
(SDEFUN |LINCOMB;dehomogenize;LR;1|
        ((|ls|
          (|List| (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F)))))
         (%
          (|Record|
           (|:| |particular|
                (|Union|
                 (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F)))
                 "failed"))
           (|:| |basis|
                (|List|
                 (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F))))))))
        (SPROG
         ((|res3|
           (|List| (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F)))))
          (|bv| #1=(|Vector| F)) (|rp| (F)) (|c| (F)) (#2=#:G25 NIL) (|be| NIL)
          (|ppv| #1#) (|ppa| (F)) (|c1inv| (F)) (|found| (|Boolean|))
          (|be1| (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F))))
          (|res2|
           (|List| (|Record| (|:| |ratpart| F) (|:| |coeffs| (|Vector| F)))))
          (#3=#:G24 NIL) (|nn| (|NonNegativeInteger|)))
         (SEQ
          (COND ((NULL |ls|) (CONS (CONS 1 "failed") NIL))
                (#4='T
                 (SEQ
                  (LETT |nn| (QVSIZE (QCDR (SPADCALL |ls| 1 (QREFELT % 13)))))
                  (LETT |found| NIL) (LETT |res2| NIL)
                  (SEQ (LETT |be| NIL) (LETT #3# |ls|) G190
                       (COND
                        ((OR (ATOM #3#) (PROGN (LETT |be| (CAR #3#)) NIL))
                         (GO G191)))
                       (SEQ (LETT |c| (SPADCALL (QCDR |be|) 1 (QREFELT % 15)))
                            (COND
                             ((OR
                               (SPADCALL |c| (|spadConstant| % 16)
                                         (QREFELT % 19))
                               |found|)
                              (EXIT (LETT |res2| (CONS |be| |res2|)))))
                            (LETT |be1| |be|) (EXIT (LETT |found| 'T)))
                       (LETT #3# (CDR #3#)) (GO G190) G191 (EXIT NIL))
                  (EXIT
                   (COND
                    (|found|
                     (SEQ
                      (LETT |c1inv|
                            (SPADCALL (|spadConstant| % 8)
                                      (SPADCALL (QCDR |be1|) 1 (QREFELT % 15))
                                      (QREFELT % 20)))
                      (LETT |ppa|
                            (SPADCALL |c1inv| (QCAR |be1|) (QREFELT % 21)))
                      (LETT |ppv|
                            (SPADCALL
                             (SPADCALL |c1inv| (QCDR |be1|) (QREFELT % 22))
                             (SPADCALL 2 |nn| (QREFELT % 24)) (QREFELT % 25)))
                      (LETT |res3| NIL)
                      (SEQ (LETT |be| NIL) (LETT #2# |res2|) G190
                           (COND
                            ((OR (ATOM #2#) (PROGN (LETT |be| (CAR #2#)) NIL))
                             (GO G191)))
                           (SEQ
                            (LETT |c| (SPADCALL (QCDR |be|) 1 (QREFELT % 15)))
                            (LETT |bv|
                                  (SPADCALL (QCDR |be|)
                                            (SPADCALL 2 |nn| (QREFELT % 24))
                                            (QREFELT % 25)))
                            (LETT |rp| (QCAR |be|))
                            (COND
                             ((SPADCALL |c| (|spadConstant| % 16)
                                        (QREFELT % 26))
                              (SEQ
                               (LETT |rp|
                                     (SPADCALL |rp|
                                               (SPADCALL |c| |ppa|
                                                         (QREFELT % 21))
                                               (QREFELT % 27)))
                               (EXIT
                                (LETT |bv|
                                      (SPADCALL |bv|
                                                (SPADCALL |c| |ppv|
                                                          (QREFELT % 22))
                                                (QREFELT % 28)))))))
                            (EXIT
                             (LETT |res3| (CONS (CONS |rp| |bv|) |res3|))))
                           (LETT #2# (CDR #2#)) (GO G190) G191 (EXIT NIL))
                      (EXIT (CONS (CONS 0 (CONS |ppa| |ppv|)) |res3|))))
                    (#4# (CONS (CONS 1 "failed") NIL)))))))))) 

