ
      (LETT |res| (SPADCALL (QREFELT $ 9) (|spadConstant| $ 10) (QREFELT $ 21))
            . #3=(|LSQM;coordinates;$VV;2|))
      (LETT |z| 0 . #3#)
      (SEQ (LETT |i| 1 . #3#) (LETT #2# (QREFELT $ 6) . #3#) G190
           (COND ((QSGREATERP |i| #2#) #4=(GO G191)))
           (SEQ
            (EXIT
             (SEQ (LETT |j| 1 . #3#) (LETT #1# (QREFELT $ 6) . #3#) G190
                  (COND ((QSGREATERP |j| #1#) #4#))
                  (SEQ (LETT |z| (+ |z| 1) . #3#)
                       (EXIT
                        (SPADCALL |res| |z|
                                  (SPADCALL |a| |i| |j| (QREFELT $ 22))
                                  (QREFELT $ 23))))
                  (LETT |j| (QSADD1 |j|) . #3#) #5=(GO G190) G191 (EXIT NIL))))
           (LETT |i| (QSADD1 |i|) . #3#) #5# G191 (EXIT NIL))
      (EXIT |res|))))) 

(DEFUN |LSQM;convDM| (|v| $)
  (PROG (|sq|)
    (RETURN
     (SEQ (LETT |sq| (|LSQM;conv| |v| $) |LSQM;convDM|)
          (EXIT (SPADCALL |sq| (QREFELT $ 26))))))) 

(DEFUN |LSQM;basis;V;4| ($)
  (PROG (|res| |ldp| #1=#:G678 #2=#:G684 |i| #3=#:G683)
    (RETURN
     (SEQ (SETELT $ 9 (* (QREFELT $ 6) (QREFELT $ 6)))
          (LETT |ldp|
                (PROGN
                 (LETT #3# NIL . #4=(|LSQM;basis;V;4|))
                 (SEQ (LETT |i| 1 . #4#) (LETT #2# (QREFELT $ 9) . #4#) G190
                      (COND ((QSGREATERP |i| #2#) (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #3#
                              (CONS
                               (SPADCALL
                                (PROG1 (LETT #1# |i| . #4#)
                                  (|check-subtype| (> #1# 0)
                                                   '(|PositiveInteger|) #1#))
                                (QREFELT $ 28))
                               #3#)
                              . #4#)))
                      (LETT |i| (QSADD1 |i|) . #4#) (GO G190) G191
                      (EXIT (NREVERSE0 #3#))))
                . #4#)
          (EXIT
           (LETT |res|
                 (SPADCALL
                  (SPADCALL (CONS (|function| |LSQM;convDM|) $) |ldp|
                            (QREFELT $ 33))
                  (QREFELT $ 35))
                 . #4#)))))) 

(DEFUN |LSQM;someBasis;V;5| ($) (SPADCALL (QREFELT $ 36))) 

(DEFUN |LSQM;rank;Pi;6| ($) (* (QREFELT $ 6) (QREFELT $ 6))) 

(DEFUN |LieSquareMatrix| (&REST #1=#:G709)
  (PROG ()
    (RETURN
     (PROG (#2=#:G710)
       (RETURN
        (COND
         ((LETT #2#
                (|lassocShiftWithFunction| (|devaluateList| #1#)
                                           (HGET |$ConstructorCache|
                                                 '|LieSquareMatrix|)
                                           '|domainEqualList|)
                . #3=(|LieSquareMatrix|))
          (|CDRwithIncrement| #2#))
         ('T
          (UNWIND-PROTECT
              (PROG1 (APPLY (|function| |LieSquareMatrix;|) #1#)
                (LETT #2# T . #3#))
            (COND
             ((NOT #2#) (HREM |$ConstructorCache| '|LieSquareMatrix|))))))))))) 

(DEFUN |LieSquareMatrix;| (|#1| |#2|)
  (PROG (|pv$| $ |dv$| DV$2 DV$1)
    (RETURN
     (PROGN
      (LETT DV$1 (|devaluate| |#1|) . #1=(|LieSquareMatrix|))
      (LETT DV$2 (|devaluate| |#2|) . #1#)
      (LETT |dv$| (LIST '|LieSquareMatrix| DV$1 DV$2) . #1#)
      (LETT $ (GETREFV 72) . #1#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3
                (LETT |pv$|
                      (|buildPredVector| 0 0
                                         (LIST
                                          (|HasCategory| |#2|
                                                         '(|PartialDifferentialRing|
                                                           (|Symbol|)))
                                          (|HasCategory| |#2|
                                                         '(|DifferentialRing|))
                                          (|HasCategory| |#2|
                                                         '(|CommutativeRing|))
                                          (|HasCategory| |#2|
