--* From BMT%WATSON.vnet.ibm.com@yktvmh.watson.ibm.com Fri Oct 15 11:35:55 1993 --* Received: from yktvmh.watson.ibm.com by radical.watson.ibm.com (AIX 3.2/UCB 5.64/900524) --* id AA21425; Fri, 15 Oct 1993 11:35:55 -0400 --* Received: from watson.vnet.ibm.com by yktvmh.watson.ibm.com (IBM VM SMTP V2R3) --* with BSMTP id 3586; Fri, 15 Oct 93 11:42:22 EDT --* Received: from YKTVMH by watson.vnet.ibm.com with "VAGENT.V1.0" --* id --* for asbugs@watson; Fri, 15 Oct 93 11:42:22 -0400 --* Received: from YKTVMH by watson.vnet.ibm.com with "VAGENT.V1.0" --* id 9342; Fri, 15 Oct 1993 11:42:20 EDT --* Received: from cyst.watson.ibm.com by yktvmh.watson.ibm.com (IBM VM SMTP V2R3) --* with TCP; Fri, 15 Oct 93 11:42:20 EDT --* Received: from spadserv.watson.ibm.com by cyst.watson.ibm.com (AIX 3.2/UCB 5.64/900528) --* id AA46001; Fri, 15 Oct 1993 11:41:47 -0400 --* Received: by spadserv.watson.ibm.com (AIX 3.2/UCB 5.64/900524) --* id AA25765; Fri, 15 Oct 1993 11:43:40 -0400 --* Date: Fri, 15 Oct 1993 11:43:40 -0400 --* From: bmt@spadserv.watson.ibm.com --* X-External-Networks: yes --* Message-Id: <9310151543.AA25765@spadserv.watson.ibm.com> --* To: asbugs@watson.ibm.com --* Subject: asharp -Wcheck -Mno-warnings gives assertion failed in tform.c line 1865 abSyme(id) [fix210.as][current] --@ Fixed by: SSD Wed Nov 2 15:15:43 EST 1994 --@ Tested by: none --@ Summary: Assertion failed message no longer appears. Error messages appear justified. --* From bmt@spadserv.watson.ibm.com Sat Apr 3 12:18:01 1993 --* Received: from spadserv.watson.ibm.com by radical.watson.ibm.com (AIX 3.2/UCB 5.64/900524) --* id AA25674; Sat, 3 Apr 1993 12:18:01 -0500 --* Received: by spadserv.watson.ibm.com (AIX 3.2/UCB 5.64/900524) --* id AA27528; Sat, 3 Apr 1993 12:19:19 -0500 --* Date: Sat, 3 Apr 1993 12:19:19 -0500 --* From: bmt@spadserv.watson.ibm.com --* X-External-Networks: yes --* Message-Id: <9304031719.AA27528@spadserv.watson.ibm.com> --* To: axc-bug@radical.watson.ibm.com, sutor@watson.vnet.ibm.com --* Subject: compiler gets segmentation violation from macros in where clause [gb2.as][27.5 (current)] --@ Fixed by: SSD Wed Nov 2 15:15:43 EST 1994 --@ Tested by: none --@ Summary: Assertion failed message no longer appears. Error messages appear justified. -- PI: not riproducible. I get only an error msg #include "aslib.as" #library DemoLib "asdem" import from DemoLib macro Void == () Arithmetic == Ring Ordered == Order Object == BasicType GcdDomain == with Object Arithmetic *: (%, %) -> % gcd: (%, %) -> % /: (%, %) -> % OrderedAbelianMonoidSup == with Object Ordered Arithmetic sup: (%, %) -> % OrderedSet == with Object Ordered PolynomialCategory(R,E) == with Object Arithmetic *: (R, %) -> % *: (%, %) -> % degree: % -> E totalDegree: % -> NonNegativeInteger monomial: (R, E) -> % reductum: % -> % leadingCoefficient: % -> R primitivePart: % -> % PositiveInteger == Integer NonNegativeInteger == Integer SmallInteger == SingleInteger NNI == Integer null xx == empty? xx messagePrint(s: String):Void == print(s)() import with (string: Literal -> %) from String (GroebnerPackage(Dom, Expon, Dpol): T == C) where default Dom: GcdDomain default Expon: OrderedAbelianMonoidSup default Dpol: PolynomialCategory(Dom, Expon) T ==> with groebner: List(Dpol) -> List(Dpol) ++ groebner(lp) computes a groebner basis for a polynomial ideal ++ generated by the list of polynomials lp. groebner: ( List(Dpol), String ) -> List(Dpol) ++ groebner(lp, infoflag) computes a groebner basis ++ for a polynomial ideal ++ generated by the list of polynomials lp. ++ Argument infoflag is used to get information