
(SDEFUN |LEXTRIPK;trueVariables|
        ((|lp|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (% (|List| (|Symbol|))))
        (SPROG
         ((|truels| (|List| (|Symbol|))) (#1=#:G19 NIL) (#2=#:G25 NIL)
          (|s| NIL) (|lv| (|List| (|OrderedVariableList| |ls|))))
         (SEQ
          (LETT |lv| (SPADCALL (SPADCALL |lp| (QREFELT % 10)) (QREFELT % 12)))
          (LETT |truels| NIL)
          (SEQ (LETT |s| NIL) (LETT #2# (QREFELT % 7)) G190
               (COND
                ((OR (ATOM #2#) (PROGN (LETT |s| (CAR #2#)) NIL)) (GO G191)))
               (SEQ
                (EXIT
                 (COND
                  ((SPADCALL
                    (PROG2 (LETT #1# (SPADCALL |s| (QREFELT % 16)))
                        (QCDR #1#)
                      (|check_union2| (QEQCAR #1# 0)
                                      (|OrderedVariableList| (QREFELT % 7))
                                      (|Union|
                                       (|OrderedVariableList| (QREFELT % 7))
                                       "failed")
                                      #1#))
                    |lv| (QREFELT % 18))
                   (LETT |truels| (CONS |s| |truels|))))))
               (LETT #2# (CDR #2#)) (GO G190) G191 (EXIT NIL))
          (EXIT (REVERSE |truels|))))) 

(SDEFUN |LEXTRIPK;zeroDimensional?;LB;2|
        ((|lp|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (% (|Boolean|)))
        (SPROG
         ((|lq1| (|List| (|Polynomial| R))) (#1=#:G31 NIL) (|p| NIL)
          (#2=#:G30 NIL)
          (|fglmpack|
           (CATEGORY |package|
            (SIGNATURE |zeroDimensional?|
             ((|Boolean|) (|List| (|Polynomial| R))))
            (SIGNATURE |fglmIfCan|
             ((|Union| (|List| (|Polynomial| R)) "failed")
              (|List| (|Polynomial| R))))
            (SIGNATURE |groebner|
             ((|List| (|Polynomial| R)) (|List| (|Polynomial| R))))))
          (|truels| (|List| (|Symbol|))))
         (SEQ (LETT |truels| (|LEXTRIPK;trueVariables| |lp| %))
              (LETT |fglmpack| (|FGLMIfCanPackage| (QREFELT % 6) |truels|))
              (LETT |lq1|
                    (PROGN
                     (LETT #2# NIL)
                     (SEQ (LETT |p| NIL) (LETT #1# |lp|) G190
                          (COND
                           ((OR (ATOM #1#) (PROGN (LETT |p| (CAR #1#)) NIL))
                            (GO G191)))
                          (SEQ
                           (EXIT
                            (LETT #2#
                                  (CONS (SPADCALL |p| (QREFELT % 21)) #2#))))
                          (LETT #1# (CDR #1#)) (GO G190) G191
                          (EXIT (NREVERSE #2#)))))
              (EXIT
               (SPADCALL |lq1|
                         (|compiledLookupCheck| '|zeroDimensional?|
                                                (LIST (LIST '|Boolean|)
                                                      (LIST '|List|
                                                            (LIST '|Polynomial|
                                                                  (|devaluate|
                                                                   (ELT %
                                                                        6)))))
                                                |fglmpack|)))))) 

(SDEFUN |LEXTRIPK;fglmIfCan;LU;3|
        ((|lp|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (%
          (|Union|
           (|List|
            (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|)))
           "failed")))
        (SPROG
         ((#1=#:G52 NIL) (|q1| NIL) (#2=#:G51 NIL) (#3=#:G48 NIL)
          (|foo| (|Union| (|List| (|Polynomial| R)) #4="failed"))
          (|lq1| (|List| (|Polynomial| R))) (#5=#:G50 NIL) (|p| NIL)
          (#6=#:G49 NIL)
          (|fglmpack|
           (CATEGORY |package|
            (SIGNATURE |zeroDimensional?|
             ((|Boolean|) (|List| (|Polynomial| R))))
            (SIGNATURE |fglmIfCan|
             ((|Union| (|List| (|Polynomial| R)) "failed")
              (|List| (|Polynomial| R))))
            (SIGNATURE |groebner|
             ((|List| (|Polynomial| R)) (|List| (|Polynomial| R))))))
          (|truels| (|List| (|Symbol|))))
         (SEQ
          (EXIT
           (SEQ (LETT |truels| (|LEXTRIPK;trueVariables| |lp| %))
                (LETT |fglmpack| (|FGLMIfCanPackage| (QREFELT % 6) |truels|))
                (LETT |lq1|
                      (PROGN
                       (LETT #6# NIL)
                       (SEQ (LETT |p| NIL) (LETT #5# |lp|) G190
                            (COND
                             ((OR (ATOM #5#) (PROGN (LETT |p| (CAR #5#)) NIL))
