(/VERSIONCHECK 2) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%List|) |PSETCAT-;elements|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Shell|) |%List|) |PSETCAT-;variables1|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Shell|) |%List|) |PSETCAT-;variables2|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%List|) |PSETCAT-;variables;SL;4|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%List|) |PSETCAT-;mainVariables;SL;5|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |PSETCAT-;mainVariable?;VarSetSB;6|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |PSETCAT-;collectUnder;SVarSetS;7|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |PSETCAT-;collectUpper;SVarSetS;8|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |PSETCAT-;collect;SVarSetS;9|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Shell|) |PSETCAT-;sort;SVarSetR;10|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |PSETCAT-;=;2SB;11|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |PSETCAT-;localInf?|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Shell|) |%Boolean|) |PSETCAT-;localTriangular?|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|) |PSETCAT-;triangular?;SB;14|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|) |PSETCAT-;trivialIdeal?;SB;15|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|) |PSETCAT-;roughUnitIdeal?;SB;16|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |PSETCAT-;relativelyPrimeLeadingMonomials?|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Boolean|) |PSETCAT-;roughBase?;SB;18|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |PSETCAT-;roughSubIdeal?;2SB;19|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |PSETCAT-;roughEqualIdeals?;2SB;20|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |PSETCAT-;exactQuo|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Pair|) |PSETCAT-;headRemainder;PSR;22|)) (DECLAIM (FTYPE (FUNCTION (|%Pair| |%Shell|) |%Pair|) |PSETCAT-;makeIrreducible!|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Shell|) |PSETCAT-;remainder;PSR;24|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Thing| |%Shell|) |%List|) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Thing| |%Shell|) |%List|) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|)) (DEFUN |PSETCAT-;elements| (|ps| $) (PROG (|lp|) (RETURN (LETT |lp| (SPADCALL |ps| (|getShellEntry| $ 12)) |PSETCAT-;elements|)))) (DEFUN |PSETCAT-;variables1| (|lp| $) (PROG (#0=#:G1558 |p| #1=#:G1559 |lvars|) (RETURN (SEQ (LETT |lvars| (PROGN (LETT #0# NIL |PSETCAT-;variables1|) (SEQ (LETT |p| NIL |PSETCAT-;variables1|) (LETT #1# |lp| |PSETCAT-;variables1|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |p| (CAR #1#) |PSETCAT-;variables1|) NIL)) (GO G191))) (SEQ (EXIT (LETT #0# (CONS (SPADCALL |p| (|getShellEntry| $ 14)) #0#) |PSETCAT-;variables1|))) (LETT #1# (CDR #1#) |PSETCAT-;variables1|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) |PSETCAT-;variables1|) (EXIT (SPADCALL (CONS #'|PSETCAT-;variables1!0| $) (SPADCALL (SPADCALL |lvars| (|getShellEntry| $ 18)) (|getShellEntry| $ 19)) (|getShellEntry| $ 21))))))) (DEFUN |PSETCAT-;variables1!0| (|#1| |#2| $) (SPADCALL |#2| |#1| (|getShellEntry| $ 16))) (DEFUN |PSETCAT-;variables2| (|lp| $) (PROG (#0=#:G1560 |p| #1=#:G1561 |lvars|) (RETURN (SEQ (LETT |lvars| (PROGN (LETT #0# NIL |PSETCAT-;variables2|) (SEQ (LETT |p| NIL |PSETCAT-;variables2|) (LETT #1# |lp| |PSETCAT-;variables2|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |p| (CAR #1#) |PSETCAT-;variables2|) NIL)) (GO G191))) (SEQ (EXIT (LETT #0# (CONS (SPADCALL |p| (|getShellEntry| $ 22)) #0#) |PSETCAT-;variables2|))) (LETT #1# (CDR #1#) |PSETCAT-;variables2|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) |PSETCAT-;variables2|) (EXIT (SPADCALL (CONS #'|PSETCAT-;variables2!0| $) (SPADCALL |lvars| (|getShellEntry| $ 19)) (|getShellEntry| $ 21))))))) (DEFUN |PSETCAT-;variables2!0| (|#1| |#2| $) (SPADCALL |#2| |#1| (|getShellEntry| $ 16))) (DEFUN |PSETCAT-;variables;SL;4| (|ps| $) (|PSETCAT-;variables1| (|PSETCAT-;elements| |ps| $) $)) (DEFUN |PSETCAT-;mainVariables;SL;5| (|ps| $) (|PSETCAT-;variables2| (SPADCALL (ELT $ 24) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) $)) (DEFUN |PSETCAT-;mainVariable?;VarSetSB;6| (|v| |ps| $) (PROG (|lp|) (RETURN (SEQ (LETT |lp| (SPADCALL (ELT $ 24) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) |PSETCAT-;mainVariable?;VarSetSB;6|) (SEQ G190 (COND ((NULL (COND ((NULL |lp|) 'NIL) ('T (SPADCALL (SPADCALL (SPADCALL (|SPADfirst| |lp|) (|getShellEntry| $ 22)) |v| (|getShellEntry| $ 28)) (|getShellEntry| $ 29))))) (GO G191))) (SEQ (EXIT (LETT |lp| (CDR |lp|) |PSETCAT-;mainVariable?;VarSetSB;6|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL (NULL |lp|) (|getShellEntry| $ 29))))))) (DEFUN |PSETCAT-;collectUnder;SVarSetS;7| (|ps| |v| $) (PROG (|p| |lp| |lq|) (RETURN (SEQ (LETT |lp| (|PSETCAT-;elements| |ps| $) |PSETCAT-;collectUnder;SVarSetS;7|) (LETT |lq| NIL |PSETCAT-;collectUnder;SVarSetS;7|) (SEQ G190 (COND ((NULL (SPADCALL (NULL |lp|) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;collectUnder;SVarSetS;7|) (LETT |lp| (CDR |lp|) |PSETCAT-;collectUnder;SVarSetS;7|) (EXIT (COND ((OR (SPADCALL |p| (|getShellEntry| $ 24)) (SPADCALL (SPADCALL |p| (|getShellEntry| $ 22)) |v| (|getShellEntry| $ 16))) (LETT |lq| (CONS |p| |lq|) |PSETCAT-;collectUnder;SVarSetS;7|))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |lq| (|getShellEntry| $ 31))))))) (DEFUN |PSETCAT-;collectUpper;SVarSetS;8| (|ps| |v| $) (PROG (|p| |lp| |lq|) (RETURN (SEQ (LETT |lp| (|PSETCAT-;elements| |ps| $) |PSETCAT-;collectUpper;SVarSetS;8|) (LETT |lq| NIL |PSETCAT-;collectUpper;SVarSetS;8|) (SEQ G190 (COND ((NULL (SPADCALL (NULL |lp|) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;collectUpper;SVarSetS;8|) (LETT |lp| (CDR |lp|) |PSETCAT-;collectUpper;SVarSetS;8|) (EXIT (COND ((NULL (SPADCALL |p| (|getShellEntry| $ 24))) (COND ((SPADCALL |v| (SPADCALL |p| (|getShellEntry| $ 22)) (|getShellEntry| $ 16)) (LETT |lq| (CONS |p| |lq|) |PSETCAT-;collectUpper;SVarSetS;8|))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |lq| (|getShellEntry| $ 31))))))) (DEFUN |PSETCAT-;collect;SVarSetS;9| (|ps| |v| $) (PROG (|p| |lp| |lq|) (RETURN (SEQ (LETT |lp| (|PSETCAT-;elements| |ps| $) |PSETCAT-;collect;SVarSetS;9|) (LETT |lq| NIL |PSETCAT-;collect;SVarSetS;9|) (SEQ G190 (COND ((NULL (SPADCALL (NULL |lp|) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;collect;SVarSetS;9|) (LETT |lp| (CDR |lp|) |PSETCAT-;collect;SVarSetS;9|) (EXIT (COND ((NULL (SPADCALL |p| (|getShellEntry| $ 24))) (COND ((SPADCALL (SPADCALL |p| (|getShellEntry| $ 22)) |v| (|getShellEntry| $ 28)) (LETT |lq| (CONS |p| |lq|) |PSETCAT-;collect;SVarSetS;9|))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |lq| (|getShellEntry| $ 