Changeset 8eb6da in git

Timestamp:

Nov 15, 2010, 10:29:11 AM (13 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')

Children:

7993adcf5a444486c5b07eacda51e7dfc6d67afc

Parents:

8b2ef529c04c7b3517f5001ff6c69e582bb9fd09

Message:

factoras  removed


git-svn-id: file:///usr/local/Singular/svn/trunk@13651 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

libfac/charset

Files:

• alg_factor.cc (modified) (3 diffs)
• algfactor.cc (modified) (1 diff)
• algfactor.h (modified) (1 diff)

libfac/charset/alg_factor.cc

@@ -117 +117 @@
 
 return resultant(fz,gz,v);
-
-  CanonicalForm h, beta, help, F, G;
-  int delta;
-
-  DEBOUTLN( CERR, "resultante: called  f= ", f);
-  DEBOUTLN( CERR, "resultante: called  g= ", g);
-  DEBOUTLN( CERR, "resultante: called  v= ", v);
-  if ( f.mvar() < v || g.mvar() < v ){
-    DEBOUTMSG(CERR, "resultante: f.mvar() < v || g.mvar() < v");
-    return 1;
-  }
-
-  if ( f.degree( v ) < 1 || g.degree( v ) < 1 ){
-    DEBOUTMSG(CERR, "resultante: f.degree( v ) < 1 || g.degree( v ) < 1");
-    // If deg(F,v) == 0 , then resultante(F,G,v) = F^n, where n=deg(G,v)
-    if ( f.degree( v ) < 1 ) return power(f,degree(g,v));
-    else return power(g,degree(f,v));
-  }
-
-   if ( f.degree( v ) >= g.degree( v ) ) { F = f; G = g; }
-   else { G = f; F = g; }
-
-  h = CanonicalForm(1);
-  while ( G != G.genZero() ) {
-     delta= degree(F,v) -degree(G,v);
-     beta = power(CanonicalForm(-1), delta+1) * LC(F,v)* power(h, delta);
-     h= (h * power(LC(G,v), delta)) / power(h, delta);
-     help= G;
-     G= mypsr(F,G,v);
-     G= G/beta;
-     F=help;
-   }
-   if ( degree(F,v) != 0 ) F= CanonicalForm(0);
-   return F;
 }
 
@@ -530 +496 @@
       if (degree(i.getItem().factor()) > 0 )
       {
-        // undo linear transformation!!!! and then gcd!
-        //CERR << "algcd(" << g << "," << fnew << ",as" << as << ")" << "\n";
-        //out_cf("g=",g,"\n");
-        //out_cf("fnew=",fnew,"\n");
-        //h= algcd(g,fnew, as, oldord);
-        //if (as.length() >1)
-        //  h= algcd(g,fnew, as, oldord);
-        //else
           h=alg_gcd(g,fnew,as);
-        //out_cf(" -> algcd=",algcd(g,fnew, as, oldord),"\n");
-        //out_cf(" -> alg_gcd=",alg_gcd(g,fnew,as),"\n");
-        //CERR << "algcd result:" << h << "\n";
         DEBOUTLN(CERR, "  alg_factor: h= ", h);
         DEBOUTLN(CERR, "  alg_factor: oldord= ", oldord);
         if ( degree(h) > 0 )
         { //otherwise it's a constant
-          //CanonicalForm c=LC(h,g.mvar());
-          //out_cf("new lc h:",c,"\n");
-          //h= divide(h,c,as);
-          //out_cf("new factor h/c:",h,"\n");
           g= divide(g, h,as);
           DEBOUTLN(CERR, "alg_factor: g/h= ", g);
@@ -736 +687 @@
   Varlist gcdord= Union(ord,newuord); gcdord.append(f.mvar());
   // This is for now. we need alg_sqrfree implemented!
-  //CERR << "algcd(" << f << "," << f.deriv() << " as:" << Astar <<"\n";
-  //CanonicalForm Fgcd= algcd(f,f.deriv(),Astar,gcdord);
   CanonicalForm Fgcd;
-        //if (Astar.length() >1)
-        //  Fgcd= algcd(f,f.deriv(),Astar,gcdord);
-        //else
           Fgcd= alg_gcd(f,f.deriv(),Astar);
-        //out_cf("algcd:",algcd(f,f.deriv(),Astar,gcdord),"\n");
-        //out_cf("alg_gcd:",alg_gcd(f,f.deriv(),Astar),"\n");
- // CERR << "algcd result:"  << Fgcd << "\n";
   if ( Fgcd == 0 ) DEBOUTMSG(CERR, "WARNING: p'th root ?");
   if (( degree(Fgcd, f.mvar()) > 0) && (!(f.deriv().isZero())) ){