                                                         '(|LinearlyExplicitRingOver|
                                                           (|Integer|)))
                                          (|HasCategory| |#2|
                                                         '(|RetractableTo|
                                                           (|Fraction|
                                                            (|Integer|))))
                                          (|HasCategory| |#2|
                                                         '(|RetractableTo|
                                                           (|Integer|)))
                                          (|HasCategory| |#2| '(|Finite|))
                                          (|HasCategory| |#2|
                                                         '(|EuclideanDomain|))
                                          (|HasCategory| |#2| '(|SetCategory|))
                                          (|HasCategory| |#2| '(|Field|))
                                          (|HasCategory| |#2|
                                                         '(|IntegralDomain|))
                                          (AND
                                           (|HasCategory| |#2|
                                                          '(|SetCategory|))
                                           (|HasCategory| |#2|
                                                          (LIST '|Evalable|
                                                                (|devaluate|
                                                                 |#2|))))
                                          (OR
                                           (AND
                                            (|HasCategory| |#2|
                                                           '(|CommutativeRing|))
                                            (|HasCategory| |#2|
                                                           (LIST '|Evalable|
                                                                 (|devaluate|
                                                                  |#2|))))
                                           (AND
                                            (|HasCategory| |#2|
                                                           '(|DifferentialRing|))
                                            (|HasCategory| |#2|
                                                           (LIST '|Evalable|
                                                                 (|devaluate|
                                                                  |#2|))))
                                           (AND
                                            (|HasCategory| |#2| '(|Finite|))
                                            (|HasCategory| |#2|
                                                           (LIST '|Evalable|
                                                                 (|devaluate|
                                                                  |#2|))))
                                           (AND
                                            (|HasCategory| |#2|
                                                           '(|SetCategory|))
                                            (|HasCategory| |#2|
                                                           (LIST '|Evalable|
                                                                 (|devaluate|
                                                                  |#2|))))
                                           (AND
                                            (|HasCategory| |#2|
                                                           (LIST '|Evalable|
                                                                 (|devaluate|
                                                                  |#2|)))
                                            (|HasCategory| |#2|
                                                           '(|LinearlyExplicitRingOver|
                                                             (|Integer|))))
                                           (AND
