
(SDEFUN |INTAF;UPUP2F1|
        ((|p| |SparseUnivariatePolynomial|
          (|Fraction| (|SparseUnivariatePolynomial| F)))
         (|t| |Fraction| (|SparseUnivariatePolynomial| F))
         (|cf| |Fraction| (|SparseUnivariatePolynomial| F)) (|kx| |Kernel| F)
         (|k| |Kernel| F) ($ F))
        (|INTAF;UPUP2F0| (SPADCALL |p| |t| |cf| (QREFELT $ 11)) |kx| |k| $)) 

(SDEFUN |INTAF;UPUP2F0|
        ((|p| |SparseUnivariatePolynomial|
          (|Fraction| (|SparseUnivariatePolynomial| F)))
         (|kx| |Kernel| F) (|k| |Kernel| F) ($ F))
        (SPROG NIL
               (SPADCALL
                (SPADCALL (CONS #'|INTAF;UPUP2F0!0| (VECTOR $ |kx|)) |p|
                          (QREFELT $ 18))
                (SPADCALL |k| (QREFELT $ 20)) (QREFELT $ 21)))) 

(SDEFUN |INTAF;UPUP2F0!0| ((|x1| NIL) ($$ NIL))
        (PROG (|kx| $)
          (LETT |kx| (QREFELT $$ 1) . #1=(|INTAF;UPUP2F0|))
          (LETT $ (QREFELT $$ 0) . #1#)
          (RETURN (PROGN (SPADCALL |x1| |kx| (QREFELT $ 14)))))) 

(SDEFUN |INTAF;F2UPUP|
        ((|f| F) (|kx| |Kernel| F) (|k| |Kernel| F)
         (|p| |SparseUnivariatePolynomial| F)
         ($ |SparseUnivariatePolynomial|
          (|Fraction| (|SparseUnivariatePolynomial| F))))
        (|INTAF;UP2UPUP| (SPADCALL |f| |k| |p| (QREFELT $ 22)) |kx| $)) 

(SDEFUN |INTAF;rootintegrate|
        ((|f| F) (|t| |Kernel| F) (|k| |Kernel| F)
         (|derivation| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         ($ |IntegrationResult| F))
        (SPROG
         ((|curve|
           (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                    (|SparseUnivariatePolynomial|
                                     (|Fraction|
                                      (|SparseUnivariatePolynomial| F)))))
          (|q| (|SparseUnivariatePolynomial| F))
          (|r|
           (|Record|
            (|:| |radicand| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |deg| (|NonNegativeInteger|))))
          (#1=#:G719 NIL)
          (|f1|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|r1|
           (|Record| (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                     (|:| |poly|
                          (|SparseUnivariatePolynomial|
                           (|Fraction| (|SparseUnivariatePolynomial| F))))))
          (|modulus|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|p| (|SparseUnivariatePolynomial| F)))
         (SEQ
          (LETT |r1|
                (SPADCALL
                 (LETT |modulus|
                       (|INTAF;UP2UPUP|
                        (LETT |p| (SPADCALL |k| (QREFELT $ 24))
                              . #2=(|INTAF;rootintegrate|))
                        |t| $)
                       . #2#)
                 (QREFELT $ 26))
                . #2#)
          (LETT |f1|
                (SPADCALL (|INTAF;F2UPUP| |f| |t| |k| |p| $)
                          (SPADCALL (SPADCALL (QCAR |r1|) (QREFELT $ 27)) 1
                                    (QREFELT $ 30))
                          (QREFELT $ 31))
                . #2#)
          (LETT |r|
                (PROG2 (LETT #1# (SPADCALL (QCDR |r1|) (QREFELT $ 34)) . #2#)
                    (QCDR #1#)
                  (|check_union2| (QEQCAR #1# 0)
                                  (|Record|
                                   (|:| |radicand|
                                        (|Fraction|
                                         (|SparseUnivariatePolynomial|
                                          (QREFELT $ 7))))
                                   (|:| |deg| (|NonNegativeInteger|)))
                                  (|Union|
                                   (|Record|
                                    (|:| |radicand|
                                         (|Fraction|
                                          (|SparseUnivariatePolynomial|
                                           (QREFELT $ 7))))
                                    (|:| |deg| (|NonNegativeInteger|)))
                                   "failed")
                                  #1#))
                . #2#)
          (LETT |q| (SPADCALL (QCAR |r|) (QREFELT $ 35)) . #2#)
          (LETT |curve|
                (|RadicalFunctionField| (QREFELT $ 7)
                                        (|SparseUnivariatePolynomial|
                                         (QREFELT $ 7))
                                        (|SparseUnivariatePolynomial|
                                         (|Fraction|
                                          (|SparseUnivariatePolynomial|
                                           (QREFELT $ 7))))
                                        (SPADCALL |q| (QREFELT $ 36))
                                        (QCDR |r|))
                . #2#)
          (EXIT
           (SPADCALL
            (CONS #'|INTAF;rootintegrate!0| (VECTOR |k| |t| |r1| |curve| $))
            (SPADCALL
             (SPADCALL |f1|
                       (|compiledLookupCheck| '|reduce|
                                              (LIST '$
                                                    (LIST
                                                     '|SparseUnivariatePolynomial|
                                                     (LIST '|Fraction|
                                                           (LIST
                                                            '|SparseUnivariatePolynomial|
                                                            (|devaluate|
                                                             (ELT $ 7))))))
                                              |curve|))
             |derivation|
             (|compiledLookupCheck| '|algintegrate|
                                    (LIST
                                     (LIST '|IntegrationResult|
                                           (|devaluate| |curve|))
                                     (|devaluate| |curve|)
                                     (LIST '|Mapping|
                                           (LIST '|SparseUnivariatePolynomial|
                                                 (|devaluate| (ELT $ 7)))
                                           (LIST '|SparseUnivariatePolynomial|
                                                 (|devaluate| (ELT $ 7)))))
                                    (|AlgebraicIntegrate| (ELT $ 6) (ELT $ 7)
                                                          (|SparseUnivariatePolynomial|
                                                           (ELT $ 7))
                                                          (|SparseUnivariatePolynomial|
                                                           (|Fraction|
                                                            (|SparseUnivariatePolynomial|
                                                             (ELT $ 7))))
                                                          |curve|)))
            (|compiledLookupCheck| '|map|
                                   (LIST
                                    (LIST '|IntegrationResult|
                                          (|devaluate| (ELT $ 7)))
                                    (LIST '|Mapping| (|devaluate| (ELT $ 7))
                                          (|devaluate| |curve|))
                                    (LIST '|IntegrationResult|
                                          (|devaluate| |curve|)))
                                   (|IntegrationResultFunctions2| |curve|
                                                                  (ELT $
                                                                       7)))))))) 