libfac/charset/algfactor.cc

@@ -182 +182 @@
   return result;
 }
-
-CFFList
-factoras( const CanonicalForm & f, const CFList & as, int & success ){
-  Variable vf=f.mvar();
-  CFListIterator i;
-  CFFListIterator jj;
-  CFList reduceresult;
-  CFFList result;
-
-  DEBINCLEVEL(CERR, "factoras");
-  DEBOUTLN(CERR, "factoras called with f= ", f);
-  DEBOUTLN(CERR, "               content(f)= ", content(f));
-  DEBOUTLN(CERR, "                       as= ", as);
-  DEBOUTLN(CERR, "factoras: cls(vf)= ", cls(vf));
-  DEBOUTLN(CERR, "factoras: cls(as.getLast())= ", cls(as.getLast()));
-  DEBOUTLN(CERR, "factoras: degree(f,vf)= ", degree(f,vf));
-
-// F1: [Test trivial cases]
-// 1) first trivial cases:
-  if ( (cls(vf) <= cls(as.getLast())) ||
-       degree(f,vf)<=1
-// ||( (as.length()==1) && (degree(f,vf)==3) && (degree(as.getFirst()==2)) )
-       ){
-    success=1;
-    DEBDECLEVEL(CERR,"factoras");
-    return CFFList(CFFactor(f,1));
-  }
-
-
-// 2) List of variables:
-// 2a) Setup list of those polys in AS having degree(AS[i], AS[i].mvar()) > 1
-// 2b) Setup variableordering
-  CFList Astar;
-  Variable x;
-  CanonicalForm elem;
-  Varlist ord, uord,oldord;
-  for ( int ii=1; ii< level(vf) ; ii++ ) { uord.append(Variable(ii));  }
-  oldord= uord; oldord.append(vf);
-
-  for ( i=as; i.hasItem(); i++ ){
-    elem= i.getItem();
-    x= elem.mvar();
-    if ( degree(elem,x) > 1){ // otherwise it's not an extension
-      //if ( degree(f,x) > 0 ){ // does it occure in f? RICHTIG?
-        Astar.append(elem);
-        ord.append(x);
-        //}
-    }
-  }
-  uord= Difference(uord,ord);
-  DEBOUTLN(CERR, "Astar is: ", Astar);
-  DEBOUTLN(CERR, "ord is: ", ord);
-  DEBOUTLN(CERR, "uord is: ", uord);
-
-// 3) second trivial cases
-  if ( Astar.length() == 0 ){
-    success=1;
-    DEBDECLEVEL(CERR,"factoras");
-    return CFFList(CFFactor(f,1));
-  }
-
-// 4) Try to obtain a partial factorization using prop2 and prop3
-  // Not yet implemented
-
-// 5) choose (d_1, ..., d_s)
-  FFRandom gen;
-  if ( getCharacteristic() == 0 ) IntRandom gen(100);
-  REvaluation D(1, ord.length(), gen);
-  //D.nextpoint(); // first we use 0 as evaluation point
-
-F2: //[Characteristic set computation]
-// 6) Compute f^* (<- fstar)
-  CanonicalForm substhin=CanonicalForm(vf), substback=CanonicalForm(vf);
-  CanonicalForm monom;
-  DEBOUTLN(CERR, "substhin= ", substhin);
-  DEBOUTLN(CERR, "substback= ", substback);
-  int j=1;
-  for ( VarlistIterator jjj=ord; jjj.hasItem(); jjj++){
-    if ( getCharacteristic() > 0 ) monom= jjj.getItem()*D[j];
-    else  monom= mapinto(jjj.getItem()*mapinto(D[j]));
-    j++;
-    substhin-= monom; substback+= monom;
-  }
-  DEBOUTLN(CERR, "substhin= ", substhin);
-  DEBOUTLN(CERR, "substback= ", substback);
-  CanonicalForm fstar=f(substhin,vf);
-  DEBOUTLN(CERR, "fstar= ", fstar);
-
-// 7) Set up Variable ordering from ord,vf to vf,ord ! i.e. vf is the variable
-//    with lowest level.
-  Varlist nord=uord;
-  nord.append(vf); nord= Union(ord,nord);
-  DEBOUTLN(CERR, "          nord= ", nord);