                                            (|HasCategory| |#2|
                                                           (LIST '|Evalable|
                                                                 (|devaluate|
                                                                  |#2|)))
                                            (|HasCategory| |#2|
                                                           '(|PartialDifferentialRing|
                                                             (|Symbol|)))))))
                      . #1#))
      (|haddProp| |$ConstructorCache| '|LieSquareMatrix| (LIST DV$1 DV$2)
                  (CONS 1 $))
      (|stuffDomainSlots| $)
      (QSETREFV $ 6 |#1|)
      (QSETREFV $ 7 |#2|)
      (AND (|HasCategory| $ '(|shallowlyMutable|))
           (|augmentPredVector| $ 8192))
      (AND (|HasCategory| $ '(|finiteAggregate|))
           (|augmentPredVector| $ 16384))
      (AND (|HasCategory| $ '(|finiteAggregate|))
           (|HasCategory| |#2| '(|SetCategory|)) (|augmentPredVector| $ 32768))
      (QSETREFV $ 8 (|AssociatedLieAlgebra| |#2| (|SquareMatrix| |#1| |#2|)))
      (QSETREFV $ 9 (* |#1| |#1|))
      $)))) 

(MAKEPROP '|LieSquareMatrix| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL (|AssociatedLieAlgebra| 7 18) (|local| |#1|)
              (|local| |#2|) '|Rep| '|n2| (0 . |Zero|) (|NonNegativeInteger|)
              (|Matrix| 7) (4 . |new|) (|Integer|) (|DirectProduct| 9 7)
              (11 . |elt|) (17 . |setelt|) (|SquareMatrix| 6 7)
              (25 . |squareMatrix|) (|Vector| 7) (30 . |new|) (36 . |elt|)
              (43 . |setelt|) (|Vector| $) |LSQM;coordinates;$VV;2|
              (50 . |coerce|) (|PositiveInteger|) (55 . |unitVector|)
              (|List| $$) (|Mapping| $$ 15) (|List| 15)
              (|ListFunctions2| 15 $$) (60 . |map|) (|Vector| $$)
              (66 . |vector|) |LSQM;basis;V;4| |LSQM;someBasis;V;5|
              |LSQM;rank;Pi;6| (|Boolean|) (|List| 7) (|List| 42)
              (|Equation| 7) (|Mapping| 39 7) (|Mapping| 7 7) (|List| 64)
              (|SparseUnivariatePolynomial| (|Polynomial| 7))
              (|Union| $ '"failed") (|List| $) (|List| 20)
              (|SparseUnivariatePolynomial| 7)
              (|Record| (|:| |particular| $) (|:| |basis| 48))
              (|Union| 51 '"failed")
              (|Record| (|:| |mat| 55) (|:| |vec| (|Vector| 14))) (|Matrix| $)
              (|Matrix| 14) (|List| 57) (|Symbol|) (|List| 11) (|Fraction| 14)
              (|Union| 59 '#1="failed") (|Union| 14 '#1#)
              (|List| (|Polynomial| 7)) (|Vector| 12) (|DirectProduct| 6 7)
              (|Record| (|:| |mat| 12) (|:| |vec| 20)) (|Union| 7 '#1#)
              (|List| 40) (|Mapping| 7 7 7) (|SingleInteger|) (|String|)
              (|OutputForm|))
           '#(~= 71 |zero?| 77 |unit| 82 |trace| 86 |symmetric?| 91
              |subtractIfCan| 96 |structuralConstants| 102 |square?| 111
              |someBasis| 116 |size?| 120 |size| 126 |scalarMatrix| 130
              |sample| 135 |rowEchelon| 139 |row| 144 |rightUnits| 150
              |rightUnit| 154 |rightTraceMatrix| 158 |rightTrace| 167
              |rightRegularRepresentation| 172 |rightRecip| 183
              |rightRankPolynomial| 188 |rightPower| 192 |rightNorm| 198
              |rightMinimalPolynomial| 203 |rightDiscriminant| 208
              |rightCharacteristicPolynomial| 217 |rightAlternative?| 222
              |retractIfCan| 226 |retract| 241 |represents| 256 |reducedSystem|
              267 |recip| 289 |rank| 294 |random| 303 |qelt| 307
              |powerAssociative?| 314 |plenaryPower| 318 |parts| 324 |one?| 329
              |nullity| 334 |nullSpace| 339 |nrows| 344
              |noncommutativeJordanAlgebra?| 349 |ncols| 353 |more?| 358
              |minordet| 364 |minRowIndex| 369 |minColIndex| 374 |members| 379
              |member?| 384 |maxRowIndex| 390 |maxColIndex| 395 |matrix| 400
              |map!| 405 |map| 411 |lookup| 424 |listOfLists| 429 |lieAlgebra?|
              434 |lieAdmissible?| 438 |less?| 442 |leftUnits| 448 |leftUnit|
