Changeset 67b671 in git

Timestamp:

Jun 29, 2019, 4:20:05 PM (5 years ago)

Author:

Sachin <sachinkm308@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

f2aefad298e7d312159153aa4bb4e8d8f2fe08b3

Parents:

d90fef85ca2c62d55b0f856b13bb352f199e2883

git-author:

Sachin <sachinkm308@gmail.com>2019-06-29 16:20:05+02:00

git-committer:

Andreas Steenpass <steenpass@mathematik.uni-kl.de>2019-07-01 14:09:41+02:00

Message:

Replaced execute with create_ring() functions

Location:

Singular/LIB

Files:

• ainvar.lib (modified) (2 diffs)
• alexpoly.lib (modified) (1 diff)
• ehv.lib (modified) (2 diffs)
• general.lib (modified) (1 diff)
• gitfan.lib (modified) (1 diff)
• grwalk.lib (modified) (6 diffs)
• hnoether.lib (modified) (8 diffs)
• linalg.lib (modified) (1 diff)
• matrix.lib (modified) (2 diffs)
• modwalk.lib (modified) (1 diff)
• mprimdec.lib (modified) (6 diffs)
• normal.lib (modified) (3 diffs)
• poly.lib (modified) (1 diff)
• primdec.lib (modified) (13 diffs)
• primdecint.lib (modified) (2 diffs)
• primitiv.lib (modified) (1 diff)
• schubert.lib (modified) (2 diffs)
• teachstd.lib (modified) (1 diff)

Singular/LIB/ainvar.lib

@@ -102 +102 @@
 
   //changes the basering bsr to bsr[@t]
-  execute("ring s="+charstr(basering)+",("+varstr(basering)+",@t),dp;");
+  ring s = create_ring(ringlist(basering)[1],"("+varstr(basering)+",@t)","dp","no_minpoly");
   poly inv,delta,tee,j;
   ideal id=imap(bsr,id);
@@ -214 +214 @@
 
   //------------- changes the basering bsr to bsr[@(0),...,@(z)] ----------
-  execute("ring s="+charstr(basering)+",("+varstr(basering)+",@(0..z)),dp;");
-
+  ring s = create_ring(ringlist(basering)[1],"("+varstr(basering)+",@(0..z))","dp","no_minpoly");
   //constructs the leading ideal of dom=(p-@(0),dom[1]-@(1),...,dom[z]-@(z))
      ideal dom=imap(bsr,dom);

Singular/LIB/alexpoly.lib

@@ -657 +657 @@
   int e=ncols(gr);
   // Define the Ring for the Alexander Polynomial and the Zeta Function of the Monodromy.
-  execute("ring ALEXring=("+charstr(basering)+"),(t,t(1..r)),dp;");
+  ring ALEXring = create_ring(ringlist(basering)[1],"(t,t(1..r))","dp","no_minpoly");
   poly hilfspoly=1;
   poly alexnumerator=1;    // numerator of the Alexander polynomial

Singular/LIB/ehv.lib

@@ -742 +742 @@
                   poly g1 = L[1][1];
                   //..and insert f in g1...
-                  execute("ring newR = (" + charstr(R) + "),(y(1)),(" + ordstr(R) + ");");
-                  poly g2 = imap(R,g1);
+                  ring newR = create_ring(ringlist(R)[1], "(y(1))", "(" + ordstr(R) + ")", "no_minpoly");
+                  poly g2 = imap(R,g1);
                   setring base;
                   h = fetch(newR,g2);
@@ -1039 +1039 @@
               ideal homoJ = fetch(base,K);
               homoJ = groebner(homoJ);
-              execute("ring newR = (" + charstr(base) + "),(x(1..n),t),dp;");
-              ideal homoK = fetch(homoR,homoJ);
+              ring newR = create_ring(ringlist(base)[1], "(x(1..n),t)", "dp", "no_minpoly");
+              ideal homoK = fetch(homoR,homoJ);
               homoK = homog(homoK,t);
               attrib(homoK,"isEquidimensional",1);

Singular/LIB/general.lib

@@ -709 +709 @@
       if ( typeof(#[1])=="string" )
       {
-         execute("ring r1 =("+charstr(P)+"),("+varstr(P)+"),("+#[1]+");");
+         ring r1 = create_ring(ringlist(P)[1],"("+varstr(P)+")","("+#[1]+")","no_minpoly");
          def i = imap(P,id);
          v = sortvec(i);

Singular/LIB/gitfan.lib

@@ -266 +266 @@
   newVars = newVars+string(var(k));
   newWeightVector[n]=weightVector[k];
-  execute("ring ringForSaturation = ("+charstr(origin)+"),("+newVars+"),(wp(newWeightVector));");
-
+  ring ringForSaturation = create_ring(ringlist(origin)[1],"("+newVars+")","(wp(newWeightVector))","no_minpoly");
   ideal I = satstd(imap(origin,I));
   I = simplify(I,2+4+32);

Singular/LIB/grwalk.lib

@@ -236 +236 @@
    def xR = basering;
 
-   execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+   ring ostR = create_ring(ringlist(xR)[1],"("+varstr(xR)+")",ord_str,"no_minpoly");
+   
    def old_ring = basering;
 
@@ -292 +293 @@
    def xR = basering;
 