-  CFList Astarnord= Astar; Astarnord.insert(fstar);
-  DEBOUTLN(CERR, "     Astarnord= ", Astarnord);
-  Astarnord= reorder(nord,Astarnord);
-  DEBOUTLN(CERR, "original Astar= ", Astar);
-  DEBOUTLN(CERR, "reorderd Astar= ", Astarnord);
-  DEBOUTLN(CERR, "             f= ", f);
-  DEBOUTLN(CERR, "         fstar= ", fstar);
-
-// 8) Compute Charset Cstar of Astar \cup { fstar } wrt. ordering {vf, ord}
-  PremForm Remembern;
-  CFList Cstar= MCharSetN(Astarnord, Remembern);
-  DEBOUTLN(CERR, " Cstar= ", Cstar );
-  DEBOUTLN(CERR, " Factors removed= ", Remembern.FS2 );
-  DEBOUTLN(CERR, " Possible Factors considered:= ", Remembern.FS1 );
-  DEBOUTLN(CERR, " Reorderd Cstar= ", reorder(nord,Cstar));
-
-// 9) Compute Delta: the set of all irr. factors (over K_0) of initials of
-//    Cstar
-  CFList iniset= initalset1(Cstar);
-  DEBOUTLN(CERR, "Set of initials: ", iniset);
-  CFFList Delta;
-  CFFList temp;
-  for ( i=iniset; i.hasItem(); i++){
-    Off(SW_RATIONAL);
-    temp= Factorize(i.getItem());
-    On(SW_RATIONAL);
-    temp.removeFirst();
-    Delta= Union(temp,Delta);
-  }
-  DEBOUTLN(CERR, "Delta= ", Delta);
-
-// 10) Compute Psi: the irreduzible factors (over K_0) of the first polynomial
-//     in Cstar, which are not factors of any polynomial in Delta
-  Off(SW_RATIONAL);
-  CFFList Psi=Factorize(Cstar.getFirst());
-  On(SW_RATIONAL);
-  Psi.removeFirst();
-  Psi= myDifference(Psi,Delta);
-  DEBOUTLN(CERR, "Psi= ", Psi);
-
-// F3: [Test quasilinearity]
-// If Cstar is quasilinear -> F4
-// else if Psi.length() > 1 then Delta<- Delta \cup Psi; Psi<- \emptyset -> F4
-// else D.nextpoint() -> F2
-  if ( isquasilinear(Cstar) ) {
-    DEBOUTLN(CERR, "Cstar is quasilinear; going to F4, Cstar= ", Cstar);
-    goto F4;
-  }
-  else if ( Psi.length() > 1 ){
-    Delta= Union(Psi,Delta);
-    Psi= CFFList();
-    DEBOUTMSG(CERR, "Psi.length() == 1; going to F4");
-    goto F4;
-  }
-  else{
-    D.nextpoint();
-    DEBOUTMSG(CERR, "Choosing next evaluation point. going to F2");
-    goto F2;
-  }
-
-F4: //[GCD Computation]
-  CanonicalForm g=f;
-  Delta= reorder(nord,Delta);
-  Psi= reorder(nord,Psi);
-  DEBOUTLN(CERR, "Reordered: Delta= ", Delta);
-  DEBOUTLN(CERR, "             Psi= ", Psi);
-  CanonicalForm fp;
-
-  DEBOUTMSG(CERR, "Testing Psi: this gives irreducible Factors!");
-  for (jj=Psi; jj.hasItem(); jj++){
-    if ( degree(g,vf) == 1 ) { // g is linear
-      break;
-    }
-    fp= jj.getItem().factor();
-    DEBOUT(CERR, "Calculating fp= gcd(", g);
-    DEBOUT(CERR, ",", fp(substback,vf));
-    DEBOUT(CERR, ") over K_r wrt ", vf);
-    fp=alg_gcd(g,fp(substback,vf), as);
-    //fp= algcd(g,fp(substback,vf), as, oldord);
-    DEBOUTLN(CERR, " = ", fp);
-    if ( degree(fp,vf) > 0 ){ //otherwise it's a constant
-      g= divide(g, fp,as);
-      DEBOUTLN(CERR, "f/fp= ", g);
-      result.append(CFFactor(fp,1));
-    }
-  }
-
-  DEBOUTMSG(CERR, "Testing Delta: this gives Factors (not nec. irreduzible!)");
-  for (jj=Delta; jj.hasItem(); jj++){