                              (GO G191)))
                            (SEQ
                             (EXIT
                              (LETT #6#
                                    (CONS (SPADCALL |p| (QREFELT % 21)) #6#))))
                            (LETT #5# (CDR #5#)) (GO G190) G191
                            (EXIT (NREVERSE #6#)))))
                (LETT |foo|
                      (SPADCALL |lq1|
                                (|compiledLookupCheck| '|fglmIfCan|
                                                       (LIST
                                                        (LIST '|Union|
                                                              (LIST '|List|
                                                                    (LIST
                                                                     '|Polynomial|
                                                                     (|devaluate|
                                                                      (ELT %
                                                                           6))))
                                                              '#4#)
                                                        (LIST '|List|
                                                              (LIST
                                                               '|Polynomial|
                                                               (|devaluate|
                                                                (ELT % 6)))))
                                                       |fglmpack|)))
                (EXIT
                 (COND
                  ((QEQCAR |foo| 1)
                   (PROGN (LETT #3# (CONS 1 "failed")) (GO #7=#:G47)))
                  ('T
                   (SEQ
                    (LETT |lp|
                          (PROGN
                           (LETT #2# NIL)
                           (SEQ (LETT |q1| NIL) (LETT #1# (QCDR |foo|)) G190
                                (COND
                                 ((OR (ATOM #1#)
                                      (PROGN (LETT |q1| (CAR #1#)) NIL))
                                  (GO G191)))
                                (SEQ
                                 (EXIT
                                  (LETT #2#
                                        (CONS (SPADCALL |q1| (QREFELT % 23))
                                              #2#))))
                                (LETT #1# (CDR #1#)) (GO G190) G191
                                (EXIT (NREVERSE #2#)))))
                    (EXIT (CONS 0 |lp|))))))))
          #7# (EXIT #3#)))) 

(SDEFUN |LEXTRIPK;groebner;2L;4|
        ((|lp|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (%
          (|List|
           (|NewSparseMultivariatePolynomial| R
                                              (|OrderedVariableList| |ls|)))))
        (SPROG
         ((#1=#:G62 NIL) (|q1| NIL) (#2=#:G61 NIL)
          (|lq1| (|List| (|Polynomial| R))) (#3=#:G60 NIL) (|p| NIL)
          (#4=#:G59 NIL)
          (|fglmpack|
           (CATEGORY |package|
            (SIGNATURE |zeroDimensional?|
             ((|Boolean|) (|List| (|Polynomial| R))))
            (SIGNATURE |fglmIfCan|
             ((|Union| (|List| (|Polynomial| R)) "failed")
              (|List| (|Polynomial| R))))
            (SIGNATURE |groebner|
             ((|List| (|Polynomial| R)) (|List| (|Polynomial| R))))))
          (|truels| (|List| (|Symbol|))))
         (SEQ (LETT |truels| (|LEXTRIPK;trueVariables| |lp| %))
              (LETT |fglmpack| (|FGLMIfCanPackage| (QREFELT % 6) |truels|))
              (LETT |lq1|
                    (PROGN
                     (LETT #4# NIL)
                     (SEQ (LETT |p| NIL) (LETT #3# |lp|) G190
                          (COND
                           ((OR (ATOM #3#) (PROGN (LETT |p| (CAR #3#)) NIL))
                            (GO G191)))
                          (SEQ
                           (EXIT
                            (LETT #4#
                                  (CONS (SPADCALL |p| (QREFELT % 21)) #4#))))
                          (LETT #3# (CDR #3#)) (GO G190) G191
                          (EXIT (NREVERSE #4#)))))
              (LETT |lq1|
                    (SPADCALL |lq1|
                              (|compiledLookupCheck| '|groebner|
                                                     (LIST
                                                      (LIST '|List|
                                                            (LIST '|Polynomial|
                                                                  (|devaluate|
                                                                   (ELT % 6))))
