
(SDEFUN |MRATFAC;numer1|
        ((|c| (|Fraction| R)) (% (|SparseMultivariatePolynomial| R OV)))
        (SPADCALL (SPADCALL |c| (QREFELT % 11)) (QREFELT % 13))) 

(SDEFUN |MRATFAC;numer2|
        ((|pol| (P)) (% (|SparseMultivariatePolynomial| R OV)))
        (SPADCALL (ELT % 14) (CONS (|function| |MRATFAC;numer1|) %) |pol|
                  (QREFELT % 18))) 

(SDEFUN |MRATFAC;coerce1| ((|d| (R)) (% (P)))
        (SPADCALL (SPADCALL |d| (QREFELT % 19)) (QREFELT % 20))) 

(SDEFUN |MRATFAC;coerce2|
        ((|pp| (|SparseMultivariatePolynomial| R OV)) (% (P)))
        (SPADCALL (ELT % 21) (CONS (|function| |MRATFAC;coerce1|) %) |pp|
                  (QREFELT % 25))) 

(SDEFUN |MRATFAC;factor;PF;5| ((|p| (P)) (% (|Factored| P)))
        (SPROG
         ((#1=#:G16 NIL) (#2=#:G15 #3=(|Factored| P)) (#4=#:G17 #3#)
          (#5=#:G24 NIL) (|u| NIL)
          (|ffact| (|Factored| (|SparseMultivariatePolynomial| R OV)))
          (|ipol| (|SparseMultivariatePolynomial| R OV)) (|pol| (P))
          (|pden| (R)) (#6=#:G23 NIL) (|c| NIL) (#7=#:G22 NIL))
         (SEQ
          (LETT |pden|
                (SPADCALL
                 (PROGN
                  (LETT #7# NIL)
                  (SEQ (LETT |c| NIL) (LETT #6# (SPADCALL |p| (QREFELT % 27)))
                       G190
                       (COND
                        ((OR (ATOM #6#) (PROGN (LETT |c| (CAR #6#)) NIL))
                         (GO G191)))
                       (SEQ
                        (EXIT
                         (LETT #7# (CONS (SPADCALL |c| (QREFELT % 28)) #7#))))
                       (LETT #6# (CDR #6#)) (GO G190) G191
                       (EXIT (NREVERSE #7#))))
                 (QREFELT % 30)))
          (LETT |pol|
                (SPADCALL (SPADCALL |pden| (QREFELT % 19)) |p| (QREFELT % 31)))
          (LETT |ipol|
                (SPADCALL (ELT % 14) (CONS (|function| |MRATFAC;numer1|) %)
                          |pol| (QREFELT % 18)))
          (LETT |ffact| (SPADCALL |ipol| (QREFELT % 34)))
          (EXIT
           (SPADCALL
            (SPADCALL (SPADCALL (|spadConstant| % 35) |pden| (QREFELT % 37))
                      (SPADCALL (ELT % 21)
                                (CONS (|function| |MRATFAC;coerce1|) %)
                                (SPADCALL |ffact| (QREFELT % 38))
                                (QREFELT % 25))
                      (QREFELT % 31))
            (PROGN
             (LETT #1# NIL)
             (SEQ (LETT |u| NIL) (LETT #5# (SPADCALL |ffact| (QREFELT % 42)))
                  G190
                  (COND
                   ((OR (ATOM #5#) (PROGN (LETT |u| (CAR #5#)) NIL))
                    (GO G191)))
                  (SEQ
                   (EXIT
                    (PROGN
                     (LETT #4#
                           (SPADCALL
                            (SPADCALL (ELT % 21)
                                      (CONS (|function| |MRATFAC;coerce1|) %)
                                      (QVELT |u| 1) (QREFELT % 25))
                            (QVELT |u| 2) (QREFELT % 45)))
                     (COND (#1# (LETT #2# (SPADCALL #2# #4# (QREFELT % 46))))
                           ('T (PROGN (LETT #2# #4#) (LETT #1# 'T)))))))
                  (LETT #5# (CDR #5#)) (GO G190) G191 (EXIT NIL))
             (COND (#1# #2#) ('T (|spadConstant| % 47))))
            (QREFELT % 48)))))) 