              452 |leftTraceMatrix| 456 |leftTrace| 465
              |leftRegularRepresentation| 470 |leftRecip| 481
              |leftRankPolynomial| 486 |leftPower| 490 |leftNorm| 496
              |leftMinimalPolynomial| 501 |leftDiscriminant| 506
              |leftCharacteristicPolynomial| 515 |leftAlternative?| 520 |latex|
              524 |jordanAlgebra?| 529 |jordanAdmissible?| 533
              |jacobiIdentity?| 537 |inverse| 541 |index| 546 |hash| 551
              |flexible?| 556 |exquo| 560 |every?| 566 |eval| 572 |eq?| 598
              |enumerate| 604 |empty?| 608 |empty| 613 |elt| 617
              |differentiate| 638 |diagonalProduct| 688 |diagonalMatrix| 693
              |diagonal?| 698 |diagonal| 703 |determinant| 708 |count| 713
              |copy| 725 |coordinates| 730 |convert| 752
              |conditionsForIdempotents| 762 |commutator| 771 |commutative?|
              777 |columnSpace| 781 |column| 786 |coerce| 792 |characteristic|
              817 |basis| 821 |associatorDependence| 825 |associator| 829
              |associative?| 836 |apply| 840 |any?| 846 |antisymmetric?| 852
              |antiCommutator| 857 |antiCommutative?| 863 |antiAssociative?|
              867 |alternative?| 871 ^ 875 |Zero| 893 |Pfaffian| 897 |One| 902
              D 906 = 956 / 962 - 968 + 979 * 985 |#| 1033)
           'NIL
           (CONS
            (|makeByteWordVec2| 13
                                '(0 0 0 0 0 0 0 3 0 0 1 2 4 0 0 0 0 0 0 0 0 0 0
                                  0 0 0 0 0 0 0 7 0 0 0 13 0 0 0 0 0 0 0 5 6
                                  13))
            (CONS
             '#(|FramedNonAssociativeAlgebra&| |SquareMatrixCategory&|
                |FiniteRankNonAssociativeAlgebra&| |DifferentialExtension&|
                |NonAssociativeAlgebra&| |FullyLinearlyExplicitRingOver&|
                |RectangularMatrixCategory&| |Algebra&| NIL |Module&|
                |PartialDifferentialRing&| |DifferentialRing&| NIL |Ring&| NIL
                |NonAssociativeRng&| NIL NIL NIL NIL |AbelianGroup&| NIL NIL
                |AbelianMonoid&| |Monoid&| NIL |Monad&| |HomogeneousAggregate&|
                |SemiGroup&| |AbelianSemiGroup&| |Finite&|
                |FullyRetractableTo&| |Aggregate&| |SetCategory&| |Evalable&|
                NIL |RetractableTo&| NIL NIL NIL |BasicType&| NIL
                |RetractableTo&| |RetractableTo&| |InnerEvalable&|)
             (CONS
              '#((|FramedNonAssociativeAlgebra| 7)
                 (|SquareMatrixCategory| 6 7 (|DirectProduct| 6 7)
                                         (|DirectProduct| 6 7))
                 (|FiniteRankNonAssociativeAlgebra| 7)
                 (|DifferentialExtension| 7) (|NonAssociativeAlgebra| 7)
                 (|FullyLinearlyExplicitRingOver| 7)
                 (|RectangularMatrixCategory| 6 6 7 (|DirectProduct| 6 7)
                                              (|DirectProduct| 6 7))
                 (|Algebra| 7) (|LinearlyExplicitRingOver| 7) (|Module| 7)
                 (|PartialDifferentialRing| 57) (|DifferentialRing|)
                 (|LinearlyExplicitRingOver| 14) (|Ring|) (|BiModule| 7 7)
                 (|NonAssociativeRng|) (|Rng|) (|RightModule| 7)
                 (|LeftModule| 7) (|LeftModule| $$) (|AbelianGroup|)
                 (|CancellationAbelianMonoid|) (|SemiRing|) (|AbelianMonoid|)
                 (|Monoid|) (|SemiRng|) (|Monad|) (|HomogeneousAggregate| 7)
                 (|SemiGroup|) (|AbelianSemiGroup|) (|Finite|)
                 (|FullyRetractableTo| 7) (|Aggregate|) (|SetCategory|)
                 (|Evalable| 7) (|CoercibleTo| (|Matrix| 7))
                 (|RetractableTo| 7) (|finiteAggregate|) (|Type|)
                 (|unitsKnown|) (|BasicType|) (|CoercibleTo| 71)
                 (|RetractableTo| 59) (|RetractableTo| 14)
                 (|InnerEvalable| 7 7))
              (|makeByteWordVec2| 71
                                  '(0 7 0 10 3 12 0 11 11 7 13 2 15 7 0 14 16 4
                                    12 7 0 14 14 7 17 1 18 0 12 19 2 20 0 11 7
                                    21 3 0 7 0 14 14 22 3 20 7 0 14 7 23 1 8 0