                                                      (LIST '|List|
                                                            (LIST '|Polynomial|
                                                                  (|devaluate|
                                                                   (ELT %
                                                                        6)))))
                                                     |fglmpack|)))
              (EXIT
               (LETT |lp|
                     (PROGN
                      (LETT #2# NIL)
                      (SEQ (LETT |q1| NIL) (LETT #1# |lq1|) G190
                           (COND
                            ((OR (ATOM #1#) (PROGN (LETT |q1| (CAR #1#)) NIL))
                             (GO G191)))
                           (SEQ
                            (EXIT
                             (LETT #2#
                                   (CONS (SPADCALL |q1| (QREFELT % 23)) #2#))))
                           (LETT #1# (CDR #1#)) (GO G190) G191
                           (EXIT (NREVERSE #2#))))))))) 

(SDEFUN |LEXTRIPK;lexTriangular;LBL;5|
        ((|base|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (|norm?| (|Boolean|)) (% (|List| (|RegularChain| R |ls|))))
        (SPROG
         ((|toSee|
           (|List|
            (|Record|
             (|:| |val|
                  #1=(|List|
                      (|NewSparseMultivariatePolynomial| R
                                                         (|OrderedVariableList|
                                                          |ls|))))
             (|:| |tower| (|RegularChain| R |ls|)))))
          (#2=#:G94 NIL)
          (|newlp|
           (|List|
            (|NewSparseMultivariatePolynomial| R
                                               (|OrderedVariableList| |ls|))))
          (|lus| (|List| (|RegularChain| R |ls|)))
          (|newp|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|)))
          (|us| (|RegularChain| R |ls|)) (|b| (|Boolean|))
          (|lbwt|
           (|List|
            (|Record| (|:| |val| (|Boolean|))
                      (|:| |tower| (|RegularChain| R |ls|)))))
          (|bwt|
           (|Record| (|:| |val| (|Boolean|))
                     (|:| |tower| (|RegularChain| R |ls|))))
          (|v| (|OrderedVariableList| |ls|)) (|lp| #1#)
          (|p|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|)))
          (|toSave| (|List| (|RegularChain| R |ls|)))
          (|ts| (|RegularChain| R |ls|))
          (|lpwt|
           (|Record|
            (|:| |val|
                 (|List|
                  (|NewSparseMultivariatePolynomial| R
                                                     (|OrderedVariableList|
                                                      |ls|))))
            (|:| |tower| (|RegularChain| R |ls|)))))
         (SEQ (LETT |base| (SPADCALL (ELT % 27) |base| (QREFELT % 29)))
              (LETT |base| (SPADCALL (ELT % 30) |base| (QREFELT % 32)))
              (EXIT
               (COND ((SPADCALL (ELT % 33) |base| (QREFELT % 34)) NIL)
                     ('T
                      (SEQ (LETT |ts| (SPADCALL (QREFELT % 36)))
                           (LETT |toSee| (LIST (CONS |base| |ts|)))
                           (LETT |toSave| NIL)
                           (SEQ G190
                                (COND ((NULL (NULL (NULL |toSee|))) (GO G191)))
                                (SEQ (LETT |lpwt| (|SPADfirst| |toSee|))
                                     (LETT |toSee| (CDR |toSee|))
                                     (LETT |lp| (QCAR |lpwt|))
                                     (LETT |ts| (QCDR |lpwt|))
                                     (EXIT
                                      (COND
                                       ((NULL |lp|)
                                        (LETT |toSave| (CONS |ts| |toSave|)))
                                       ('T
                                        (SEQ (LETT |p| (|SPADfirst| |lp|))
                                             (LETT |lp| (CDR |lp|))
                                             (LETT |v|
                                                   (SPADCALL |p|
                                                             (QREFELT % 37)))
                                             (EXIT
                                              (COND
                                               ((SPADCALL |v| |ts|
                                                          (QREFELT % 38))
                                                (|error|
                                                 "lexTriangular$LEXTRIPK: should never happen !"))