(SDEFUN |LINCOMB;lin_comb;VLF;2| ((|v| (|Vector| F)) (|lf| (|List| F)) (% (F)))
        (SPROG ((|res| (F)) (#1=#:G30 NIL) (|i| NIL) (#2=#:G31 NIL) (|f| NIL))
               (SEQ (LETT |res| (|spadConstant| % 16))
                    (SEQ (LETT |f| NIL) (LETT #2# |lf|) (LETT |i| 1)
                         (LETT #1# (QVSIZE |v|)) G190
                         (COND
                          ((OR (|greater_SI| |i| #1#) (ATOM #2#)
                               (PROGN (LETT |f| (CAR #2#)) NIL))
                           (GO G191)))
                         (SEQ
                          (EXIT
                           (LETT |res|
                                 (SPADCALL |res|
                                           (SPADCALL
                                            (SPADCALL |v| |i| (QREFELT % 15))
                                            |f| (QREFELT % 21))
                                           (QREFELT % 32)))))
                         (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #2# (CDR #2#))))
                         (GO G190) G191 (EXIT NIL))
                    (EXIT |res|)))) 

(SDEFUN |LINCOMB;lin_comb;VLF;3|
        ((|v| (|Vector| (|Fraction| (|Integer|)))) (|lf| (|List| F)) (% (F)))
        (SPROG ((|res| (F)) (#1=#:G36 NIL) (|i| NIL) (#2=#:G37 NIL) (|f| NIL))
               (SEQ (LETT |res| (|spadConstant| % 16))
                    (SEQ (LETT |f| NIL) (LETT #2# |lf|) (LETT |i| 1)
                         (LETT #1# (QVSIZE |v|)) G190
                         (COND
                          ((OR (|greater_SI| |i| #1#) (ATOM #2#)
                               (PROGN (LETT |f| (CAR #2#)) NIL))
                           (GO G191)))
                         (SEQ
                          (EXIT
                           (LETT |res|
                                 (SPADCALL |res|
                                           (SPADCALL
                                            (SPADCALL
                                             (SPADCALL |v| |i| (QREFELT % 37))
                                             (QREFELT % 38))
                                            |f| (QREFELT % 21))
                                           (QREFELT % 32)))))
                         (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #2# (CDR #2#))))
                         (GO G190) G191 (EXIT NIL))
                    (EXIT |res|)))) 

(SDEFUN |LINCOMB;lin_comb!;2VLV;4|
        ((|u| (|Vector| F)) (|v| (|Vector| F)) (|lw| (|List| (|Vector| F)))
         (% (|Vector| F)))
        (SPROG
         ((#1=#:G47 NIL) (|j| NIL) (|c| (F)) (#2=#:G45 NIL) (|i| NIL)
          (#3=#:G46 NIL) (|w| NIL) (|n| (|NonNegativeInteger|))
          (|res| (|Vector| F)))
         (SEQ (LETT |res| |v|) (LETT |n| (QVSIZE |res|))
              (SEQ (LETT |w| NIL) (LETT #3# |lw|) (LETT |i| 1)
                   (LETT #2# (QVSIZE |u|)) G190
                   (COND
                    ((OR (|greater_SI| |i| #2#) (ATOM #3#)
                         (PROGN (LETT |w| (CAR #3#)) NIL))
                     (GO G191)))
                   (SEQ (LETT |c| (SPADCALL |u| |i| (QREFELT % 15)))
                        (EXIT
                         (SEQ (LETT |j| 1) (LETT #1# |n|) G190
                              (COND ((|greater_SI| |j| #1#) (GO G191)))
                              (SEQ
                               (EXIT
                                (SPADCALL |res| |j|
                                          (SPADCALL
                                           (SPADCALL |res| |j| (QREFELT % 15))
                                           (SPADCALL |c|
                                                     (SPADCALL |w| |j|
                                                               (QREFELT % 15))
                                                     (QREFELT % 21))
                                           (QREFELT % 32))
                                          (QREFELT % 40))))
                              (LETT |j| (|inc_SI| |j|)) (GO G190) G191
                              (EXIT NIL))))
                   (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #3# (CDR #3#))))
                   (GO G190) G191 (EXIT NIL))
              (EXIT |res|)))) 