31))))))) (DEFUN |PSETCAT-;sort;SVarSetR;10| (|ps| |v| $) (PROG (|p| |lp| |us| |vs| |ws|) (RETURN (SEQ (LETT |lp| (|PSETCAT-;elements| |ps| $) |PSETCAT-;sort;SVarSetR;10|) (LETT |us| NIL |PSETCAT-;sort;SVarSetR;10|) (LETT |vs| NIL |PSETCAT-;sort;SVarSetR;10|) (LETT |ws| NIL |PSETCAT-;sort;SVarSetR;10|) (SEQ G190 (COND ((NULL (SPADCALL (NULL |lp|) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;sort;SVarSetR;10|) (LETT |lp| (CDR |lp|) |PSETCAT-;sort;SVarSetR;10|) (EXIT (COND ((OR (SPADCALL |p| (|getShellEntry| $ 24)) (SPADCALL (SPADCALL |p| (|getShellEntry| $ 22)) |v| (|getShellEntry| $ 16))) (LETT |us| (CONS |p| |us|) |PSETCAT-;sort;SVarSetR;10|)) ((SPADCALL (SPADCALL |p| (|getShellEntry| $ 22)) |v| (|getShellEntry| $ 28)) (LETT |vs| (CONS |p| |vs|) |PSETCAT-;sort;SVarSetR;10|)) ('T (LETT |ws| (CONS |p| |ws|) |PSETCAT-;sort;SVarSetR;10|))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (VECTOR (SPADCALL |us| (|getShellEntry| $ 31)) (SPADCALL |vs| (|getShellEntry| $ 31)) (SPADCALL |ws| (|getShellEntry| $ 31)))))))) (DEFUN |PSETCAT-;=;2SB;11| (|ps1| |ps2| $) (PROG (#0=#:G1562 #1=#:G1563 #2=#:G1564 |p| #3=#:G1565) (RETURN (SEQ (SPADCALL (SPADCALL (PROGN (LETT #0# NIL |PSETCAT-;=;2SB;11|) (SEQ (LETT |p| NIL |PSETCAT-;=;2SB;11|) (LETT #1# (|PSETCAT-;elements| |ps1| $) |PSETCAT-;=;2SB;11|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |p| (CAR #1#) |PSETCAT-;=;2SB;11|) NIL)) (GO G191))) (SEQ (EXIT (LETT #0# (CONS |p| #0#) |PSETCAT-;=;2SB;11|))) (LETT #1# (CDR #1#) |PSETCAT-;=;2SB;11|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) (|getShellEntry| $ 38)) (SPADCALL (PROGN (LETT #2# NIL |PSETCAT-;=;2SB;11|) (SEQ (LETT |p| NIL |PSETCAT-;=;2SB;11|) (LETT #3# (|PSETCAT-;elements| |ps2| $) |PSETCAT-;=;2SB;11|) G190 (COND ((OR (ATOM #3#) (PROGN (LETT |p| (CAR #3#) |PSETCAT-;=;2SB;11|) NIL)) (GO G191))) (SEQ (EXIT (LETT #2# (CONS |p| #2#) |PSETCAT-;=;2SB;11|))) (LETT #3# (CDR #3#) |PSETCAT-;=;2SB;11|) (GO G190) G191 (EXIT (NREVERSE0 #2#)))) (|getShellEntry| $ 38)) (|getShellEntry| $ 39)))))) (DEFUN |PSETCAT-;localInf?| (|p| |q| $) (SPADCALL (SPADCALL |p| (|getShellEntry| $ 41)) (SPADCALL |q| (|getShellEntry| $ 41)) (|getShellEntry| $ 42))) (DEFUN |PSETCAT-;localTriangular?| (|lp| $) (PROG (|q| |p|) (RETURN (SEQ (LETT |lp| (SPADCALL (ELT $ 43) |lp| (|getShellEntry| $ 26)) |PSETCAT-;localTriangular?|) (EXIT (COND ((NULL |lp|) 'T) ((SPADCALL (ELT $ 24) |lp| (|getShellEntry| $ 44)) 'NIL) ('T (SEQ (LETT |lp| (SPADCALL (CONS #'|PSETCAT-;localTriangular?!0| $) |lp| (|getShellEntry| $ 46)) |PSETCAT-;localTriangular?|) (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;localTriangular?|) (LETT |lp| (CDR |lp|) |PSETCAT-;localTriangular?|) (SEQ G190 (COND ((NULL (COND ((NULL |lp|) 'NIL) ('T (SPADCALL (SPADCALL (LETT |q| (|SPADfirst| |lp|) |PSETCAT-;localTriangular?|) (|getShellEntry| $ 22)) (SPADCALL |p| (|getShellEntry| $ 22)) (|getShellEntry| $ 16))))) (GO G191))) (SEQ (LETT |p| |q| |PSETCAT-;localTriangular?|) (EXIT (LETT |lp| (CDR |lp|) |PSETCAT-;localTriangular?|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (NULL |lp|)))))))))) (DEFUN |PSETCAT-;localTriangular?!0| (|#1| |#2| $) (SPADCALL (SPADCALL |#2| (|getShellEntry| $ 22)) (SPADCALL |#1| (|getShellEntry| $ 22)) (|getShellEntry| $ 16))) (DEFUN |PSETCAT-;triangular?;SB;14| (|ps| $) (|PSETCAT-;localTriangular?