                                               ('T
                                                (SEQ
                                                 (COND
                                                  (|norm?|
                                                   (COND
                                                    ((SPADCALL
                                                      (QVELT
                                                       (SPADCALL
                                                        (SPADCALL |p|
                                                                  (QREFELT %
                                                                           39))
                                                        |ts| (QREFELT % 41))
                                                       1)
                                                      (QREFELT % 30))
                                                     (EXIT
                                                      (LETT |toSee|
                                                            (CONS
                                                             (CONS |lp| |ts|)
                                                             |toSee|)))))))
                                                 (COND
                                                  ((NULL |norm?|)
                                                   (COND
                                                    ((SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL |p|
                                                                 (QREFELT %
                                                                          39))
                                                       |ts| (QREFELT % 42))
                                                      (QREFELT % 30))
                                                     (EXIT
                                                      (LETT |toSee|
                                                            (CONS
                                                             (CONS |lp| |ts|)
                                                             |toSee|)))))))
                                                 (LETT |lbwt|
                                                       (SPADCALL
                                                        (SPADCALL |p|
                                                                  (QREFELT %
                                                                           39))
                                                        |ts| (QREFELT % 45)))
                                                 (EXIT
                                                  (SEQ G190
                                                       (COND
                                                        ((NULL
                                                          (NULL (NULL |lbwt|)))
                                                         (GO G191)))
                                                       (SEQ
                                                        (LETT |bwt|
                                                              (|SPADfirst|
                                                               |lbwt|))
                                                        (LETT |lbwt|
                                                              (CDR |lbwt|))
                                                        (LETT |b| (QCAR |bwt|))
                                                        (LETT |us|
                                                              (QCDR |bwt|))
                                                        (EXIT
                                                         (COND
                                                          (|b|
                                                           (SEQ
                                                            (COND
                                                             (|norm?|
                                                              (SEQ
                                                               (LETT |newp|
                                                                     (SPADCALL
                                                                      |p| |us|
                                                                      (QREFELT
                                                                       % 47)))
                                                               (EXIT
                                                                (LETT |lus|
                                                                      (LIST
                                                                       (SPADCALL
                                                                        |newp|
                                                                        |us|
                                                                        (QREFELT
                                                                         %
                                                                         48)))))))
                                                             ('T
                                                              (SEQ
                                                               (LETT |newp|
                                                                     |p|)
                                                               (EXIT
                                                                (LETT |lus|
                                                                      (SPADCALL
                                                                       |newp|
                                                                       |us|
                                                                       (QREFELT
                                                                        %
                                                                        50)))))))
                                                            (LETT |newlp| |lp|)
                                                            (SEQ G190
                                                                 (COND
                                                                  ((NULL
                                                                    (COND
                                                                     ((NULL
                                                                       |newlp|)
                                                                      NIL)
                                                                     ('T
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (|SPADfirst|
                                                                         |newlp|)
                                                                        (QREFELT
                                                                         % 37))
                                                                       |v|
                                                                       (QREFELT
                                                                        %
                                                                        51)))))
                                                                   (GO G191)))
                                                                 (SEQ
                                                                  (EXIT
                                                                   (LETT
                                                                    |newlp|
                                                                    (CDR
                                                                     |newlp|))))
                                                                 NIL (GO G190)
                                                                 G191
                                                                 (EXIT NIL))
                                                            (EXIT
                                                             (SEQ
                                                              (LETT #2# |lus|)
                                                              G190
                                                              (COND
                                                               ((OR (ATOM #2#)
                                                                    (PROGN
                                                                     (LETT |us|
                                                                           (CAR
                                                                            #2#))
                                                                     NIL))
                                                                (GO G191)))
                                                              (SEQ
                                                               (EXIT
                                                                (LETT |toSee|
                                                                      (CONS
                                                                       (CONS
                                                                        |newlp|
                                                                        |us|)
                                                                       |toSee|))))
                                                              (LETT #2#
                                                                    (CDR #2#))
                                                              (GO G190) G191
                                                              (EXIT NIL)))))