(SDEFUN |INTAF;rootintegrate!0| ((|x1| NIL) ($$ NIL))
        (PROG ($ |curve| |r1| |t| |k|)
          (LETT $ (QREFELT $$ 4) . #1=(|INTAF;rootintegrate|))
          (LETT |curve| (QREFELT $$ 3) . #1#)
          (LETT |r1| (QREFELT $$ 2) . #1#)
          (LETT |t| (QREFELT $$ 1) . #1#)
          (LETT |k| (QREFELT $$ 0) . #1#)
          (RETURN
           (PROGN
            (|INTAF;UPUP2F|
             (SPADCALL |x1|
                       (|compiledLookupCheck| '|lift|
                                              (LIST
                                               (LIST
                                                '|SparseUnivariatePolynomial|
                                                (LIST '|Fraction|
                                                      (LIST
                                                       '|SparseUnivariatePolynomial|
                                                       (|devaluate|
                                                        (ELT $ 7)))))
                                               '$)
                                              |curve|))
             (QCAR |r1|) |t| |k| $))))) 

(SDEFUN |INTAF;algintegrate|
        ((|f| F) (|t| |Kernel| F) (|k| |Kernel| F)
         (|derivation| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         ($ |IntegrationResult| F))
        (SPROG
         ((|curve|
           (|Join|
            (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                     (|SparseUnivariatePolynomial|
                                      (|Fraction|
                                       (|SparseUnivariatePolynomial| F))))
            (CATEGORY |package|
             (SIGNATURE |knownInfBasis| ((|Void|) (|NonNegativeInteger|))))))
          (|modulus|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|p| (|SparseUnivariatePolynomial| F))
          (|f1|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|r1|
           (|Record| (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                     (|:| |poly|
                          (|SparseUnivariatePolynomial|
                           (|Fraction| (|SparseUnivariatePolynomial| F)))))))
         (SEQ
          (LETT |r1|
                (SPADCALL
                 (LETT |modulus|
                       (|INTAF;UP2UPUP|
                        (LETT |p| (SPADCALL |k| (QREFELT $ 24))
                              . #1=(|INTAF;algintegrate|))
                        |t| $)
                       . #1#)
                 (QREFELT $ 26))
                . #1#)
          (LETT |f1|
                (SPADCALL (|INTAF;F2UPUP| |f| |t| |k| |p| $)
                          (SPADCALL (SPADCALL (QCAR |r1|) (QREFELT $ 27)) 1
                                    (QREFELT $ 30))
                          (QREFELT $ 31))
                . #1#)
          (LETT |modulus|
                (|INTAF;UP2UPUP| (LETT |p| (SPADCALL |k| (QREFELT $ 24)) . #1#)
                 |t| $)
                . #1#)
          (LETT |curve|
                (|AlgebraicFunctionField| (QREFELT $ 7)
                                          (|SparseUnivariatePolynomial|
                                           (QREFELT $ 7))
                                          (|SparseUnivariatePolynomial|
                                           (|Fraction|
                                            (|SparseUnivariatePolynomial|
                                             (QREFELT $ 7))))
                                          (QCDR |r1|))
                . #1#)
          (EXIT
           (SPADCALL
            (CONS #'|INTAF;algintegrate!0| (VECTOR |k| |t| |r1| |curve| $))
            (SPADCALL
             (SPADCALL |f1|
                       (|compiledLookupCheck| '|reduce|
                                              (LIST '$
                                                    (LIST
                                                     '|SparseUnivariatePolynomial|
                                                     (LIST '|Fraction|
                                                           (LIST
                                                            '|SparseUnivariatePolynomial|
                                                            (|devaluate|
                                                             (ELT $ 7))))))
                                              |curve|))
             |derivation|
             (|compiledLookupCheck| '|algintegrate|
                                    (LIST
                                     (LIST '|IntegrationResult|
                                           (|devaluate| |curve|))
                                     (|devaluate| |curve|)
                                     (LIST '|Mapping|
                                           (LIST '|SparseUnivariatePolynomial|
                                                 (|devaluate| (ELT $ 7)))
                                           (LIST '|SparseUnivariatePolynomial|
                                                 (|devaluate| (ELT $ 7)))))
                                    (|AlgebraicIntegrate| (ELT $ 6) (ELT $ 7)
                                                          (|SparseUnivariatePolynomial|
                                                           (ELT $ 7))
                                                          (|SparseUnivariatePolynomial|
                                                           (|Fraction|
                                                            (|SparseUnivariatePolynomial|
                                                             (ELT $ 7))))
                                                          |curve|)))
            (|compiledLookupCheck| '|map|
                                   (LIST
                                    (LIST '|IntegrationResult|
                                          (|devaluate| (ELT $ 7)))
                                    (LIST '|Mapping| (|devaluate| (ELT $ 7))
                                          (|devaluate| |curve|))
                                    (LIST '|IntegrationResult|
                                          (|devaluate| |curve|)))
                                   (|IntegrationResultFunctions2| |curve|
                                                                  (ELT $
                                                                       7)))))))) 