(SDEFUN |LINCOMB;lin_comb;VLV;5|
        ((|u| (|Vector| F)) (|lw| (|List| (|Vector| F))) (% (|Vector| F)))
        (SPROG ((|n| (|NonNegativeInteger|)))
               (SEQ (LETT |n| (QVSIZE (|SPADfirst| |lw|)))
                    (EXIT
                     (SPADCALL |u| (MAKEARR1 |n| (|spadConstant| % 16)) |lw|
                               (QREFELT % 42)))))) 

(SDEFUN |LINCOMB;lin_comb;VLF;6|
        ((|v| (|Vector| F)) (|lf| (|List| (|Fraction| UP)))
         (% (|Fraction| UP)))
        (SPROG
         ((|res| (|Fraction| UP)) (#1=#:G54 NIL) (|i| NIL) (#2=#:G55 NIL)
          (|f| NIL))
         (SEQ (LETT |res| (|spadConstant| % 45))
              (SEQ (LETT |f| NIL) (LETT #2# |lf|) (LETT |i| 1)
                   (LETT #1# (QVSIZE |v|)) G190
                   (COND
                    ((OR (|greater_SI| |i| #1#) (ATOM #2#)
                         (PROGN (LETT |f| (CAR #2#)) NIL))
                     (GO G191)))
                   (SEQ
                    (EXIT
                     (LETT |res|
                           (SPADCALL |res|
                                     (SPADCALL
                                      (SPADCALL
                                       (SPADCALL |v| |i| (QREFELT % 15))
                                       (QREFELT % 46))
                                      |f| (QREFELT % 47))
                                     (QREFELT % 48)))))
                   (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #2# (CDR #2#))))
                   (GO G190) G191 (EXIT NIL))
              (EXIT |res|)))) 

(SDEFUN |LINCOMB;lin_comb;VLF;7|
        ((|v| (|Vector| (|Fraction| (|Integer|))))
         (|lg| (|List| (|Fraction| UP))) (% (|Fraction| UP)))
        (SPROG
         ((|res| (|Fraction| UP)) (#1=#:G60 NIL) (|i| NIL) (#2=#:G61 NIL)
          (|g| NIL))
         (SEQ (LETT |res| (|spadConstant| % 45))
              (SEQ (LETT |g| NIL) (LETT #2# |lg|) (LETT |i| 1)
                   (LETT #1# (QVSIZE |v|)) G190
                   (COND
                    ((OR (|greater_SI| |i| #1#) (ATOM #2#)
                         (PROGN (LETT |g| (CAR #2#)) NIL))
                     (GO G191)))
                   (SEQ
                    (EXIT
                     (LETT |res|
                           (SPADCALL |res|
                                     (SPADCALL
                                      (SPADCALL
                                       (SPADCALL
                                        (SPADCALL
                                         (SPADCALL |v| |i| (QREFELT % 37))
                                         (QREFELT % 38))
                                        (QREFELT % 46))
                                       (QREFELT % 51))
                                      |g| (QREFELT % 52))
                                     (QREFELT % 48)))))
                   (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #2# (CDR #2#))))
                   (GO G190) G191 (EXIT NIL))
              (EXIT |res|)))) 

(SDEFUN |LINCOMB;lin_comb;VLLp;8|
        ((|v| (|Vector| F)) (|lf| (|List| (|LaurentPolynomial| F UP)))
         (% (|LaurentPolynomial| F UP)))
        (SPROG
         ((|res| (|LaurentPolynomial| F UP)) (#1=#:G66 NIL) (|i| NIL)
          (#2=#:G67 NIL) (|f| NIL))
         (SEQ (LETT |res| (|spadConstant| % 55))
              (SEQ (LETT |f| NIL) (LETT #2# |lf|) (LETT |i| 1)
                   (LETT #1# (QVSIZE |v|)) G190
                   (COND
                    ((OR (|greater_SI| |i| #1#) (ATOM #2#)
                         (PROGN (LETT |f| (CAR #2#)) NIL))
                     (GO G191)))
                   (SEQ
                    (EXIT
                     (LETT |res|
                           (SPADCALL |res|
                                     (SPADCALL
                                      (SPADCALL
                                       (SPADCALL |v| |i| (QREFELT % 15))
                                       (QREFELT % 56))
                                      |f| (QREFELT % 57))
                                     (QREFELT % 58)))))
                   (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #2# (CDR #2#))))
                   (GO G190) G191 (EXIT NIL))
              (EXIT |res|)))) 