                                                          ('T
                                                           (LETT |toSee|
                                                                 (CONS
                                                                  (CONS |lp|
                                                                        |us|)
                                                                  |toSee|))))))
                                                       NIL (GO G190) G191
                                                       (EXIT NIL))))))))))))
                                NIL (GO G190) G191 (EXIT NIL))
                           (EXIT (SPADCALL |toSave| (QREFELT % 54)))))))))) 

(SDEFUN |LEXTRIPK;zeroSetSplit;LBL;6|
        ((|lp|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (|norm?| (|Boolean|)) (% (|List| (|RegularChain| R |ls|))))
        (SPROG
         ((|bar|
           (|Union|
            (|List|
             (|NewSparseMultivariatePolynomial| R
                                                (|OrderedVariableList| |ls|)))
            "failed")))
         (SEQ (LETT |bar| (SPADCALL |lp| (QREFELT % 25)))
              (EXIT
               (COND
                ((QEQCAR |bar| 1)
                 (|error| "zeroSetSplit$LEXTRIPK: #1 not zero-dimensional"))
                ('T (SPADCALL (QCDR |bar|) |norm?| (QREFELT % 55)))))))) 

(SDEFUN |LEXTRIPK;squareFreeLexTriangular;LBL;7|
        ((|base|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (|norm?| (|Boolean|))
         (%
          (|List|
           (|SquareFreeRegularTriangularSet| R
                                             (|IndexedExponents|
                                              (|OrderedVariableList| |ls|))
                                             (|OrderedVariableList| |ls|)
                                             (|NewSparseMultivariatePolynomial|
                                              R
                                              (|OrderedVariableList| |ls|))))))
        (SPROG
         ((|toSee|
           (|List|
            (|Record|
             (|:| |val|
                  #1=(|List|
                      (|NewSparseMultivariatePolynomial| R
                                                         (|OrderedVariableList|
                                                          |ls|))))
             (|:| |tower|
                  (|SquareFreeRegularTriangularSet| R
                                                    (|IndexedExponents|
                                                     (|OrderedVariableList|
                                                      |ls|))
                                                    (|OrderedVariableList|
                                                     |ls|)
                                                    (|NewSparseMultivariatePolynomial|
                                                     R
                                                     (|OrderedVariableList|
                                                      |ls|)))))))
          (#2=#:G130 NIL)
          (|newlp|
           (|List|
            (|NewSparseMultivariatePolynomial| R
                                               (|OrderedVariableList| |ls|))))
          (|lus|
           (|List|
            (|SquareFreeRegularTriangularSet| R
                                              (|IndexedExponents|
                                               (|OrderedVariableList| |ls|))
                                              (|OrderedVariableList| |ls|)
                                              (|NewSparseMultivariatePolynomial|
                                               R
                                               (|OrderedVariableList| |ls|)))))
          (|newp|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|)))
          (|us|
           (|SquareFreeRegularTriangularSet| R
                                             (|IndexedExponents|
                                              (|OrderedVariableList| |ls|))
                                             (|OrderedVariableList| |ls|)
                                             (|NewSparseMultivariatePolynomial|
                                              R (|OrderedVariableList| |ls|))))
          (|b| (|Boolean|))
          (|lbwt|
           (|List|
            (|Record| (|:| |val| (|Boolean|))
                      (|:| |tower|
                           (|SquareFreeRegularTriangularSet| R
                                                             (|IndexedExponents|
                                                              (|OrderedVariableList|
                                                               |ls|))
                                                             (|OrderedVariableList|
                                                              |ls|)
                                                             (|NewSparseMultivariatePolynomial|
                                                              R
                                                              (|OrderedVariableList|
                                                               |ls|)))))))
          (|bwt|
           (|Record| (|:| |val| (|Boolean|))
                     (|:| |tower|
                          (|SquareFreeRegularTriangularSet| R
                                                            (|IndexedExponents|
                                                             (|OrderedVariableList|
                                                              |ls|))
                                                            (|OrderedVariableList|
                                                             |ls|)
                                                            (|NewSparseMultivariatePolynomial|
                                                             R
                                                             (|OrderedVariableList|
                                                              |ls|))))))
          (|v| (|OrderedVariableList| |ls|)) (|lp| #1#)
          (|p|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|)))
          (|toSave|
           (|List|
            (|SquareFreeRegularTriangularSet| R
                                              (|IndexedExponents|
                                               (|OrderedVariableList| |ls|))
                                              (|OrderedVariableList| |ls|)
                                              (|NewSparseMultivariatePolynomial|
                                               R
                                               (|OrderedVariableList| |ls|)))))
          (|ts|
           (|SquareFreeRegularTriangularSet| R
                                             (|IndexedExponents|
                                              (|OrderedVariableList| |ls|))
                                             (|OrderedVariableList| |ls|)
                                             (|NewSparseMultivariatePolynomial|
                                              R (|OrderedVariableList| |ls|))))
          (|lpwt|
           (|Record|
            (|:| |val|
                 (|List|
                  (|NewSparseMultivariatePolynomial| R
                                                     (|OrderedVariableList|
                                                      |ls|))))
            (|:| |tower|
                 (|SquareFreeRegularTriangularSet| R
                                                   (|IndexedExponents|
                                                    (|OrderedVariableList|
                                                     |ls|))
                                                   (|OrderedVariableList| |ls|)
                                                   (|NewSparseMultivariatePolynomial|
                                                    R
                                                    (|OrderedVariableList|
                                                     |ls|)))))))
         (SEQ (LETT |base| (SPADCALL (ELT % 27) |base| (QREFELT % 29)))
              (LETT |base| (SPADCALL (ELT % 30) |base| (QREFELT % 32)))
              (EXIT
               (COND ((SPADCALL (ELT % 33) |base| (QREFELT % 34)) NIL)
                     ('T
                      (SEQ (LETT |ts| (SPADCALL (QREFELT % 58)))
                           (LETT |toSee| (LIST (CONS |base| |ts|)))
                           (LETT |toSave| NIL)
                           (SEQ G190
                                (COND ((NULL (NULL (NULL |toSee|))) (GO G191)))
                                (SEQ (LETT |lpwt| (|SPADfirst| |toSee|))
                                     (LETT |toSee| (CDR |toSee|))
                                     (LETT |lp| (QCAR |lpwt|))
                                     (LETT |ts| (QCDR |lpwt|))
                                     (EXIT
                                      (COND
                                       ((NULL |lp|)
                                        (LETT |toSave| (CONS |ts| |toSave|)))
                                       ('T
                                        (SEQ (LETT |p| (|SPADfirst| |lp|))
                                             (LETT |lp| (CDR |lp|))
                                             (LETT |v|
                                                   (SPADCALL |p|
                                                             (QREFELT % 37)))
                                             (EXIT
                                              (COND
                                               ((SPADCALL |v| |ts|
                                                          (QREFELT % 59))
                                                (|error|
                                                 "lexTriangular$LEXTRIPK: should never happen !"))