| (|PSETCAT-;elements| |ps| $) $)) (DEFUN |PSETCAT-;trivialIdeal?;SB;15| (|ps| $) (NULL (SPADCALL (ELT $ 43) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)))) (DEFUN |PSETCAT-;roughUnitIdeal?;SB;16| (|ps| $) (SPADCALL (ELT $ 24) (SPADCALL (ELT $ 43) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) (|getShellEntry| $ 44))) (DEFUN |PSETCAT-;relativelyPrimeLeadingMonomials?| (|p| |q| $) (PROG (|dp| |dq|) (RETURN (SEQ (LETT |dp| (SPADCALL |p| (|getShellEntry| $ 41)) |PSETCAT-;relativelyPrimeLeadingMonomials?|) (LETT |dq| (SPADCALL |q| (|getShellEntry| $ 41)) |PSETCAT-;relativelyPrimeLeadingMonomials?|) (EXIT (SPADCALL (SPADCALL |dp| |dq| (|getShellEntry| $ 50)) (SPADCALL |dp| |dq| (|getShellEntry| $ 51)) (|getShellEntry| $ 52))))))) (DEFUN |PSETCAT-;roughBase?;SB;18| (|ps| $) (PROG (|p| |lp| |rB?| |copylp|) (RETURN (SEQ (LETT |lp| (SPADCALL (ELT $ 43) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) |PSETCAT-;roughBase?;SB;18|) (EXIT (COND ((NULL |lp|) 'T) ('T (SEQ (LETT |rB?| 'T |PSETCAT-;roughBase?;SB;18|) (SEQ G190 (COND ((NULL (COND ((NULL |lp|) 'NIL) ('T |rB?|))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;roughBase?;SB;18|) (LETT |lp| (CDR |lp|) |PSETCAT-;roughBase?;SB;18|) (LETT |copylp| |lp| |PSETCAT-;roughBase?;SB;18|) (EXIT (SEQ G190 (COND ((NULL (COND ((NULL |copylp|) 'NIL) ('T |rB?|))) (GO G191))) (SEQ (LETT |rB?| (|PSETCAT-;relativelyPrimeLeadingMonomials?| |p| (|SPADfirst| |copylp|) $) |PSETCAT-;roughBase?;SB;18|) (EXIT (LETT |copylp| (CDR |copylp|) |PSETCAT-;roughBase?;SB;18|))) NIL (GO G190) G191 (EXIT NIL)))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |rB?|))))))))) (DEFUN |PSETCAT-;roughSubIdeal?;2SB;19| (|ps1| |ps2| $) (PROG (|lp|) (RETURN (SEQ (LETT |lp| (SPADCALL (|PSETCAT-;elements| |ps1| $) |ps2| (|getShellEntry| $ 54)) |PSETCAT-;roughSubIdeal?;2SB;19|) (EXIT (NULL (SPADCALL (ELT $ 43) |lp| (|getShellEntry| $ 26)))))))) (DEFUN |PSETCAT-;roughEqualIdeals?;2SB;20| (|ps1| |ps2| $) (COND ((SPADCALL |ps1| |ps2| (|getShellEntry| $ 56)) 'T) ((SPADCALL |ps1| |ps2| (|getShellEntry| $ 57)) (SPADCALL |ps2| |ps1| (|getShellEntry| $ 57))) ('T 'NIL))) (DEFUN |PSETCAT-;exactQuo| (|r| |s| $) (PROG (#0=#:G1507) (RETURN (COND ((|HasCategory| (|getShellEntry| $ 7) '(|EuclideanDomain|)) (SPADCALL |r| |s| (|getShellEntry| $ 59))) ('T (PROG2 (LETT #0# (SPADCALL |r| |s| (|getShellEntry| $ 61)) |PSETCAT-;exactQuo|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 7) #0#))))))) (DEFUN |PSETCAT-;headRemainder;PSR;22| (|a| |ps| $) (PROG (|lp1| |p| |e| |g| |#G45| |#G46| |lca| |lcp| |r| |lp2|) (RETURN (SEQ (LETT |lp1| (SPADCALL (ELT $ 43) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) |PSETCAT-;headRemainder;PSR;22|) (EXIT (COND ((NULL |lp1|) (CONS |a| (|spadConstant| $ 62))) ((SPADCALL (ELT $ 24) |lp1| (|getShellEntry| $ 44)) (CONS (SPADCALL |a| (|getShellEntry| $ 63)) (|spadConstant| $ 62))) ('T (SEQ (LETT |r| (|spadConstant| $ 62) |PSETCAT-;headRemainder;PSR;22|) (LETT |lp1| (SPADCALL (CONS (|function| |PSETCAT-;localInf?