-    if ( degree(g,vf) <= 1 ) { // g is linear (or a constant..)
-      break;
-    }
-    fp= jj.getItem().factor();
-    DEBOUT(CERR, "Calculating fp= gcd(", g);
-    DEBOUT(CERR, ",", fp(substback,vf));
-    DEBOUT(CERR, ") over K_r wrt ", vf);
-    fp= alg_gcd(g,fp(substback,vf), as);
-    //fp= algcd(g,fp(substback,vf), as, oldord);
-    DEBOUTLN(CERR, " = ", fp);
-    if ( degree(fp,vf) > 0 ){ //otherwise it's a constant
-      g= divide(g, fp,as);
-      DEBOUTLN(CERR, "f/fp= ", g);
-//      reduceresult.append(fp); // a facctor but not nec. irreduzible
-      result.append(CFFactor(fp,1));
-      success=0;
-    }
-  }
-
-//  if (reduceresult.length() > 0){ //we have factors;
-//    for ( CFListIterator I=reduceresult; I.hasItem(); I++ ){
-//      // try to obtain an irreducible factorization
-//      result= Union( result,
-//                     factoras(I.getItem(), Astar, success) );
-//    }
-//  }
-
-  if ( result.length()==0 ){
-    if ( isquasilinear(Cstar) ){ // Cstar quasilinear => f is irreduzible
-      success=1;
-      DEBDECLEVEL(CERR,"factoras");
-      return CFFList(CFFactor(f,1));
-    }
-    else {
-      DEBOUTMSG(CERR, "Going to F2!");
-      D.nextpoint(); // choose a new set of int's.
-      goto F2;
-    }
-  }
-  // result.length() > 0 ==> we have factors!
-  success=1;
-  result.append(CFFactor(g,1)); //append the rest
-  DEBDECLEVEL(CERR,"factoras");
-  return result;
-}
-
-// for now: success=-1 no success, success=1   factored poly,
-// success = 0 factored poly partially
-CFFList
-cfactor(const CanonicalForm & f, const CFList & as, int success ){
-  Off(SW_RATIONAL);
-  CFFList Output, output, Factors=Factorize(f); On(SW_RATIONAL);
-  int csuccess=0;
-  Factors.removeFirst();
-
-  if ( as.length() == 0 ){ success=1; return Factors;}
-  if ( cls(f) <= cls(as.getLast()) ) { success=1; return Factors;}
-
-  success=1;
-  for ( CFFListIterator i=Factors; i.hasItem(); i++ ){
-    CFFList CERR=factoras(i.getItem().factor(),as,csuccess);
-    success= min(success,csuccess);
-    for ( CFFListIterator j=CERR; j.hasItem(); j++)
-      Output = myappend(Output,CFFactor(j.getItem().factor(),j.getItem().exp()*i.getItem().exp()));
-  }
-  return Output;
-}
-
-// Gegenbeispiel: char(k)=0 (original maple von wang):
-// f:= x^2*z^2-6909*x*z^2-3537*z^2-14344*x^2;
-// as:= [x^3-9977*x^2+15570*x-961]
-// ord:= [x,z]
-// cfactor(f,as,ord)=
-// -1/153600624478379*(-153600624478379*z^2+96784194432*x^2-246879593179080*x+
-// 13599716437688)*(x^2-6909*x-3537)
-//
-// maple:
-//  alias(alpha=RootOf(x^3-9977*x^2+15570*x-961,x));
-//  factor(f,alpha); // faktorisierung in char=0
-// x^2*z^2-6909*x*z^2-3537*z^2-14344*x^2
-

libfac/charset/algfactor.h

@@ -12 +12 @@
 
 CanonicalForm algcd(const CanonicalForm & f, const CanonicalForm & g, const CFList & as, const Varlist & order);
-CFFList factoras( const CanonicalForm & f, const CFList & as, int & success );
-CFFList cfactor(const CanonicalForm & f, const CFList & as, int success );
 /*BEGINPUBLIC*/
 int hasVar(const CanonicalForm &f, const Variable &v);