                                               ('T
                                                (SEQ
                                                 (COND
                                                  (|norm?|
                                                   (COND
                                                    ((SPADCALL
                                                      (QVELT
                                                       (SPADCALL
                                                        (SPADCALL |p|
                                                                  (QREFELT %
                                                                           39))
                                                        |ts| (QREFELT % 60))
                                                       1)
                                                      (QREFELT % 30))
                                                     (EXIT
                                                      (LETT |toSee|
                                                            (CONS
                                                             (CONS |lp| |ts|)
                                                             |toSee|)))))))
                                                 (COND
                                                  ((NULL |norm?|)
                                                   (COND
                                                    ((SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL |p|
                                                                 (QREFELT %
                                                                          39))
                                                       |ts| (QREFELT % 61))
                                                      (QREFELT % 30))
                                                     (EXIT
                                                      (LETT |toSee|
                                                            (CONS
                                                             (CONS |lp| |ts|)
                                                             |toSee|)))))))
                                                 (LETT |lbwt|
                                                       (SPADCALL
                                                        (SPADCALL |p|
                                                                  (QREFELT %
                                                                           39))
                                                        |ts| (QREFELT % 62)))
                                                 (EXIT
                                                  (SEQ G190
                                                       (COND
                                                        ((NULL
                                                          (NULL (NULL |lbwt|)))
                                                         (GO G191)))
                                                       (SEQ
                                                        (LETT |bwt|
                                                              (|SPADfirst|
                                                               |lbwt|))
                                                        (LETT |lbwt|
                                                              (CDR |lbwt|))
                                                        (LETT |b| (QCAR |bwt|))
                                                        (LETT |us|
                                                              (QCDR |bwt|))
                                                        (EXIT
                                                         (COND
                                                          (|b|
                                                           (SEQ
                                                            (COND
                                                             (|norm?|
                                                              (SEQ
                                                               (LETT |newp|
                                                                     (SPADCALL
                                                                      |p| |us|
                                                                      (QREFELT
                                                                       % 64)))
                                                               (EXIT
                                                                (LETT |lus|
                                                                      (SPADCALL
                                                                       |newp|
                                                                       |us|
                                                                       (QREFELT
                                                                        %
                                                                        65))))))
                                                             ('T
                                                              (LETT |lus|
                                                                    (SPADCALL
                                                                     |p| |us|
                                                                     (QREFELT %
                                                                              65)))))
                                                            (LETT |newlp| |lp|)
                                                            (SEQ G190
                                                                 (COND
                                                                  ((NULL
                                                                    (COND
                                                                     ((NULL
                                                                       |newlp|)
                                                                      NIL)
                                                                     ('T
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (|SPADfirst|
                                                                         |newlp|)
                                                                        (QREFELT
                                                                         % 37))
                                                                       |v|
                                                                       (QREFELT