(SDEFUN |INTAF;algintegrate!0| ((|x1| NIL) ($$ NIL))
        (PROG ($ |curve| |r1| |t| |k|)
          (LETT $ (QREFELT $$ 4) . #1=(|INTAF;algintegrate|))
          (LETT |curve| (QREFELT $$ 3) . #1#)
          (LETT |r1| (QREFELT $$ 2) . #1#)
          (LETT |t| (QREFELT $$ 1) . #1#)
          (LETT |k| (QREFELT $$ 0) . #1#)
          (RETURN
           (PROGN
            (|INTAF;UPUP2F|
             (SPADCALL |x1|
                       (|compiledLookupCheck| '|lift|
                                              (LIST
                                               (LIST
                                                '|SparseUnivariatePolynomial|
                                                (LIST '|Fraction|
                                                      (LIST
                                                       '|SparseUnivariatePolynomial|
                                                       (|devaluate|
                                                        (ELT $ 7)))))
                                               '$)
                                              |curve|))
             (QCAR |r1|) |t| |k| $))))) 

(SDEFUN |INTAF;rootcurve|
        ((|lf| |List| F) (|t| |Kernel| F) (|k| |Kernel| F)
         (|derivation| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         ($ |Record|
          (|:| |funs|
               (|List|
                (|SparseUnivariatePolynomial|
                 (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (|:| |irec|
               (|Record|
                (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                (|:| |poly|
                     (|SparseUnivariatePolynomial|
                      (|Fraction| (|SparseUnivariatePolynomial| F))))))
          (|:| |curve_dom|
               (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                        (|SparseUnivariatePolynomial|
                                         (|Fraction|
                                          (|SparseUnivariatePolynomial|
                                           F)))))))
        (SPROG
         ((|curve|
           (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                    (|SparseUnivariatePolynomial|
                                     (|Fraction|
                                      (|SparseUnivariatePolynomial| F)))))
          (|q| (|SparseUnivariatePolynomial| F))
          (|r|
           (|Record|
            (|:| |radicand| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |deg| (|NonNegativeInteger|))))
          (#1=#:G742 NIL)
          (|lf1|
           (|List|
            (|SparseUnivariatePolynomial|
             (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (#2=#:G747 NIL) (|f| NIL) (#3=#:G746 NIL)
          (|mon1|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|r1|
           (|Record| (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                     (|:| |poly|
                          (|SparseUnivariatePolynomial|
                           (|Fraction| (|SparseUnivariatePolynomial| F))))))
          (|modulus|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|p| (|SparseUnivariatePolynomial| F)))
         (SEQ
          (LETT |r1|
                (SPADCALL
                 (LETT |modulus|
                       (|INTAF;UP2UPUP|
                        (LETT |p| (SPADCALL |k| (QREFELT $ 24))
                              . #4=(|INTAF;rootcurve|))
                        |t| $)
                       . #4#)
                 (QREFELT $ 26))
                . #4#)
          (LETT |mon1|
                (SPADCALL (SPADCALL (QCAR |r1|) (QREFELT $ 27)) 1
                          (QREFELT $ 30))
                . #4#)
          (LETT |lf1|
                (PROGN
                 (LETT #3# NIL . #4#)
                 (SEQ (LETT |f| NIL . #4#) (LETT #2# |lf| . #4#) G190
                      (COND
                       ((OR (ATOM #2#) (PROGN (LETT |f| (CAR #2#) . #4#) NIL))
                        (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #3#
                              (CONS
                               (SPADCALL (|INTAF;F2UPUP| |f| |t| |k| |p| $)
                                         |mon1| (QREFELT $ 31))
                               #3#)
                              . #4#)))
                      (LETT #2# (CDR #2#) . #4#) (GO G190) G191
                      (EXIT (NREVERSE #3#))))
                . #4#)
          (LETT |r|
                (PROG2 (LETT #1# (SPADCALL (QCDR |r1|) (QREFELT $ 34)) . #4#)
                    (QCDR #1#)
                  (|check_union2| (QEQCAR #1# 0)
                                  (|Record|
                                   (|:| |radicand|
                                        (|Fraction|
                                         (|SparseUnivariatePolynomial|
                                          (QREFELT $ 7))))
                                   (|:| |deg| (|NonNegativeInteger|)))
                                  (|Union|
                                   (|Record|
                                    (|:| |radicand|
                                         (|Fraction|
                                          (|SparseUnivariatePolynomial|
                                           (QREFELT $ 7))))
                                    (|:| |deg| (|NonNegativeInteger|)))
                                   "failed")
                                  #1#))
                . #4#)
          (LETT |q| (SPADCALL (QCAR |r|) (QREFELT $ 35)) . #4#)
          (LETT |curve|
                (|RadicalFunctionField| (QREFELT $ 7)
                                        (|SparseUnivariatePolynomial|
                                         (QREFELT $ 7))
                                        (|SparseUnivariatePolynomial|
                                         (|Fraction|
                                          (|SparseUnivariatePolynomial|
                                           (QREFELT $ 7))))
                                        (SPADCALL |q| (QREFELT $ 36))
                                        (QCDR |r|))
                . #4#)
          (EXIT (VECTOR |lf1| |r1| |curve|))))) 