|) $) (REVERSE (|PSETCAT-;elements| |ps| $)) (|getShellEntry| $ 46)) |PSETCAT-;headRemainder;PSR;22|) (LETT |lp2| |lp1| |PSETCAT-;headRemainder;PSR;22|) (SEQ G190 (COND ((NULL (COND ((SPADCALL |a| (|getShellEntry| $ 43)) 'NIL) ('T (SPADCALL (NULL |lp2|) (|getShellEntry| $ 29))))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |lp2|) |PSETCAT-;headRemainder;PSR;22|) (LETT |e| (SPADCALL (SPADCALL |a| (|getShellEntry| $ 41)) (SPADCALL |p| (|getShellEntry| $ 41)) (|getShellEntry| $ 64)) |PSETCAT-;headRemainder;PSR;22|) (EXIT (COND ((QEQCAR |e| 0) (SEQ (LETT |g| (SPADCALL (LETT |lca| (SPADCALL |a| (|getShellEntry| $ 65)) |PSETCAT-;headRemainder;PSR;22|) (LETT |lcp| (SPADCALL |p| (|getShellEntry| $ 65)) |PSETCAT-;headRemainder;PSR;22|) (|getShellEntry| $ 66)) |PSETCAT-;headRemainder;PSR;22|) (PROGN (LETT |#G45| (|PSETCAT-;exactQuo| |lca| |g| $) |PSETCAT-;headRemainder;PSR;22|) (LETT |#G46| (|PSETCAT-;exactQuo| |lcp| |g| $) |PSETCAT-;headRemainder;PSR;22|) (LETT |lca| |#G45| |PSETCAT-;headRemainder;PSR;22|) (LETT |lcp| |#G46| |PSETCAT-;headRemainder;PSR;22|)) (LETT |a| (SPADCALL (SPADCALL |lcp| (SPADCALL |a| (|getShellEntry| $ 63)) (|getShellEntry| $ 67)) (SPADCALL (SPADCALL |lca| (QCDR |e|) (|getShellEntry| $ 68)) (SPADCALL |p| (|getShellEntry| $ 63)) (|getShellEntry| $ 69)) (|getShellEntry| $ 70)) |PSETCAT-;headRemainder;PSR;22|) (LETT |r| (SPADCALL |r| |lcp| (|getShellEntry| $ 71)) |PSETCAT-;headRemainder;PSR;22|) (EXIT (LETT |lp2| |lp1| |PSETCAT-;headRemainder;PSR;22|)))) ('T (LETT |lp2| (CDR |lp2|) |PSETCAT-;headRemainder;PSR;22|))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (CONS |a| |r|)))))))))) (DEFUN |PSETCAT-;makeIrreducible!| (|frac| $) (PROG (|g|) (RETURN (SEQ (LETT |g| (SPADCALL (QCDR |frac|) (QCAR |frac|) (|getShellEntry| $ 74)) |PSETCAT-;makeIrreducible!|) (EXIT (COND ((SPADCALL |g| (|spadConstant| $ 62) (|getShellEntry| $ 76)) |frac|) ('T (SEQ (PROGN (RPLACA |frac| (SPADCALL (QCAR |frac|) |g| (|getShellEntry| $ 77))) (QCAR |frac|)) (PROGN (RPLACD |frac| (|PSETCAT-;exactQuo| (QCDR |frac|) |g| $)) (QCDR |frac|)) (EXIT |frac|))))))))) (DEFUN |PSETCAT-;remainder;PSR;24| (|a| |ps| $) (PROG (|hRa| |r| |lca| |g| |b| |c|) (RETURN (SEQ (LETT |hRa| (|PSETCAT-;makeIrreducible!| (SPADCALL |a| |ps| (|getShellEntry| $ 78)) $) |PSETCAT-;remainder;PSR;24|) (LETT |a| (QCAR |hRa|) |PSETCAT-;remainder;PSR;24|) (LETT |r| (QCDR |hRa|) |PSETCAT-;remainder;PSR;24|) (EXIT (COND ((SPADCALL |a| (|getShellEntry| $ 43)) (VECTOR (|spadConstant| $ 62) |a| |r|)) ('T (SEQ (LETT |b| (SPADCALL (|spadConstant| $ 62) (SPADCALL |a| (|getShellEntry| $ 41)) (|getShellEntry| $ 68)) |PSETCAT-;remainder;PSR;24|) (LETT |c| (SPADCALL |a| (|getShellEntry| $ 65)) |PSETCAT-;remainder;PSR;24|) (SEQ G190 (COND ((NULL (SPADCALL (SPADCALL (LETT |a| (SPADCALL |a| (|getShellEntry| $ 63)) |PSETCAT-;remainder;PSR;24|) (|getShellEntry| $ 43)) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |hRa| (|PSETCAT-;makeIrreducible!| (SPADCALL |a| |ps| (|getShellEntry| $ 78)) $) |PSETCAT-;remainder;PSR;24|) (LETT |a| (QCAR |hRa|) |PSETCAT-;remainder;PSR;24|) (LETT |r| (SPADCALL |r| (QCDR |hRa|) (|getShellEntry| $ 71)) |PSETCAT-;remainder;PSR;24|) (LETT |g| (SPADCALL |c| (LETT |lca| (SPADCALL |a| (|getShellEntry| $ 65)) |PSETCAT-;remainder;PSR;24|) (|getShellEntry| $ 66)) |PSETCAT-;remainder;PSR;24|) (LETT |b| (SPADCALL (SPADCALL (SPADCALL (QCDR |hRa|) (|PSETCAT-;exactQuo| |c| |g| $) (|getShellEntry| $ 71)) |b| (|getShellEntry| $ 67)) (SPADCALL (|PSETCAT-;exactQuo| |lca| |g| $) (SPADCALL |a| (|getShellEntry| $ 41)) (|getShellEntry| $ 68)) (|getShellEntry| $ 79)) |PSETCAT-;remainder;PSR;24|) (EXIT (LETT |c| |g| |PSETCAT-;remainder;PSR;24|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (VECTOR |c| |b| |r|)))))))))) (DEFUN |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25| (|ps| |cs| $) (PROG (|p| |rs|) (RETURN (SEQ (COND ((SPADCALL |cs| (|getShellEntry| $ 82)) |ps|) ((SPADCALL |cs| (|getShellEntry| $ 83)) (LIST (|spadConstant| $ 84))) ('T (SEQ (LETT |ps| (SPADCALL (ELT $ 43) |ps| (|getShellEntry| $ 26)) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (EXIT (COND ((NULL |ps|) |ps|) ((SPADCALL (ELT $ 24) |ps| (|getShellEntry| $ 44)) (LIST (|spadConstant| $ 75))) ('T (SEQ (LETT |rs| NIL |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (SEQ G190 (COND ((NULL (SPADCALL (NULL |ps|) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |ps|) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (LETT |ps| (CDR |ps|) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (LETT |p| (QCAR (SPADCALL |p| |cs| (|getShellEntry| $ 78))) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (EXIT (COND ((NULL (SPADCALL |p| (|getShellEntry| $ 43))) (COND ((SPADCALL |p| (|getShellEntry| $ 24)) (SEQ (LETT |ps| NIL |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (EXIT (LETT |rs| (LIST (|spadConstant| $ 75)) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|)))) ('T (SEQ (SPADCALL |p| (|getShellEntry| $ 85)) (EXIT (LETT |rs| (CONS |p| |rs|) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|))))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |rs| (|getShellEntry| $ 86)))))))))))))) (DEFUN |PSETCAT-;rewriteIdealWithRemainder;LSL;26| (|ps| |cs| $) (PROG (|p| |rs|) (RETURN (SEQ (COND ((SPADCALL |cs| (|getShellEntry| $ 82)) |ps|) ((SPADCALL |cs| (|getShellEntry| $ 83)) (LIST (|spadConstant| $ 84))) ('T (SEQ (LETT |ps| (SPADCALL (ELT $ 43) |ps| (|getShellEntry| $ 26)) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (EXIT (COND ((NULL |ps|) |ps|) ((SPADCALL (ELT $ 24) |ps| (|getShellEntry| $ 44)) (LIST (|spadConstant| $ 75))) ('T (SEQ (LETT |rs| NIL |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (SEQ G190 (COND ((NULL (SPADCALL (NULL |ps|) (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |p| (|SPADfirst| |ps|) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (LETT |ps| (CDR |ps|) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (LETT |p| (QVELT (SPADCALL |p| |cs| (|getShellEntry| $ 88)) 1) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (EXIT (COND ((NULL (SPADCALL |p| (|getShellEntry| $ 43))) (COND ((SPADCALL |p| (|getShellEntry| $ 24)) (SEQ (LETT |ps| NIL |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (EXIT (LETT |rs| (LIST (|spadConstant| $ 75)) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|)))) ('T (LETT |rs| (CONS (SPADCALL |p| (|getShellEntry| $ 89)) |rs|) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |rs| (|getShellEntry| $ 86)))))))))))))) (DEFUN |PolynomialSetCategory&| (|#1| |#2| |#3| |#4| |#5|) (PROG (|dv$1| |dv$2| |dv$3| |dv$4| |dv$5| |dv$| $ |pv$|) (RETURN (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|PolynomialSetCategory&|)) (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$3| (|devaluate| |#3|) . #0#) (LETT |dv$4| (|devaluate| |#4|) . #0#) (LETT |dv$5| (|devaluate| |#5|) . #0#) (LETT |dv$| (LIST '|PolynomialSetCategory&| |dv$1| |dv$2| |dv$3| |dv$4| |dv$5|) . #0#) (LETT $ (|newShell| 91) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 (LIST (|HasCategory| |#2| '(|IntegralDomain|)))) . #0#)) (|stuffDomainSlots| $) (|setShellEntry| $ 6 |#1|) (|setShellEntry| $ 7 |#2|) (|setShellEntry| $ 8 |#3|) (|setShellEntry| $ 9 |#4|) (|setShellEntry| $ 10 |#5|) (COND ((|testBitVector| |pv$| 1) (PROGN (|setShellEntry| $ 49 (CONS (|dispatchFunction| |PSETCAT-;roughUnitIdeal?;SB;16|) $)) (|setShellEntry| $ 53 (CONS (|dispatchFunction| |PSETCAT-;roughBase?;SB;18|) $)) (|setShellEntry| $ 55 (CONS (|dispatchFunction| |PSETCAT-;roughSubIdeal?;2SB;19|) $)) (|setShellEntry| $ 58 (CONS (|dispatchFunction| |PSETCAT-;roughEqualIdeals?;2SB;20|) $))))) (COND ((|HasCategory| |#2| '(|GcdDomain|)) (COND ((|HasCategory| |#4| '(|ConvertibleTo| (|Symbol|))) (PROGN (|setShellEntry| $ 73 (CONS (|dispatchFunction| |PSETCAT-;headRemainder;PSR;22|) $)) (|setShellEntry| $ 81 (CONS (|dispatchFunction| |PSETCAT-;remainder;PSR;24|) $)) (|setShellEntry| $ 87 (CONS (|dispatchFunction| |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) $)) (|setShellEntry| $ 90 (CONS (|dispatchFunction| |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) $))))))) $)))) (MAKEPROP '|PolynomialSetCategory&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|local| |#3|) (|local| |#4|) (|local| |#5|) (|List| 10) (0 . |members|) (|List| 9) (5 . |variables|) (|Boolean|) (10 . <) (|List| $) (16 . |concat|) (21 . |removeDuplicates|) (|Mapping| 15 9 9) (26 . |sort|) (32 . |mvar|) |PSETCAT-;variables;SL;4| (37 . |ground?|) (|Mapping| 15 10) (42 . |remove|) |PSETCAT-;mainVariables;SL;5| (48 . =) (54 . |not|) |PSETCAT-;mainVariable?;VarSetSB;6| (59 . |construct|) |PSETCAT-;collectUnder;SVarSetS;7| |PSETCAT-;collectUpper;SVarSetS;8| |PSETCAT-;collect;SVarSetS;9| (|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) |PSETCAT-;sort;SVarSetR;10| (|Set| 10) (64 . |brace|) (69 . =) |PSETCAT-;=;2SB;11| (75 . |degree|) (80 . <) (86 . |zero?|) (91 . |any?|) (|Mapping| 15 10 10) (97 . |sort|) |PSETCAT-;triangular?;SB;14| |PSETCAT-;trivialIdeal?;SB;15| (103 . |roughUnitIdeal?|) (108 . |sup|) (114 . +) (120 . =) (126 . |roughBase?|) (131 . |rewriteIdealWithRemainder|) (137 . |roughSubIdeal?|) (143 . =) (149 . |roughSubIdeal?|) (155 . |roughEqualIdeals?|) (161 . |quo|) (|Union| $ '"failed") (167 . |exquo|) (173 . |One|) (177 . |reductum|) (182 . |subtractIfCan|) (188 . |leadingCoefficient|) (193 . |gcd|) (199 . *) (205 . |monomial|) (211 . *) (217 . -) (223 . *) (|Record| (|:| |num| 10) (|:| |den| 7)) (229 . |headRemainder|) (235 . |gcd|) (241 . |One|) (245 . =) (251 . |exactQuotient!|) (257 . |headRemainder|) (263 . +) (|Record| (|:| |rnum| 7) (|:| |polnum| 10) (|:| |den| 7)) (269 . |remainder|) (275 . |trivialIdeal?|) (280 . |roughUnitIdeal?|) (285 . |Zero|) (289 . |primitivePart!|) (294 . |removeDuplicates|) (299 . |rewriteIdealWithHeadRemainder|) (305 . |remainder|) (311 . |unitCanonical|) (316 . |rewriteIdealWithRemainder|)) '#(|variables| 322 |trivialIdeal?| 327 |triangular?| 332 |sort| 337 |roughUnitIdeal?| 343 |roughSubIdeal?| 348 |roughEqualIdeals?| 354 |roughBase?| 360 |rewriteIdealWithRemainder| 365 |rewriteIdealWithHeadRemainder| 371 |remainder| 377 |mainVariables| 383 |mainVariable?