                                                                        %
                                                                        51)))))
                                                                   (GO G191)))
                                                                 (SEQ
                                                                  (EXIT
                                                                   (LETT
                                                                    |newlp|
                                                                    (CDR
                                                                     |newlp|))))
                                                                 NIL (GO G190)
                                                                 G191
                                                                 (EXIT NIL))
                                                            (EXIT
                                                             (SEQ
                                                              (LETT #2# |lus|)
                                                              G190
                                                              (COND
                                                               ((OR (ATOM #2#)
                                                                    (PROGN
                                                                     (LETT |us|
                                                                           (CAR
                                                                            #2#))
                                                                     NIL))
                                                                (GO G191)))
                                                              (SEQ
                                                               (EXIT
                                                                (LETT |toSee|
                                                                      (CONS
                                                                       (CONS
                                                                        |newlp|
                                                                        |us|)
                                                                       |toSee|))))
                                                              (LETT #2#
                                                                    (CDR #2#))
                                                              (GO G190) G191
                                                              (EXIT NIL)))))
                                                          ('T
                                                           (LETT |toSee|
                                                                 (CONS
                                                                  (CONS |lp|
                                                                        |us|)
                                                                  |toSee|))))))
                                                       NIL (GO G190) G191
                                                       (EXIT NIL))))))))))))
                                NIL (GO G190) G191 (EXIT NIL))
                           (EXIT (SPADCALL |toSave| (QREFELT % 68)))))))))) 

(SDEFUN |LEXTRIPK;zeroSetSplit;LBL;8|
        ((|lp|
          (|List|
           (|NewSparseMultivariatePolynomial| R (|OrderedVariableList| |ls|))))
         (|norm?| (|Boolean|))
         (%
          (|List|
           (|SquareFreeRegularTriangularSet| R
                                             (|IndexedExponents|
                                              (|OrderedVariableList| |ls|))
                                             (|OrderedVariableList| |ls|)
                                             (|NewSparseMultivariatePolynomial|
                                              R
                                              (|OrderedVariableList| |ls|))))))
        (SPROG
         ((|bar|
           (|Union|
            (|List|
             (|NewSparseMultivariatePolynomial| R
                                                (|OrderedVariableList| |ls|)))
            "failed")))
         (SEQ (LETT |bar| (SPADCALL |lp| (QREFELT % 25)))
              (EXIT
               (COND
                ((QEQCAR |bar| 1)
                 (|error| "zeroSetSplit$LEXTRIPK: #1 not zero-dimensional"))
                ('T (SPADCALL (QCDR |bar|) |norm?| (QREFELT % 69)))))))) 

(DECLAIM (NOTINLINE |LexTriangularPackage;|)) 

(DEFUN |LexTriangularPackage;| (|#1| |#2|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|))
          (LETT DV$2 |#2|)
          (LETT |dv$| (LIST '|LexTriangularPackage| DV$1 DV$2))
          (LETT % (GETREFV 71))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3 (LETT |pv$| (|buildPredVector| 0 0 NIL)))
          (|haddProp| |$ConstructorCache| '|LexTriangularPackage|
                      (LIST DV$1 DV$2) (CONS 1 %))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (QSETREFV % 7 |#2|)
          (SETF |pv$| (QREFELT % 3))
          %))) 

(DEFUN |LexTriangularPackage| (&REST #1=#:G136)
  (SPROG NIL
         (PROG (#2=#:G137)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluate_sig| #1# '(T NIL))
                                               (HGET |$ConstructorCache|
                                                     '|LexTriangularPackage|)
                                               '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |LexTriangularPackage;|) #1#)
                    (LETT #2# T))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache| '|LexTriangularPackage|)))))))))) 

(MAKEPROP '|LexTriangularPackage| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|List| 20)
              (|GeneralPolynomialSet| 6 (|IndexedExponents| 15) 15 20)
              (0 . |construct|) (|List| 15) (5 . |variables|)
              (|Union| % '"failed") (|Symbol|)
              (|OrderedVariableList| (NRTEVAL (QREFELT % 7))) (10 . |variable|)
              (|Boolean|) (15 . |member?|) (|Polynomial| 6)
              (|NewSparseMultivariatePolynomial| 6 15) (21 . |coerce|)
              |LEXTRIPK;zeroDimensional?;LB;2| (26 . |retract|)
              (|Union| 8 '"failed") |LEXTRIPK;fglmIfCan;LU;3|
              |LEXTRIPK;groebner;2L;4| (31 . |infRittWu?|) (|Mapping| 17 20 20)
              (37 . |sort|) (43 . |zero?|) (|Mapping| 17 20) (48 . |remove|)
              (54 . |ground?|) (59 . |any?|)
              (|RegularChain| 6 (NRTEVAL (QREFELT % 7))) (65 . |empty|)