on the computation. ++ If infoflag is "info", then summary information ++ is displayed for each s-polynomial generated. ++ If infoflag is "redcrit", the reduced critical pairs are displayed. ++ If infoflag is any other string, no information is printed during computation. groebner: ( List(Dpol), String, String ) -> List(Dpol) ++ groebner(lp, "info", "redcrit") computes a groebner basis ++ for a polynomial ideal generated by the list of polynomials lp, ++ displaying both a summary of the critical pairs considered ("info") ++ and the result of reducing each critical pair ("redcrit"). ++ If the second or third arguments have any other string value, ++ the indicated information is suppressed. -- if Dom has Field then normalForm: (Dpol, List(Dpol)) -> Dpol ++ normalForm(poly,gb) reduces the polynomial poly modulo the ++ precomputed groebner basis gb giving a canonical representative ++ of the residue class. C ==> add import from Dpol import from Expon import from Dom import from ListSort(Dpol) import from GroebnerInternalPackage(Dom,Expon,Dpol) normalForm(p:Dpol,l:List Dpol):Dpol == redPol(p,l)$GroebnerInternalPackage(Dom,Expon,Dpol) groebner (Pol:List Dpol):List Dpol == import from Boolean import from Integer Pol = [] => Pol Pol := [x for x in Pol | not (x = 0)] Pol = [] => [0] minGbasis sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1, gbasis(Pol,0,0)) groebner(Pol:List Dpol,xx1:String):List Dpol == import from Boolean import from Integer import from PositiveInteger Pol = [] => Pol Pol := [x for x in Pol | not (x = 0)] Pol = [] => [0] xx1 = "redcrit" => minGbasis sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1, gbasis(Pol,1,0)) xx1 = "info" => minGbasis sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1, gbasis(Pol,2,1)) messagePrint " " messagePrint "WARNING: options are - redcrit and/or info - " messagePrint " you didn't type them correct" messagePrint " please try again" messagePrint " " [] groebner(Pol:List Dpol,xx1:String,xx2:String):List Dpol == import from Boolean import from Integer import from PositiveInteger Pol = [] => Pol Pol := [x for x in Pol | not (x = 0)] Pol = [] => [0] xx1 = "redcrit" and xx2 = "info" or xx1 = "info" and xx2 = "redcrit" => minGbasis sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1, gbasis(Pol,1,1)) xx1 = "redcrit" and xx2 = "redcrit" => minGbasis sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1, gbasis(Pol,1,0)) xx1 = "info" and xx2 = "info" => minGbasis sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1, gbasis(Pol,2,1)) messagePrint " " messagePrint "WARNING: options are - redcrit and/or info - " messagePrint " you didn't type them correctly" messagePrint " please try again " messagePrint " " [] --critPair ==> Record( lcmfij: Expon, totdeg: NonNegativeInteger, -- poli: Dpol, polj: Dpol ) critPair(Expon:with Object, Dpol:with Object):with Object bracket: (Expon, NNI, Dpol, Dpol) -> % apply: (%, Enumeration(lcmfij)) -> Expon apply: (%, Enumeration(totdeg)) -> NNI apply: (%, Enumeration(poli)) -> Dpol apply: (%, Enumeration(polj)) -> Dpol == add Rep ==> Record( lcmfij: Expon, totdeg: NonNegativeInteger, poli: Dpol, polj: Dpol ) import from Expon import from NNI import from Dpol import from Rep (c1:%) = (c2:%):Boolean == rep(c1).lcmfij = rep(c2).lcmfij and rep(c1).poli = rep(c2).poli and rep(c1).polj = rep(c2).polj (c1:%) ~= (c2:%):Boolean == not(c1=c2) apply(c:%, tag:Enumeration(lcmfij)):Expon == rep(c).lcmfij apply(c:%, tag:Enumeration(totdeg)):NNI == rep(c).totdeg apply(c:%, tag:Enumeration(poli)):Dpol == rep(c).poli apply(c:%, tag:Enumeration(polj)):Dpol == rep(c).polj [e:Expon, d:NNI, p1:Dpol, p2:Dpol]:% == per [e,d,p1,p2] apply(p: Outport, c: %): Outport == import from String p("(")(rep(c).poli)(",")(rep(c).polj)(")") --sugarPol ==> Record( totdeg: NonNegativeInteger, pol : Dpol) sugarPol(Dpol:with Object): with Object bracket: (NNI, Dpol) -> % apply: (%, Enumeration(totdeg)) -> NNI apply: (%, Enumeration(pol)) -> Dpol == add Rep ==> Record( totdeg: NonNegativeInteger, pol : Dpol) import from Rep import from Dpol (p1:%) = (p2:%):Boolean == rep(p1).pol = rep(p2).pol (p1:%) ~= (p2:%):Boolean == not(p1=p2) apply(p:%, tag:Enumeration(totdeg)):NNI == rep(p).totdeg apply(p:%, tag:Enumeration(pol)):Dpol == rep(p).pol [deg:NNI, p:Dpol]:% == per [deg,p] apply(p: Outport, spol: %): Outport == p(rep(spol).pol) Prinp ==> Record( ci:Dpol,tci:Integer,cj:Dpol,tcj:Integer,c:Dpol, tc:Integer,rc:Dpol,trc:Integer,tF:Integer,tD:Integer) Prinpp ==> Record( ci:Dpol,tci:Integer,cj:Dpol,tcj:Integer,c:Dpol, tc:Integer,rc:Dpol,trc:Integer,tF:Integer,tDD:Integer, tDF:Integer) GroebnerInternalPackage(Dom:GcdDomain, _ Expon:OrderedAbelianMonoidSup, _ Dpol:PolynomialCategory(Dom,Expon)):with redPol: (Dpol, List(Dpol)) -> Dpol gbasis: (List(Dpol), Integer, Integer) -> List(Dpol) minGbasis: List(Dpol) -> List(Dpol) == add import from Dpol import from VarSet import from Expon import from Dom import from ListSort(Dpol) -- if Dpol has totalDegree: Dpol -> NonNegativeInteger then virtualDegree (p:Dpol):NonNegativeInteger == totalDegree p -- else -- virtualDegree (p:Dpol):NonNegativeInteger == 0 critpOrder(cp1:critPair(Expon, Dpol),cp2:critPair(Expon, Dpol)):Boolean == import from NonNegativeInteger import from Enumeration(totdeg) import from Enumeration(lcmfij) cp1 totdeg < cp2 totdeg => true cp2 totdeg < cp1 totdeg => false cp1 lcmfij < cp2 lcmfij makeCrit(sp1:sugarPol(Dpol),p2:Dpol,totdeg2:NonNegativeInteger):critPair(Expon, Dpol) == import from Union(Expon,"failed") import from Enumeration(pol) import from Enumeration(totdeg) p1 := sp1 pol deg := sup(degree p1,degree p2) e1 := (deg - degree p1)::Expon e2 := (deg - degree p2)::Expon tdeg := max(sp1 totdeg + virtualDegree monomial(1,e1),totdeg2 + virtualDegree monomial(1,e2)) [deg,tdeg,p1,p2]$critPair(Expon, Dpol) gbasis(Pol:List Dpol,xx1:Integer,xx2:Integer):List Dpol == import from Boolean import from NonNegativeInteger import from ListSort critPair(Expon, Dpol) import from List sugarPol(Dpol) default D,D1:List critPair(Expon, Dpol) import from critPair(Expon, Dpol) Pol1 := sort(((%1:Dpol,%2:Dpol):Boolean) +-> degree %2 < degree %1,Pol) basPols := updatF(hMonic first Pol1,virtualDegree first Pol1,[]) Pol1 := rest Pol1 D := nil while not(null Pol1) repeat h := hMonic first Pol1 Pol1 := rest Pol1 toth := virtualDegree h D1 := [makeCrit(x,h,toth) for x in basPols] D := updatD(critMTonD1 sort(critpOrder,D1),critBonD(h,D)) basPols := updatF(h,toth,basPols) D := sort(critpOrder,D) xx := xx2 import from sugarPol(Dpol) import from Enumeration(pol) import from Enumeration(totdeg) redPols := [x pol for x in basPols] while not(null D) repeat D0 := first D s := hMonic sPol D0 D := rest D h := hMonic redPol(s,redPols) if xx1 = 1 then prinshINFO h h = 0 => if xx2 = 1 then prindINFO(D0,s,h,#basPols::Integer,#D::Integer,xx) xx := 2 " go to top of while " degree h = 0 => D := nil if xx2 = 1 then prindINFO(D0,s,h,#basPols::Integer,#D::Integer,xx) xx := 2 basPols := updatF(h,0,[]) break D1 := [makeCrit(x,h,D0 totdeg) for x in basPols] D := updatD(critMTonD1 sort(critpOrder,D1),critBonD(h,D)) basPols := updatF(h,D0 totdeg,basPols) redPols := concat(redPols,h) xx2 = 1 => prindINFO(D0,s,h,#basPols::Integer,#D::Integer,xx) xx := 2 Pol := [x pol for x in basPols] if xx2 = 1 then prinpolINFO Pol messagePrint " THE GROEBNER BASIS POLYNOMIALS" if xx1 = 1 and not (xx2 = 1) then messagePrint " THE GROEBNER BASIS POLYNOMIALS" Pol critMonD1(e:Expon,D2:List critPair(Expon, Dpol)):List critPair(Expon, Dpol) == import from critPair(Expon, Dpol) import from Enumeration lcmfij null D2 => nil x := first D2 critM(e,x lcmfij) => critMonD1(e,rest D2) cons(x,critMonD1(e,rest D2)) critMTonD1 (D1:List critPair(Expon, Dpol)):List critPair(Expon, Dpol) == import from NonNegativeInteger import from Boolean import from critPair(Expon, Dpol) import from Enumeration lcmfij null D1 => nil f1 := first D1 s1 := #D1 :: Integer cT1 := critT f1 s1 = 1 and cT1 => nil s1 = 1 => D1 e1 := f1 lcmfij r1 := rest D1 e1 = (first r1).lcmfij => cT1 => critMTonD1 cons(f1,rest r1) critMTonD1 r1 D1 := critMonD1(e1,r1) cT1 => critMTonD1 D1 cons(f1,critMTonD1 D1) critBonD(h:Dpol,D:List critPair(Expon, Dpol)):List critPair(Expon, Dpol) == import from critPair(Expon, Dpol) import from Enumeration lcmfij import from Enumeration poli import from Enumeration polj null D => nil x := first D critB(degree h,x lcmfij,degree x poli,degree x polj) => critBonD(h,rest D) cons(x,critBonD(h,rest D)) updatF(h:Dpol,deg:NNI,F:List sugarPol(Dpol)):List sugarPol(Dpol) == import from sugarPol(Dpol) import from Enumeration pol null F => [[deg,h]] f1 := first F critM(degree h,degree f1 pol) => updatF(h,deg,rest F) cons(f1,updatF(h,deg,rest F)) updatD(D1:List critPair(Expon, Dpol),D2:List critPair(Expon, Dpol)):List critPair(Expon, Dpol) == null D1 => D2 null D2 => D1 dl1 := first D1 dl2 := first D2 critpOrder(dl1,dl2) => cons(dl1,updatD(rest D1,D2)) cons(dl2,updatD(D1,rest D2)) gcdCo(c1:Dom,c2:Dom):Record(co1:Dom,co2:Dom) == d := gcd(c1,c2) [c1/d, c2/d] sPol (p:critPair(Expon, Dpol)):Dpol == import from Union(Expon,"failed") import from Enumeration lcmfij import from Enumeration poli import from Enumeration polj Tij := p lcmfij fi := p poli fj := p polj cc := gcdCo(leadingCoefficient fi,leadingCoefficient fj) import from Record(co1:Dom,co2:Dom) reductum fi * monomial(cc co2,(Tij - degree fi)::Expon) - reductum fj * monomial(cc co1,(Tij - degree fj)::Expon) redPo(s:Dpol,F:List Dpol):Record(poly:Dpol,mult:Dom) == import from Boolean m:Dom := 1 Fh := F while not(s = 0 or null F) repeat f1 := first F s1 := degree s e:Union(Expon,"failed") (e := s1 - degree f1) case Expon => cc := gcdCo(leadingCoefficient f1,leadingCoefficient s) import from Record(co1:Dom,co2:Dom) s := cc co1 * reductum s - monomial(cc co2,e::Expon) * reductum f1 m := m * cc co1 F := Fh F := rest F [s,m] redPol(s:Dpol,F:List Dpol):Dpol == import from Record(poly:Dpol,mult:Dom) credPol((redPo(s,F)).poly,F) critT (p:critPair(Expon, Dpol)):Boolean == p lcmfij = degree p poli + degree p polj critM(e1:Expon,e2:Expon):Boolean == en:Union(Expon,"failed") (en := e2 - e1) case Expon critB(eh:Expon,eik:Expon,ei:Expon,ek:Expon):Boolean == critM(eh,eik) and not (eik = sup(eh,ei)) and not (eik = sup(eh,ek)) hMonic (p:Dpol):Dpol == if p = 0 then p else primitivePart p credPol(h:Dpol,F:List Dpol):Dpol == import from Boolean null F => h h0:Dpol := monomial(leadingCoefficient h,degree h) while not ((h := reductum h) = 0) repeat hred := redPo(h,F) import from Record(poly:Dpol,mult:Dom) h := hred poly h0 := hred mult * h0 + monomial(leadingCoefficient h,degree h) h0 minGbasis (F:List Dpol):List Dpol == null F => nil newbas := minGbasis rest F cons(hMonic credPol(first F,newbas),newbas) lepol (p1:Dpol):Integer == import from Boolean n:Integer n := 0 while