(DECLAIM (NOTINLINE |MRationalFactorize;|)) 

(DEFUN |MRationalFactorize;| (|#1| |#2| |#3| |#4|)
  (SPROG
   ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$4 NIL) (DV$3 NIL) (DV$2 NIL)
    (DV$1 NIL))
   (PROGN
    (LETT DV$1 (|devaluate| |#1|))
    (LETT DV$2 (|devaluate| |#2|))
    (LETT DV$3 (|devaluate| |#3|))
    (LETT DV$4 (|devaluate| |#4|))
    (LETT |dv$| (LIST '|MRationalFactorize| DV$1 DV$2 DV$3 DV$4))
    (LETT % (GETREFV 50))
    (QSETREFV % 0 |dv$|)
    (QSETREFV % 3 (LETT |pv$| (|buildPredVector| 0 0 NIL)))
    (|haddProp| |$ConstructorCache| '|MRationalFactorize|
                (LIST DV$1 DV$2 DV$3 DV$4) (CONS 1 %))
    (|stuffDomainSlots| %)
    (QSETREFV % 6 |#1|)
    (QSETREFV % 7 |#2|)
    (QSETREFV % 8 |#3|)
    (QSETREFV % 9 |#4|)
    (SETF |pv$| (QREFELT % 3))
    %))) 

(DEFUN |MRationalFactorize| (&REST #1=#:G25)
  (SPROG NIL
         (PROG (#2=#:G26)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluateList| #1#)
                                               (HGET |$ConstructorCache|
                                                     '|MRationalFactorize|)
                                               '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |MRationalFactorize;|) #1#)
                    (LETT #2# T))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache| '|MRationalFactorize|)))))))))) 

(MAKEPROP '|MRationalFactorize| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|local| |#3|) (|local| |#4|) (|Fraction| 8) (0 . |numer|)
              (|SparseMultivariatePolynomial| 8 7) (5 . |coerce|)
              (10 . |coerce|) (|Mapping| 12 7) (|Mapping| 12 10)
              (|PolynomialCategoryLifting| 6 7 10 9 12) (15 . |map|)
              (22 . |coerce|) (27 . |coerce|) (32 . |coerce|) (|Mapping| 9 7)
              (|Mapping| 9 8)
              (|PolynomialCategoryLifting| (|IndexedExponents| 7) 7 8 12 9)
              (37 . |map|) (|List| 10) (44 . |coefficients|) (49 . |denom|)
              (|List| %) (54 . |lcm|) (59 . *) (|Factored| 12)
              (|MultivariateFactorize| 7 (|IndexedExponents| 7) 8 12)
              (65 . |factor|) (70 . |One|) (74 . |One|) (78 . /) (84 . |unit|)
              (|Union| '"nil" '"sqfr" '"irred" '"prime")
              (|Record| (|:| |flag| 39) (|:| |factor| 12) (|:| |exponent| 43))
              (|List| 40) (89 . |factorList|) (|NonNegativeInteger|)
              (|Factored| 9) (94 . |primeFactor|) (100 . *) (106 . |One|)
              (110 . *) |MRATFAC;factor;PF;5|)
           '#(|factor| 116) 'NIL
           (CONS (|makeByteWordVec2| 1 '(0))
                 (CONS '#(NIL)
                       (CONS
                        '#((|Join|
                            (|mkCategory|
                             (LIST '((|factor| ((|Factored| |#4|) |#4|)) T))
                             (LIST) NIL NIL)))
                        (|makeByteWordVec2| 49
                                            '(1 10 8 0 11 1 12 0 8 13 1 12 0 7
                                              14 3 17 12 15 16 9 18 1 10 0 8 19
                                              1 9 0 10 20 1 9 0 7 21 3 24 9 22
                                              23 12 25 1 9 26 0 27 1 10 8 0 28
                                              1 8 0 29 30 2 9 0 10 0 31 1 33 32
                                              12 34 0 8 0 35 0 9 0 36 2 10 0 8
                                              8 37 1 32 12 0 38 1 32 41 0 42 2
                                              44 0 9 43 45 2 44 0 0 0 46 0 44 0
                                              47 2 44 0 9 0 48 1 0 44 9 49)))))
           '|lookupComplete|)) 