(SDEFUN |LINCOMB;lin_comb;VLUP;9|
        ((|v| (|Vector| F)) (|lf| (|List| UP)) (% (UP)))
        (SPROG ((|res| (UP)) (#1=#:G72 NIL) (|i| NIL) (#2=#:G73 NIL) (|f| NIL))
               (SEQ (LETT |res| (|spadConstant| % 17))
                    (SEQ (LETT |f| NIL) (LETT #2# |lf|) (LETT |i| 1)
                         (LETT #1# (QVSIZE |v|)) G190
                         (COND
                          ((OR (|greater_SI| |i| #1#) (ATOM #2#)
                               (PROGN (LETT |f| (CAR #2#)) NIL))
                           (GO G191)))
                         (SEQ
                          (EXIT
                           (LETT |res|
                                 (SPADCALL |res|
                                           (SPADCALL
                                            (SPADCALL |v| |i| (QREFELT % 15))
                                            |f| (QREFELT % 61))
                                           (QREFELT % 62)))))
                         (LETT |i| (PROG1 (|inc_SI| |i|) (LETT #2# (CDR #2#))))
                         (GO G190) G191 (EXIT NIL))
                    (EXIT |res|)))) 

(DECLAIM (NOTINLINE |LinearCombinationUtilities;|)) 

(DEFUN |LinearCombinationUtilities;| (|#1| |#2|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|))
          (LETT DV$2 (|devaluate| |#2|))
          (LETT |dv$| (LIST '|LinearCombinationUtilities| DV$1 DV$2))
          (LETT % (GETREFV 65))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3 (LETT |pv$| (|buildPredVector| 0 0 NIL)))
          (|haddProp| |$ConstructorCache| '|LinearCombinationUtilities|
                      (LIST DV$1 DV$2) (CONS 1 %))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (QSETREFV % 7 |#2|)
          (SETF |pv$| (QREFELT % 3))
          %))) 

(DEFUN |LinearCombinationUtilities| (&REST #1=#:G74)
  (SPROG NIL
         (PROG (#2=#:G75)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluateList| #1#)
                                               (HGET |$ConstructorCache|
                                                     '|LinearCombinationUtilities|)
                                               '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |LinearCombinationUtilities;|) #1#)
                    (LETT #2# T))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache|
                        '|LinearCombinationUtilities|)))))))))) 