| 388 |headRemainder| 394 |collectUpper| 400 |collectUnder| 406 |collect| 412 = 418) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() (|makeByteWordVec2| 90 '(1 6 11 0 12 1 10 13 0 14 2 9 15 0 0 16 1 13 0 17 18 1 13 0 0 19 2 13 0 20 0 21 1 10 9 0 22 1 10 15 0 24 2 11 0 25 0 26 2 9 15 0 0 28 1 15 0 0 29 1 6 0 11 31 1 37 0 11 38 2 37 15 0 0 39 1 10 8 0 41 2 8 15 0 0 42 1 10 15 0 43 2 11 15 25 0 44 2 11 0 45 0 46 1 0 15 0 49 2 8 0 0 0 50 2 8 0 0 0 51 2 8 15 0 0 52 1 0 15 0 53 2 6 11 11 0 54 2 0 15 0 0 55 2 6 15 0 0 56 2 6 15 0 0 57 2 0 15 0 0 58 2 7 0 0 0 59 2 7 60 0 0 61 0 7 0 62 1 10 0 0 63 2 8 60 0 0 64 1 10 7 0 65 2 7 0 0 0 66 2 10 0 7 0 67 2 10 0 7 8 68 2 10 0 0 0 69 2 10 0 0 0 70 2 7 0 0 0 71 2 0 72 10 0 73 2 10 7 7 0 74 0 10 0 75 2 7 15 0 0 76 2 10 0 0 7 77 2 6 72 10 0 78 2 10 0 0 0 79 2 0 80 10 0 81 1 6 15 0 82 1 6 15 0 83 0 10 0 84 1 10 0 0 85 1 11 0 0 86 2 0 11 11 0 87 2 6 80 10 0 88 1 10 0 0 89 2 0 11 11 0 90 1 0 13 0 23 1 0 15 0 48 1 0 15 0 47 2 0 35 0 9 36 1 0 15 0 49 2 0 15 0 0 55 2 0 15 0 0 58 1 0 15 0 53 2 0 11 11 0 90 2 0 11 11 0 87 2 0 80 10 0 81 1 0 13 0 27 2 0 15 9 0 30 2 0 72 10 0 73 2 0 0 0 9 33 2 0 0 0 9 32 2 0 0 0 9 34 2 0 15 0 0 40))))) '|lookupComplete|)) (SETQ |$CategoryFrame| (|put| '|PolynomialSetCategory&| '|isFunctor| '(((|triangular?| ((|Boolean|) $)) T (ELT $ 47)) ((|rewriteIdealWithRemainder| ((|List| |#5|) (|List| |#5|) $)) T (ELT $ 90)) ((|rewriteIdealWithHeadRemainder| ((|List| |#5|) (|List| |#5|) $)) T (ELT $ 87)) ((|remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $)) T (ELT $ 81)) ((|headRemainder| ((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $)) T (ELT $ 73)) ((|roughUnitIdeal?| ((|Boolean|) $)) T (ELT $ 49)) ((|roughEqualIdeals?| ((|Boolean|) $ $)) T (ELT $ 58)) ((|roughSubIdeal?| ((|Boolean|) $ $)) T (ELT $ 55)) ((|roughBase?| ((|Boolean|) $)) T (ELT $ 53)) ((|trivialIdeal?| ((|Boolean|) $)) T (ELT $ 48)) ((|sort| ((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|)) T (ELT $ 36)) ((|collectUpper| ($ $ |#4|)) T (ELT $ 33)) ((|collect| ($ $ |#4|)) T (ELT $ 34)) ((|collectUnder| ($ $ |#4|)) T (ELT $ 32)) ((|mainVariable?| ((|Boolean|) |#4| $)) T (ELT $ 30)) ((|mainVariables| ((|List| |#4|) $)) T (ELT $ 27)) ((|variables| ((|List| |#4|) $)) T (ELT $ 23)) ((= ((|Boolean|) $ $)) T (ELT $ 40))) (|addModemap| '|PolynomialSetCategory&| '(|PolynomialSetCategory&| |#1| |#2| |#3| |#4| |#5|) '((CATEGORY |domain| (SIGNATURE |triangular?| ((|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |roughEqualIdeals?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughSubIdeal?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughBase?| ((|Boolean|) |#1|)) (SIGNATURE |trivialIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) (SIGNATURE |collect| (|#1| |#1| |#4|)) (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) (SIGNATURE |mainVariable?| ((|Boolean|) |#4| |#1|)) (SIGNATURE |mainVariables| ((|List| |#4|) |#1|)) (SIGNATURE |variables| ((|List| |#4|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) T '|PolynomialSetCategory&| (|put| '|PolynomialSetCategory&| '|mode| '(|Mapping| (CATEGORY |domain| (SIGNATURE |triangular?| ((|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |roughEqualIdeals?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughSubIdeal?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughBase?| ((|Boolean|) |#1|)) (SIGNATURE |trivialIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) (SIGNATURE |collect| (|#1| |#1| |#4|)) (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) (SIGNATURE |mainVariable?| ((|Boolean|) |#4| |#1|)) (SIGNATURE |mainVariables| ((|List| |#4|) |#1|)) (SIGNATURE |variables| ((|List| |#4|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) |$CategoryFrame|))))