(SDEFUN |INTAF;algcurve|
        ((|lf| |List| F) (|t| |Kernel| F) (|k| |Kernel| F)
         (|derivation| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         ($ |Record|
          (|:| |funs|
               (|List|
                (|SparseUnivariatePolynomial|
                 (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (|:| |irec|
               (|Record|
                (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                (|:| |poly|
                     (|SparseUnivariatePolynomial|
                      (|Fraction| (|SparseUnivariatePolynomial| F))))))
          (|:| |curve_dom|
               (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                        (|SparseUnivariatePolynomial|
                                         (|Fraction|
                                          (|SparseUnivariatePolynomial|
                                           F)))))))
        (SPROG
         ((|curve|
           (|Join|
            (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                     (|SparseUnivariatePolynomial|
                                      (|Fraction|
                                       (|SparseUnivariatePolynomial| F))))
            (CATEGORY |package|
             (SIGNATURE |knownInfBasis| ((|Void|) (|NonNegativeInteger|))))))
          (|lf1|
           (|List|
            (|SparseUnivariatePolynomial|
             (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (#1=#:G753 NIL) (|f| NIL) (#2=#:G752 NIL)
          (|mon1|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|r1|
           (|Record| (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                     (|:| |poly|
                          (|SparseUnivariatePolynomial|
                           (|Fraction| (|SparseUnivariatePolynomial| F))))))
          (|modulus|
           (|SparseUnivariatePolynomial|
            (|Fraction| (|SparseUnivariatePolynomial| F))))
          (|p| (|SparseUnivariatePolynomial| F)))
         (SEQ
          (LETT |r1|
                (SPADCALL
                 (LETT |modulus|
                       (|INTAF;UP2UPUP|
                        (LETT |p| (SPADCALL |k| (QREFELT $ 24))
                              . #3=(|INTAF;algcurve|))
                        |t| $)
                       . #3#)
                 (QREFELT $ 26))
                . #3#)
          (LETT |mon1|
                (SPADCALL (SPADCALL (QCAR |r1|) (QREFELT $ 27)) 1
                          (QREFELT $ 30))
                . #3#)
          (LETT |lf1|
                (PROGN
                 (LETT #2# NIL . #3#)
                 (SEQ (LETT |f| NIL . #3#) (LETT #1# |lf| . #3#) G190
                      (COND
                       ((OR (ATOM #1#) (PROGN (LETT |f| (CAR #1#) . #3#) NIL))
                        (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #2#
                              (CONS
                               (SPADCALL (|INTAF;F2UPUP| |f| |t| |k| |p| $)
                                         |mon1| (QREFELT $ 31))
                               #2#)
                              . #3#)))
                      (LETT #1# (CDR #1#) . #3#) (GO G190) G191
                      (EXIT (NREVERSE #2#))))
                . #3#)
          (LETT |curve|
                (|AlgebraicFunctionField| (QREFELT $ 7)
                                          (|SparseUnivariatePolynomial|
                                           (QREFELT $ 7))
                                          (|SparseUnivariatePolynomial|
                                           (|Fraction|
                                            (|SparseUnivariatePolynomial|
                                             (QREFELT $ 7))))
                                          (QCDR |r1|))
                . #3#)
          (EXIT (VECTOR |lf1| |r1| |curve|))))) 