(MAKEPROP '|LinearCombinationUtilities| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (0 . |One|)
              (4 . |One|) (|Record| (|:| |ratpart| 6) (|:| |coeffs| 14))
              (|Integer|) (|List| 10) (8 . |elt|) (|Vector| 6) (14 . |elt|)
              (20 . |Zero|) (24 . |Zero|) (|Boolean|) (28 . =) (34 . /)
              (40 . *) (46 . *) (|UniversalSegment| 11) (52 . SEGMENT)
              (58 . |elt|) (64 . ~=) (70 . -) (76 . -)
              (|Union| 10 '#1="failed")
              (|Record| (|:| |particular| 29) (|:| |basis| 12))
              |LINCOMB;dehomogenize;LR;1| (82 . +) (|List| 6)
              |LINCOMB;lin_comb;VLF;2| (|Fraction| 11) (|Vector| 35)
              (88 . |elt|) (94 . |coerce|) |LINCOMB;lin_comb;VLF;3|
              (99 . |setelt!|) (|List| 14) |LINCOMB;lin_comb!;2VLV;4|
              |LINCOMB;lin_comb;VLV;5| (|Fraction| 7) (106 . |Zero|)
              (110 . |coerce|) (115 . *) (121 . +) (|List| 44)
              |LINCOMB;lin_comb;VLF;6| (127 . |coerce|) (132 . *)
              |LINCOMB;lin_comb;VLF;7| (|LaurentPolynomial| 6 7) (138 . |Zero|)
              (142 . |coerce|) (147 . *) (153 . +) (|List| 54)
              |LINCOMB;lin_comb;VLLp;8| (159 . *) (165 . +) (|List| 7)
              |LINCOMB;lin_comb;VLUP;9|)
           '#(|lin_comb!| 171 |lin_comb| 178 |dehomogenize| 220) 'NIL
           (CONS (|makeByteWordVec2| 1 '(0))
                 (CONS '#(NIL)
                       (CONS
                        '#((|Join|
                            (|mkCategory|
                             (LIST
                              '((|dehomogenize|
                                 ((|Record|
                                   (|:| |particular|
                                        (|Union|
                                         (|Record| (|:| |ratpart| |#1|)
                                                   (|:| |coeffs|
                                                        (|Vector| |#1|)))
                                         #1#))
                                   (|:| |basis|
                                        (|List|
                                         (|Record| (|:| |ratpart| |#1|)
                                                   (|:| |coeffs|
                                                        (|Vector| |#1|))))))
                                  (|List|
                                   (|Record| (|:| |ratpart| |#1|)
                                             (|:| |coeffs| (|Vector| |#1|))))))
                                T)
                              '((|lin_comb|
                                 (|#1| (|Vector| |#1|) (|List| |#1|)))
                                T)
                              '((|lin_comb|
                                 (|#1| (|Vector| (|Fraction| (|Integer|)))
                                  (|List| |#1|)))
                                T)
                              '((|lin_comb!|
                                 ((|Vector| |#1|) (|Vector| |#1|)
                                  (|Vector| |#1|) (|List| (|Vector| |#1|))))
                                T)
                              '((|lin_comb|
                                 ((|Vector| |#1|) (|Vector| |#1|)
                                  (|List| (|Vector| |#1|))))
                                T)
                              '((|lin_comb|
                                 ((|Fraction| |#2|) (|Vector| |#1|)
                                  (|List| (|Fraction| |#2|))))
                                T)
                              '((|lin_comb|
                                 ((|Fraction| |#2|)
                                  (|Vector| (|Fraction| (|Integer|)))
                                  (|List| (|Fraction| |#2|))))
                                T)
                              '((|lin_comb|
                                 ((|LaurentPolynomial| |#1| |#2|)
                                  (|Vector| |#1|)
                                  (|List| (|LaurentPolynomial| |#1| |#2|))))
                                T)
                              '((|lin_comb|
                                 (|#2| (|Vector| |#1|) (|List| |#2|)))
                                T))
                             (LIST) NIL NIL)))
                        (|makeByteWordVec2| 64
                                            '(0 6 0 8 0 7 0 9 2 12 10 0 11 13 2
                                              14 6 0 11 15 0 6 0 16 0 7 0 17 2
                                              6 18 0 0 19 2 6 0 0 0 20 2 6 0 0
                                              0 21 2 14 0 6 0 22 2 23 0 11 11
                                              24 2 14 0 0 23 25 2 6 18 0 0 26 2
                                              6 0 0 0 27 2 14 0 0 0 28 2 6 0 0
                                              0 32 2 36 35 0 11 37 1 6 0 35 38
                                              3 14 6 0 11 6 40 0 44 0 45 1 7 0
                                              6 46 2 44 0 7 0 47 2 44 0 0 0 48
                                              1 44 0 7 51 2 44 0 0 0 52 0 54 0
                                              55 1 54 0 6 56 2 54 0 0 0 57 2 54
                                              0 0 0 58 2 7 0 6 0 61 2 7 0 0 0
                                              62 3 0 14 14 14 41 42 2 0 54 14
                                              59 60 2 0 7 14 63 64 2 0 44 36 49
                                              53 2 0 14 14 41 43 2 0 44 14 49
                                              50 2 0 6 36 33 39 2 0 6 14 33 34
                                              1 0 30 12 31)))))
           '|lookupComplete|)) 