              (69 . |mvar|) (74 . |algebraic?|) (80 . |init|)
              (|Record| (|:| |rnum| 6) (|:| |polnum| 20) (|:| |den| 6))
              (85 . |remainder|) (91 . |initiallyReduce|)
              (|Record| (|:| |val| 17) (|:| |tower| %)) (|List| 43)
              (97 . |invertible?|)
              (|NormalizationPackage| 6 (|IndexedExponents| 15) 15 20 35)
              (103 . |normalizedAssociate|) (109 . |internalAugment|)
              (|List| %) (115 . |augment|) (121 . =) (|List| 35)
              (|QuasiComponentPackage| 6 (|IndexedExponents| 15) 15 20 35)
              (127 . |algebraicSort|) |LEXTRIPK;lexTriangular;LBL;5|
              |LEXTRIPK;zeroSetSplit;LBL;6|
              (|SquareFreeRegularTriangularSet| 6 (|IndexedExponents| 15) 15
                                                20)
              (132 . |empty|) (136 . |algebraic?|) (142 . |remainder|)
              (148 . |initiallyReduce|) (154 . |invertible?|)
              (|NormalizationPackage| 6 (|IndexedExponents| 15) 15 20 57)
              (160 . |normalizedAssociate|) (166 . |augment|) (|List| 57)
              (|QuasiComponentPackage| 6 (|IndexedExponents| 15) 15 20 57)
              (172 . |algebraicSort|) |LEXTRIPK;squareFreeLexTriangular;LBL;7|
              |LEXTRIPK;zeroSetSplit;LBL;8|)
           '#(|zeroSetSplit| 177 |zeroDimensional?| 189
              |squareFreeLexTriangular| 194 |lexTriangular| 200 |groebner| 206
              |fglmIfCan| 211)
           'NIL
           (CONS (|makeByteWordVec2| 1 '(0))
                 (CONS '#(NIL)
                       (CONS
                        '#((|Join|
                            (|mkCategory|
                             (LIST
                              '((|zeroDimensional?|
                                 ((|Boolean|)
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))))
                                T)
                              '((|fglmIfCan|
                                 ((|Union|
                                   (|List|
                                    (|NewSparseMultivariatePolynomial| |#1|
                                                                       (|OrderedVariableList|
                                                                        |#2|)))
                                   "failed")
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))))
                                T)
                              '((|groebner|
                                 ((|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))))
                                T)
                              '((|lexTriangular|
                                 ((|List| (|RegularChain| |#1| |#2|))
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))
                                  (|Boolean|)))
                                T)
                              '((|squareFreeLexTriangular|
                                 ((|List|
                                   (|SquareFreeRegularTriangularSet| |#1|
                                                                     (|IndexedExponents|
                                                                      (|OrderedVariableList|
                                                                       |#2|))
                                                                     (|OrderedVariableList|
                                                                      |#2|)
                                                                     (|NewSparseMultivariatePolynomial|
                                                                      |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|))))
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))
                                  (|Boolean|)))
                                T)
                              '((|zeroSetSplit|
                                 ((|List| (|RegularChain| |#1| |#2|))
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))
                                  (|Boolean|)))
                                T)
                              '((|zeroSetSplit|
                                 ((|List|
                                   (|SquareFreeRegularTriangularSet| |#1|
                                                                     (|IndexedExponents|
                                                                      (|OrderedVariableList|
                                                                       |#2|))
                                                                     (|OrderedVariableList|
                                                                      |#2|)
                                                                     (|NewSparseMultivariatePolynomial|
                                                                      |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|))))
                                  (|List|
                                   (|NewSparseMultivariatePolynomial| |#1|
                                                                      (|OrderedVariableList|
                                                                       |#2|)))
                                  (|Boolean|)))
                                T))
                             (LIST) NIL NIL)))
                        (|makeByteWordVec2| 70
                                            '(1 9 0 8 10 1 9 11 0 12 1 15 13 14
                                              16 2 11 17 15 0 18 1 20 19 0 21 1
                                              20 0 19 23 2 20 17 0 0 27 2 8 0
                                              28 0 29 1 20 17 0 30 2 8 0 31 0
                                              32 1 20 17 0 33 2 8 17 31 0 34 0
                                              35 0 36 1 20 15 0 37 2 35 17 15 0
                                              38 1 20 0 0 39 2 35 40 20 0 41 2
                                              35 20 20 0 42 2 35 44 20 0 45 2
                                              46 20 20 35 47 2 35 0 20 0 48 2
                                              35 49 20 0 50 2 15 17 0 0 51 1 53
                                              52 52 54 0 57 0 58 2 57 17 15 0
                                              59 2 57 40 20 0 60 2 57 20 20 0
                                              61 2 57 44 20 0 62 2 63 20 20 57
                                              64 2 57 49 20 0 65 1 67 66 66 68
                                              2 0 52 8 17 56 2 0 66 8 17 70 1 0
                                              17 8 22 2 0 66 8 17 69 2 0 52 8
                                              17 55 1 0 8 8 26 1 0 24 8 25)))))
           '|lookupComplete|)) 