(SDEFUN |INTAF;algextint;2KMMMMLL;8|
        ((|t| |Kernel| F) (|y| |Kernel| F)
         (|der| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         (|ext| |Mapping|
          (|List|
           (|Record|
            (|:| |ratpart| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |coeffs| (|Vector| F))))
          (|List| (|Fraction| (|SparseUnivariatePolynomial| F))))
         (|rde| |Mapping|
          (|List|
           (|Record|
            (|:| |ratpart| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |coeffs| (|Vector| F))))
          (|Fraction| (|SparseUnivariatePolynomial| F))
          (|List| (|Fraction| (|SparseUnivariatePolynomial| F))))
         (|csolve| |Mapping| (|List| (|Vector| F)) (|Matrix| F))
         (|lg| |List| F)
         ($ |List| (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F)))))
        (SPROG
         ((#1=#:G783 NIL) (|be| NIL) (#2=#:G782 NIL)
          (|res1|
           (|List|
            (|Record| (|:| |ratpart| |curve|) (|:| |coeffs| (|Vector| F)))))
          (#3=#:G781 NIL) (|f| NIL) (#4=#:G780 NIL)
          (|cc| (|Fraction| (|SparseUnivariatePolynomial| F)))
          (|red|
           (|Mapping| |curve|
                      (|SparseUnivariatePolynomial|
                       (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (|curve|
           (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                    (|SparseUnivariatePolynomial|
                                     (|Fraction|
                                      (|SparseUnivariatePolynomial| F)))))
          (|c_rec|
           (|Record|
            (|:| |funs|
                 (|List|
                  (|SparseUnivariatePolynomial|
                   (|Fraction| (|SparseUnivariatePolynomial| F)))))
            (|:| |irec|
                 (|Record|
                  (|:| |coef| (|Fraction| (|SparseUnivariatePolynomial| F)))
                  (|:| |poly|
                       (|SparseUnivariatePolynomial|
                        (|Fraction| (|SparseUnivariatePolynomial| F))))))
            (|:| |curve_dom|
                 (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                          (|SparseUnivariatePolynomial|
                                           (|Fraction|
                                            (|SparseUnivariatePolynomial|
                                             F))))))))
         (SEQ
          (LETT |c_rec|
                (COND
                 ((SPADCALL |y| '|nthRoot| (QREFELT $ 39))
                  (|INTAF;rootcurve| |lg| |t| |y| |der| $))
                 ((SPADCALL |y| '|rootOf| (QREFELT $ 39))
                  (|INTAF;algcurve| |lg| |t| |y| |der| $))
                 ('T (|error| "failed - cannot handle that integrand")))
                . #5=(|INTAF;algextint;2KMMMMLL;8|))
          (LETT |curve| (QVELT |c_rec| 2) . #5#)
          (LETT |red|
                (|compiledLookupCheck| '|reduce|
                                       (LIST '$
                                             (LIST
                                              '|SparseUnivariatePolynomial|
                                              (LIST '|Fraction|
                                                    (LIST
                                                     '|SparseUnivariatePolynomial|
                                                     (|devaluate|
                                                      (ELT $ 7))))))
                                       |curve|)
                . #5#)
          (LETT |cc| (QCAR (QVELT |c_rec| 1)) . #5#)
          (LETT |res1|
                (SPADCALL |der| |ext| |rde| |csolve|
                          (PROGN
                           (LETT #4# NIL . #5#)
                           (SEQ (LETT |f| NIL . #5#)
                                (LETT #3# (QVELT |c_rec| 0) . #5#) G190
                                (COND
                                 ((OR (ATOM #3#)
                                      (PROGN (LETT |f| (CAR #3#) . #5#) NIL))
                                  (GO G191)))
                                (SEQ
                                 (EXIT
                                  (LETT #4# (CONS (SPADCALL |f| |red|) #4#)
                                        . #5#)))
                                (LETT #3# (CDR #3#) . #5#) (GO G190) G191
                                (EXIT (NREVERSE #4#))))
                          (|compiledLookupCheck| '|algextint|
                                                 (LIST
                                                  (LIST '|List|
                                                        (LIST '|Record|
                                                              (LIST '|:|
                                                                    '|ratpart|
                                                                    (|devaluate|
                                                                     |curve|))
                                                              (LIST '|:|
                                                                    '|coeffs|
                                                                    (LIST
                                                                     '|Vector|
                                                                     (|devaluate|
                                                                      (ELT $
                                                                           7))))))
                                                  (LIST '|Mapping|
                                                        (LIST
                                                         '|SparseUnivariatePolynomial|
                                                         (|devaluate|
                                                          (ELT $ 7)))
                                                        (LIST
                                                         '|SparseUnivariatePolynomial|
                                                         (|devaluate|
                                                          (ELT $ 7))))
                                                  (LIST '|Mapping|
                                                        (LIST '|List|
                                                              (LIST '|Record|
                                                                    (LIST '|:|
                                                                          '|ratpart|
                                                                          (LIST
                                                                           '|Fraction|
                                                                           (LIST
                                                                            '|SparseUnivariatePolynomial|
                                                                            (|devaluate|
                                                                             (ELT
                                                                              $
                                                                              7)))))
                                                                    (LIST '|:|
                                                                          '|coeffs|
                                                                          (LIST
                                                                           '|Vector|
                                                                           (|devaluate|
                                                                            (ELT
                                                                             $
                                                                             7))))))
                                                        (LIST '|List|
                                                              (LIST '|Fraction|
                                                                    (LIST
                                                                     '|SparseUnivariatePolynomial|
                                                                     (|devaluate|
                                                                      (ELT $
                                                                           7))))))
                                                  (LIST '|Mapping|
                                                        (LIST '|List|
                                                              (LIST '|Record|
                                                                    (LIST '|:|
                                                                          '|ratpart|
                                                                          (LIST
                                                                           '|Fraction|
                                                                           (LIST
                                                                            '|SparseUnivariatePolynomial|
                                                                            (|devaluate|
                                                                             (ELT
                                                                              $
                                                                              7)))))
                                                                    (LIST '|:|
                                                                          '|coeffs|
                                                                          (LIST
                                                                           '|Vector|
                                                                           (|devaluate|
                                                                            (ELT
                                                                             $
                                                                             7))))))
                                                        (LIST '|Fraction|
                                                              (LIST
                                                               '|SparseUnivariatePolynomial|
                                                               (|devaluate|
                                                                (ELT $ 7))))
                                                        (LIST '|List|
                                                              (LIST '|Fraction|
                                                                    (LIST
                                                                     '|SparseUnivariatePolynomial|
                                                                     (|devaluate|
                                                                      (ELT $
                                                                           7))))))
                                                  (LIST '|Mapping|
                                                        (LIST '|List|
                                                              (LIST '|Vector|
                                                                    (|devaluate|
                                                                     (ELT $
                                                                          7))))
                                                        (LIST '|Matrix|
                                                              (|devaluate|
                                                               (ELT $ 7))))
                                                  (LIST '|List|
                                                        (|devaluate| |curve|)))
                                                 (|AlgebraicIntegrate2|
                                                  (ELT $ 6) (ELT $ 7)
                                                  |curve|)))
                . #5#)
          (EXIT
           (PROGN
            (LETT #2# NIL . #5#)
            (SEQ (LETT |be| NIL . #5#) (LETT #1# |res1| . #5#) G190
                 (COND
                  ((OR (ATOM #1#) (PROGN (LETT |be| (CAR #1#) . #5#) NIL))
                   (GO G191)))
                 (SEQ
                  (EXIT
                   (LETT #2#
                         (CONS
                          (CONS
                           (|INTAF;UPUP2F|
                            (SPADCALL (QCAR |be|)
                                      (|compiledLookupCheck| '|lift|
                                                             (LIST
                                                              (LIST
                                                               '|SparseUnivariatePolynomial|
                                                               (LIST
                                                                '|Fraction|
                                                                (LIST
                                                                 '|SparseUnivariatePolynomial|
                                                                 (|devaluate|
                                                                  (ELT $ 7)))))
                                                              '$)
                                                             |curve|))
                            |cc| |t| |y| $)
                           (QCDR |be|))
                          #2#)
                         . #5#)))
                 (LETT #1# (CDR #1#) . #5#) (GO G190) G191
                 (EXIT (NREVERSE #2#)))))))) 