                                    18 26 1 15 0 27 28 2 32 29 30 31 33 1 34 0
                                    29 35 2 0 39 0 0 1 1 0 39 0 1 0 11 47 1 1 0
                                    7 0 1 1 0 39 0 1 2 0 47 0 0 1 1 0 63 24 1 0
                                    0 63 1 1 0 39 0 1 0 0 24 37 2 0 39 0 11 1 0
                                    7 11 1 1 0 0 7 1 0 0 0 1 1 8 0 0 1 2 0 64 0
                                    14 1 0 11 52 1 0 11 47 1 1 0 12 24 1 0 0 12
                                    1 1 0 7 0 1 2 0 12 0 24 1 1 0 12 0 1 1 11
                                    47 0 1 0 10 46 1 2 0 0 0 27 1 1 0 7 0 1 1
                                    11 50 0 1 1 0 7 24 1 0 0 7 1 1 0 50 0 1 0 0
                                    39 1 1 5 60 0 1 1 6 61 0 1 1 0 66 0 1 1 5
                                    59 0 1 1 6 14 0 1 1 0 7 0 1 2 0 0 20 24 1 1
                                    0 0 20 1 2 4 53 54 24 1 1 4 55 54 1 2 0 65
                                    54 24 1 1 0 12 54 1 1 0 47 0 1 1 11 11 0 1
                                    0 0 27 38 0 7 0 1 3 0 7 0 14 14 1 0 0 39 1
                                    2 0 0 0 27 1 1 15 40 0 1 1 0 39 0 1 1 11 11
                                    0 1 1 11 45 0 1 1 0 11 0 1 0 0 39 1 1 0 11
                                    0 1 2 0 39 0 11 1 1 3 7 0 1 1 0 14 0 1 1 0
                                    14 0 1 1 15 40 0 1 2 16 39 7 0 1 1 0 14 0 1
                                    1 0 14 0 1 1 0 0 67 1 2 14 0 44 0 1 2 0 0
                                    44 0 1 3 0 0 68 0 0 1 1 7 27 0 1 1 0 67 0 1
                                    0 0 39 1 0 0 39 1 2 0 39 0 11 1 0 11 52 1 0
                                    11 47 1 1 0 12 24 1 0 0 12 1 1 0 7 0 1 2 0
                                    12 0 24 1 1 0 12 0 1 1 11 47 0 1 0 10 46 1
                                    2 0 0 0 27 1 1 0 7 0 1 1 11 50 0 1 1 0 7 24
                                    1 0 0 7 1 1 0 50 0 1 0 0 39 1 1 0 70 0 1 0
                                    0 39 1 0 0 39 1 0 0 39 1 1 10 47 0 1 1 7 0
                                    27 1 1 0 69 0 1 0 0 39 1 2 11 47 0 7 1 2 15
                                    39 43 0 1 3 12 0 0 40 40 1 3 12 0 0 7 7 1 2
                                    12 0 0 41 1 2 12 0 0 42 1 2 0 39 0 0 1 0 7
                                    48 1 1 0 39 0 1 0 0 0 1 2 0 7 0 14 1 3 0 7
                                    0 14 14 22 4 0 7 0 14 14 7 1 1 2 0 0 1 2 2
                                    0 0 11 1 2 1 0 0 56 1 2 1 0 0 57 1 3 1 0 0
                                    57 11 1 3 1 0 0 56 58 1 3 0 0 0 44 11 1 2 0
                                    0 0 44 1 1 0 7 0 1 1 0 0 40 1 1 0 39 0 1 1
                                    0 64 0 1 1 3 7 0 1 2 16 11 7 0 1 2 15 11 43
                                    0 1 1 0 0 0 1 2 0 20 0 24 25 2 0 12 24 24 1
                                    1 0 20 0 1 1 0 12 24 1 1 0 20 0 1 1 0 0 20
                                    1 1 0 62 24 1 0 0 62 1 2 0 0 0 0 1 0 0 39 1
                                    1 8 45 0 1 2 0 64 0 14 1 1 5 0 59 1 1 0 12
                                    0 1 1 0 0 7 1 1 0 0 14 1 1 0 71 0 1 0 0 11
                                    1 0 0 24 36 0 11 49 1 3 0 0 0 0 0 1 0 0 39
                                    1 2 0 0 12 0 1 2 15 39 43 0 1 1 0 39 0 1 2
                                    0 0 0 0 1 0 0 39 1 0 0 39 1 0 0 39 1 2 10 0
                                    0 14 1 2 0 0 0 11 1 2 0 0 0 27 1 0 0 0 1 1
                                    3 7 0 1 0 0 0 1 1 2 0 0 1 2 2 0 0 11 1 2 1
                                    0 0 57 1 2 1 0 0 56 1 3 1 0 0 56 58 1 3 1 0
                                    0 57 11 1 3 0 0 0 44 11 1 2 0 0 0 44 1 2 0
                                    39 0 0 1 2 10 0 0 7 1 1 0 0 0 1 2 0 0 0 0 1
                                    2 0 0 0 0 1 2 0 64 64 0 1 2 0 64 0 64 1 2 0
                                    0 0 7 1 2 0 0 7 0 1 2 0 0 0 0 1 2 0 0 14 0
                                    1 2 0 0 11 0 1 2 0 0 27 0 1 1 15 11 0
                                    1)))))
           '|lookupComplete|)) 