not (p1 = 0) repeat n := n + 1 p1 := reductum p1 n prinb (n:Integer):Void == import from SmallInteger import from NonNegativeInteger import from Segment Integer for x in 1..n repeat messagePrint " " never prinshINFO (h:Dpol):Void == import from Integer prinb 2 messagePrint " reduced Critpair - Polynom :" prinb 2 print (h)() prinb 2 prindINFO(cp:critPair(Expon, Dpol),ps:Dpol,ph:Dpol,i1:Integer,i2:Integer,n:Integer): Integer == import from PositiveInteger import from NonNegativeInteger a:Dom ll:Prinp cpi := cp poli cpj := cp polj if n = 1 then prinb 1 messagePrint "you choose option -info- " messagePrint "abbrev. for the following information strings are" messagePrint " ci => Leading monomial for critpair calculation" messagePrint " tci => Number of terms of polynomial i" messagePrint " cj => Leading monomial for critpair calculation" messagePrint " tcj => Number of terms of polynomial j" messagePrint " c => Leading monomial of critpair polynomial" messagePrint " tc => Number of terms of critpair polynomial" messagePrint " rc => Leading monomial of redcritpair polynomial" messagePrint " trc => Number of terms of redcritpair polynomial" messagePrint " tF => Number of polynomials in reduction list F" messagePrint " tD => Number of critpairs still to do" prinb 4 n := 2 prinb 1 a := 1 ph = 0 => ps = 0 => ll := [monomial(a,degree(cpi)),lepol(cpi),monomial(a,degree(cpj)), lepol(cpj),ps,0,ph,0,i1,i2]$Prinp print (ll)() prinb 1 n ll := [monomial(a,degree(cpi)),lepol(cpi),monomial(a,degree(cpj)), lepol(cpj),monomial(a,degree(ps)),lepol(ps),ph,0,i1,i2]$Prinp print (ll)() prinb 1 n ll := [monomial(a,degree(cpi)),lepol(cpi),monomial(a,degree(cpj)), lepol(cpj),monomial(a,degree(ps)),lepol(ps), monomial(a,degree(ph)),lepol(ph),i1,i2]$Prinp print (ll)() prinb 1 n prinpolINFO (pl:List Dpol):Void == import from Integer import from PositiveInteger n:Integer n := #pl::Integer prinb 1 n = 1 => messagePrint " There is 1 Groebner Basis Polynomial " prinb 2 messagePrint " There are " prinb 1 print (n) prinb 1 messagePrint " Groebner Basis Polynomials. " prinb 2 fprindINFO(cp:critPair(Expon, Dpol),ps:Dpol,ph:Dpol,i1:Integer,i2:Integer,i3:Integer,n: Integer ):Integer == import from PositiveInteger import from NonNegativeInteger ll:Prinpp a:Dom cpi := cp poli cpj := cp polj if n = 1 then prinb 1 messagePrint "you choose option -info- " messagePrint "abbrev. for the following information strings are" messagePrint " ci => Leading monomial for critpair calculation" messagePrint " tci => Number of terms of polynomial i" messagePrint " cj => Leading monomial for critpair calculation" messagePrint " tcj => Number of terms of polynomial j" messagePrint " c => Leading monomial of critpair polynomial" messagePrint " tc => Number of terms of critpair polynomial" messagePrint " rc => Leading monomial of redcritpair polynomial" messagePrint " trc => Number of terms of redcritpair polynomial" messagePrint " tF => Number of polynomials in reduction list F" messagePrint " tD => Number of critpairs still to do" messagePrint " tDF => Number of subproblems still to do" prinb 4 n := 2 prinb 1 a := 1 ph = 0 => ps = 0 => ll := [monomial(a,degree(cpi)),lepol(cpi),monomial(a,degree(cpj)), lepol(cpj),ps,0,ph,0,i1,i2,i3]$Prinpp print (ll)() prinb 1 n ll := [monomial(a,degree(cpi)),lepol(cpi),monomial(a,degree(cpj)), lepol(cpj),monomial(a,degree(ps)),lepol(ps),ph,0,i1,i2,i3]$Prinpp print (ll)() prinb 1 n ll := [monomial(a,degree(cpi)),lepol(cpi),monomial(a,degree(cpj)), lepol(cpj),monomial(a,degree(ps)),lepol(ps), monomial(a,degree(ph)),lepol(ph),i1,i2,i3]$Prinpp print (ll)() prinb 1 n