(SDEFUN |INTAF;algextint_base;2KMMLL;9|
        ((|x| |Kernel| F) (|y| |Kernel| F)
         (|der| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         (|csolve| |Mapping| (|List| (|Vector| F)) (|Matrix| F))
         (|lg| |List| F)
         ($ |List| (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F)))))
        (SPROG
         ((#1=#:G807 NIL) (|be| NIL) (#2=#:G806 NIL)
          (|res1|
           (|List|
            (|Record| (|:| |ratpart| |curve|) (|:| |coeffs| (|Vector| F)))))
          (#3=#:G805 NIL) (|f| NIL) (#4=#:G804 NIL)
          (|red|
           (|Mapping| |curve|
                      (|SparseUnivariatePolynomial|
                       (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (|curve|
           (|FunctionFieldCategory| F (|SparseUnivariatePolynomial| F)
                                    (|SparseUnivariatePolynomial|
                                     (|Fraction|
                                      (|SparseUnivariatePolynomial| F)))))
          (|r|
           (|Record|
            (|:| |radicand| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |deg| (|NonNegativeInteger|))))
          (#5=#:G789 NIL)
          (|cv|
           (|Record|
            (|:| |func|
                 (|List|
                  (|SparseUnivariatePolynomial|
                   (|Fraction| (|SparseUnivariatePolynomial| F)))))
            (|:| |poly|
                 (|SparseUnivariatePolynomial|
                  (|Fraction| (|SparseUnivariatePolynomial| F))))
            (|:| |c1| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |c2| (|Fraction| (|SparseUnivariatePolynomial| F)))
            (|:| |deg| (|NonNegativeInteger|))))
          (|lg1|
           (|List|
            (|SparseUnivariatePolynomial|
             (|Fraction| (|SparseUnivariatePolynomial| F)))))
          (#6=#:G803 NIL) (|g| NIL) (#7=#:G802 NIL)
          (|p| (|SparseUnivariatePolynomial| F)))
         (SEQ
          (LETT |p| (SPADCALL |y| (QREFELT $ 24))
                . #8=(|INTAF;algextint_base;2KMMLL;9|))
          (LETT |lg1|
                (PROGN
                 (LETT #7# NIL . #8#)
                 (SEQ (LETT |g| NIL . #8#) (LETT #6# |lg| . #8#) G190
                      (COND
                       ((OR (ATOM #6#) (PROGN (LETT |g| (CAR #6#) . #8#) NIL))
                        (GO G191)))
                      (SEQ
                       (EXIT
                        (LETT #7# (CONS (|INTAF;F2UPUP| |g| |x| |y| |p| $) #7#)
                              . #8#)))
                      (LETT #6# (CDR #6#) . #8#) (GO G190) G191
                      (EXIT (NREVERSE #7#))))
                . #8#)
          (LETT |cv|
                (SPADCALL |lg1| (|INTAF;UP2UPUP| |p| |x| $) (QREFELT $ 51))
                . #8#)
          (LETT |curve|
                (COND
                 ((SPADCALL |y| '|rootOf| (QREFELT $ 39))
                  (|AlgebraicFunctionField| (QREFELT $ 7)
                                            (|SparseUnivariatePolynomial|
                                             (QREFELT $ 7))
                                            (|SparseUnivariatePolynomial|
                                             (|Fraction|
                                              (|SparseUnivariatePolynomial|
                                               (QREFELT $ 7))))
                                            (QVELT |cv| 1)))
                 ((SPADCALL |y| '|nthRoot| (QREFELT $ 39))
                  (SEQ
                   (LETT |r|
                         (PROG2
                             (LETT #5# (SPADCALL (QVELT |cv| 1) (QREFELT $ 34))
                                   . #8#)
                             (QCDR #5#)
                           (|check_union2| (QEQCAR #5# 0)
                                           (|Record|
                                            (|:| |radicand|
                                                 (|Fraction|
                                                  (|SparseUnivariatePolynomial|
                                                   (QREFELT $ 7))))
                                            (|:| |deg| (|NonNegativeInteger|)))
                                           (|Union|
                                            (|Record|
                                             (|:| |radicand|
                                                  (|Fraction|
                                                   (|SparseUnivariatePolynomial|
                                                    (QREFELT $ 7))))
                                             (|:| |deg|
                                                  (|NonNegativeInteger|)))
                                            "failed")
                                           #5#))
                         . #8#)
                   (EXIT
                    (|RadicalFunctionField| (QREFELT $ 7)
                                            (|SparseUnivariatePolynomial|
                                             (QREFELT $ 7))
                                            (|SparseUnivariatePolynomial|
                                             (|Fraction|
                                              (|SparseUnivariatePolynomial|
                                               (QREFELT $ 7))))
                                            (QCAR |r|) (QCDR |r|)))))
                 ('T (|error| "failed - cannot handle that integrand")))
                . #8#)
          (LETT |red|
                (|compiledLookupCheck| '|reduce|
                                       (LIST '$
                                             (LIST
                                              '|SparseUnivariatePolynomial|
                                              (LIST '|Fraction|
                                                    (LIST
                                                     '|SparseUnivariatePolynomial|
                                                     (|devaluate|
                                                      (ELT $ 7))))))
                                       |curve|)
                . #8#)
          (LETT |res1|
                (SPADCALL |der| |csolve|
                          (PROGN
                           (LETT #4# NIL . #8#)
                           (SEQ (LETT |f| NIL . #8#)
                                (LETT #3# (QVELT |cv| 0) . #8#) G190
                                (COND
                                 ((OR (ATOM #3#)
                                      (PROGN (LETT |f| (CAR #3#) . #8#) NIL))
                                  (GO G191)))
                                (SEQ
                                 (EXIT
                                  (LETT #4# (CONS (SPADCALL |f| |red|) #4#)
                                        . #8#)))
                                (LETT #3# (CDR #3#) . #8#) (GO G190) G191
                                (EXIT (NREVERSE #4#))))
                          (|compiledLookupCheck| '|algextint_base|
                                                 (LIST
                                                  (LIST '|List|
                                                        (LIST '|Record|
                                                              (LIST '|:|
                                                                    '|ratpart|
                                                                    (|devaluate|
                                                                     |curve|))
                                                              (LIST '|:|
                                                                    '|coeffs|
                                                                    (LIST
                                                                     '|Vector|
                                                                     (|devaluate|
                                                                      (ELT $
                                                                           7))))))
                                                  (LIST '|Mapping|
                                                        (LIST
                                                         '|SparseUnivariatePolynomial|
                                                         (|devaluate|
                                                          (ELT $ 7)))
                                                        (LIST
                                                         '|SparseUnivariatePolynomial|
                                                         (|devaluate|
                                                          (ELT $ 7))))
                                                  (LIST '|Mapping|
                                                        (LIST '|List|
                                                              (LIST '|Vector|
                                                                    (|devaluate|
                                                                     (ELT $
                                                                          7))))
                                                        (LIST '|Matrix|
                                                              (|devaluate|
                                                               (ELT $ 7))))
                                                  (LIST '|List|
                                                        (|devaluate| |curve|)))
                                                 (|AlgebraicIntegrate2|
                                                  (ELT $ 6) (ELT $ 7)
                                                  |curve|)))
                . #8#)
          (EXIT
           (PROGN
            (LETT #2# NIL . #8#)
            (SEQ (LETT |be| NIL . #8#) (LETT #1# |res1| . #8#) G190
                 (COND
                  ((OR (ATOM #1#) (PROGN (LETT |be| (CAR #1#) . #8#) NIL))
                   (GO G191)))
                 (SEQ
                  (EXIT
                   (LETT #2#
                         (CONS
                          (CONS
                           (|INTAF;UPUP2F1|
                            (SPADCALL (QCAR |be|)
                                      (|compiledLookupCheck| '|lift|
                                                             (LIST
                                                              (LIST
                                                               '|SparseUnivariatePolynomial|
                                                               (LIST
                                                                '|Fraction|
                                                                (LIST
                                                                 '|SparseUnivariatePolynomial|
                                                                 (|devaluate|
                                                                  (ELT $ 7)))))
                                                              '$)
                                                             |curve|))
                            (QVELT |cv| 2) (QVELT |cv| 3) |x| |y| $)
                           (QCDR |be|))
                          #2#)
                         . #8#)))
                 (LETT #1# (CDR #1#) . #8#) (GO G190) G191
                 (EXIT (NREVERSE #2#)))))))) 

(SDEFUN |INTAF;UP2UPUP|
        ((|p| |SparseUnivariatePolynomial| F) (|k| |Kernel| F)
         ($ |SparseUnivariatePolynomial|
          (|Fraction| (|SparseUnivariatePolynomial| F))))
        (SPROG NIL
               (SPADCALL (CONS #'|INTAF;UP2UPUP!0| (VECTOR $ |k|)) |p|
                         (QREFELT $ 57)))) 

(SDEFUN |INTAF;UP2UPUP!0| ((|x1| NIL) ($$ NIL))
        (PROG (|k| $)
          (LETT |k| (QREFELT $$ 1) . #1=(|INTAF;UP2UPUP|))
          (LETT $ (QREFELT $$ 0) . #1#)
          (RETURN (PROGN (SPADCALL |x1| |k| (QREFELT $ 54)))))) 

(SDEFUN |INTAF;UPUP2F|
        ((|p| |SparseUnivariatePolynomial|
          (|Fraction| (|SparseUnivariatePolynomial| F)))
         (|cf| |Fraction| (|SparseUnivariatePolynomial| F)) (|t| |Kernel| F)
         (|k| |Kernel| F) ($ F))
        (SPROG NIL
               (SPADCALL
                (SPADCALL (CONS #'|INTAF;UPUP2F!0| (VECTOR $ |t|)) |p|
                          (QREFELT $ 18))
                (SPADCALL (SPADCALL |cf| |t| (QREFELT $ 14))
                          (SPADCALL |k| (QREFELT $ 20)) (QREFELT $ 58))
                (QREFELT $ 21)))) 

(SDEFUN |INTAF;UPUP2F!0| ((|x1| NIL) ($$ NIL))
        (PROG (|t| $)
          (LETT |t| (QREFELT $$ 1) . #1=(|INTAF;UPUP2F|))
          (LETT $ (QREFELT $$ 0) . #1#)
          (RETURN (PROGN (SPADCALL |x1| |t| (QREFELT $ 14)))))) 

(SDEFUN |INTAF;algint;F2KMIr;12|
        ((|f| F) (|t| |Kernel| F) (|y| |Kernel| F)
         (|derivation| |Mapping| (|SparseUnivariatePolynomial| F)
          (|SparseUnivariatePolynomial| F))
         ($ |IntegrationResult| F))
        (COND
         ((SPADCALL |y| '|nthRoot| (QREFELT $ 39))
          (|INTAF;rootintegrate| |f| |t| |y| |derivation| $))
         ((SPADCALL |y| '|rootOf| (QREFELT $ 39))
          (|INTAF;algintegrate| |f| |t| |y| |derivation| $))
         ('T (|error| "failed - cannot handle that integrand")))) 

(DECLAIM (NOTINLINE |AlgebraicIntegration;|)) 

(DEFUN |AlgebraicIntegration| (&REST #1=#:G822)
  (SPROG NIL
         (PROG (#2=#:G823)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluateList| #1#)
                                               (HGET |$ConstructorCache|
                                                     '|AlgebraicIntegration|)
                                               '|domainEqualList|)
                    . #3=(|AlgebraicIntegration|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |AlgebraicIntegration;|) #1#)
                    (LETT #2# T . #3#))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache| '|AlgebraicIntegration|)))))))))) 

(DEFUN |AlgebraicIntegration;| (|#1| |#2|)
  (SPROG ((|pv$| NIL) ($ NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|) . #1=(|AlgebraicIntegration|))
          (LETT DV$2 (|devaluate| |#2|) . #1#)
          (LETT |dv$| (LIST '|AlgebraicIntegration| DV$1 DV$2) . #1#)
          (LETT $ (GETREFV 61) . #1#)
          (QSETREFV $ 0 |dv$|)
          (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
          (|haddProp| |$ConstructorCache| '|AlgebraicIntegration|
                      (LIST DV$1 DV$2) (CONS 1 $))
          (|stuffDomainSlots| $)
          (QSETREFV $ 6 |#1|)
          (QSETREFV $ 7 |#2|)
          (SETF |pv$| (QREFELT $ 3))
          $))) 

(MAKEPROP '|AlgebraicIntegration| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|SparseUnivariatePolynomial| 9) (|Fraction| 15)
              (|ChangeOfVariable| 7 15 8) (0 . |eval|) (|Kernel| 7)
              (|PolynomialCategoryQuotientFunctions| (|IndexedExponents| 12) 12
                                                     6
                                                     (|SparseMultivariatePolynomial|
                                                      6 12)
                                                     7)
              (7 . |multivariate|) (|SparseUnivariatePolynomial| 7)
              (|Mapping| 7 9) (|SparseUnivariatePolynomialFunctions2| 9 7)
              (13 . |map|) (|Kernel| $) (19 . |coerce|) (24 . |elt|)
              (30 . |univariate|) (|SparseUnivariatePolynomial| $)
              (37 . |minPoly|) (|Record| (|:| |coef| 9) (|:| |poly| 8))
              (42 . |mkIntegral|) (47 . |inv|) (52 . |One|)
              (|NonNegativeInteger|) (56 . |monomial|) (62 . |elt|)
              (|Record| (|:| |radicand| 9) (|:| |deg| 29))
              (|Union| 32 '"failed") (68 . |radPoly|) (73 . |retract|)
              (78 . |coerce|) (|Boolean|) (|Symbol|) (83 . |is?|)
              (|Record| (|:| |ratpart| 7) (|:| |coeffs| (|Vector| 7)))
              (|List| 40) (|Mapping| 15 15)
              (|Record| (|:| |ratpart| 9) (|:| |coeffs| (|Vector| 7)))
              (|Mapping| (|List| 43) (|List| 9))
              (|Mapping| (|List| 43) 9 (|List| 9))
              (|Mapping| (|List| (|Vector| 7)) (|Matrix| 7)) (|List| 7)
              |INTAF;algextint;2KMMMMLL;8|
              (|Record| (|:| |func| 50) (|:| |poly| 8) (|:| |c1| 9)
                        (|:| |c2| 9) (|:| |deg| 29))
              (|List| 8) (89 . |chvar|) |INTAF;algextint_base;2KMMLL;9|
              (|Fraction| 23) (95 . |univariate|) (|Mapping| 9 7)
              (|SparseUnivariatePolynomialFunctions2| 7 9) (101 . |map|)
              (107 . *) (|IntegrationResult| 7) |INTAF;algint;F2KMIr;12|)
           '#(|algint| 113 |algextint_base| 121 |algextint| 130) 'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 60
                                                 '(3 10 8 8 9 9 11 2 13 7 9 12
                                                   14 2 17 15 16 8 18 1 7 0 19
                                                   20 2 15 7 0 7 21 3 13 15 7
                                                   12 15 22 1 7 23 19 24 1 10
                                                   25 8 26 1 9 0 0 27 0 6 0 28
                                                   2 8 0 9 29 30 2 8 0 0 0 31 1
                                                   10 33 8 34 1 9 15 0 35 1 9 0
                                                   15 36 2 12 37 0 38 39 2 10
                                                   49 50 8 51 2 7 53 0 19 54 2
                                                   56 8 55 15 57 2 7 0 0 0 58 4
                                                   0 59 7 12 12 42 60 5 0 41 12
                                                   12 42 46 47 52 7 0 41 12 12
                                                   42 44 45 46 47 48)))))
           '|lookupComplete|)) 