-   execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+   ring ostR = create_ring(ringlist(xR)[1],"("+varstr(xR)+")",ord_str,"no_minpoly");
    def old_ring = basering;
    //print("//** help ring = " + string(basering));
@@ -328 +329 @@
    option(redSB);
    def xR = basering;
-
-   execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+   ring ostR = create_ring(ringlist(xR)[1],"("+varstr(xR)+")",ord_str,"no_minpoly");
    def old_ring = basering;
    //print("//** help ring = " + string(basering));
@@ -377 +377 @@
    option(redSB);   def xR = basering;
 
-   execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+   ring ostR = create_ring(ringlist(xR)[1],"("+varstr(xR)+")",ord_str,"no_minpoly");
    def old_ring = basering;
 
@@ -435 +435 @@
   def xR = basering;
 
-  execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+  ring ostR = create_ring(ringlist(xR)[1],"("+varstr(xR)+")",ord_str,"no_minpoly");
   def old_ring = basering;
 
@@ -483 +483 @@
   def xR = basering;
 
-  execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+  ring ostR = create_ring(ringlist(xR)[1],"("+varstr(xR)+")",ord_str,"no_minpoly");
   def old_ring = basering;
 

Singular/LIB/hnoether.lib

@@ -281 +281 @@
   //if ((char(basering)!=0) and (charstr(basering)!=string(char(basering))))
   int gcd_ok= ! hasGFCoefficient(basering);
-  execute("ring rsqrf = ("+charstr(altring)+"),(x,y),dp;");
+  ring rsqrf = create_ring(ringlist(altring)[1],"(x,y)","dp","no_minpoly");
   if ((gcd_ok!=0) && (mipl!="0")) { execute("minpoly="+mipl+";"); }
   poly f=fetch(altring,f);
@@ -365 +365 @@
    ERROR(" Sorry -- not implemented for this ring (gcd doesn't work)");
  }
- execute("ring rsqrf = ("+charstr(altring)+"),(x,y),dp;");
+ ring rsqrf = create_ring(ringlist(altring)[1],"(x,y)","dp","no_minpoly");
  if (mipl!="0") { execute("minpoly="+mipl+";"); }
  poly f=fetch(altring,f);
@@ -552 +552 @@
  if (ringwechsel) {
    string mipl=string(minpoly);
-   execute("ring guenstig = ("+charstr(altring)+"),(x,y),ls;");
+   ring guenstig = create_ring(ringlist(altring)[1],"(x,y)","ls","no_minpoly");
    if ((char(basering)==0) && (mipl!="0")) {
      execute("minpoly="+mipl+";");
@@ -2168 +2168 @@
   {
     def @Rold=basering;
-    execute("ring @RR=("+charstr(basering)+"),("+varstr(basering)+"),ls;");
+    ring @RR = create_ring(ringlist(basering)[1],"("+varstr(basering)+")","ls","no_minpoly");
     poly f=imap(@Rold,f);
   }
@@ -2457 +2457 @@
      {
        if (npars(basering)>1) {         // ring (p,a,..),...
-        execute("ring extdguenstig=("+charstr(basering)+"),(x,y),ls;");
-       }
+        ring extdguenstig = create_ring(ringlist(basering)[1],"(x,y)","ls","no_minpoly");
+     }
        else {                                  // ring (p,a),...
         string mipl=string(minpoly);
@@ -2466 +2466 @@
      }
      else {
-       execute("ring extdguenstig=("+charstr(basering)+"),(x,y),ls;");
+       ring extdguenstig = create_ring(ringlist(basering)[1],"(x,y)","ls","no_minpoly");
      }
   }
@@ -2922 +2922 @@
      "// ** extension occurs during the calculation, we cannot proceed with";
      "// ** the corresponding branches.";
-     execute("ring HNEring=("+charstr(basering)+"),(x,y),ls;");
+     ring HNEring = create_ring(ringlist(basering)[1],"(x,y)","ls","no_minpoly");
    }
    else {
@@ -4053 +4053 @@
    { // Ringwechsel hatte stattgefunden
      string mipl_alt = string(minpoly);
-     execute("ring tempRing = ("+charstr(basering)+"),("+varstr(basering)+
-                              "),("+ordstr(basering)+");");
+     ring tempRing = create_ring(ringlist(basering)[1],"("+varstr(basering)+")","("+ordstr(basering)+")","no_minpoly");
      execute("minpoly="+ mipl_alt +";");
      list HNEs=imap(EXTHNEring(EXTHNEnumber),HNEs);

Singular/LIB/linalg.lib

@@ -370 +370 @@
   def BR=basering;
   //setze R[t]
-  execute("ring rt=("+charstr(basering)+"),(@t,"+varstr(basering)+"),lp;");
+  ring rt = create_ring(ringlist(basering)[1], "(@t,"+varstr(basering)+")", "lp", "no_minpoly");
   execute("minpoly="+mp+";");
   matrix A=imap(BR,A);

Singular/LIB/matrix.lib

@@ -1068 +1068 @@
 
 //------------------------- create ring container for symmetric power basis-
-  execute("ring @@@SYM_POWER_RING_NAME=(0),("+S+"(1.."+string(n)+")),dp;");
-
+  ring @@@SYM_POWER_RING_NAME = create_ring(0,"("+S+"(1.."+string(n)+"))","dp","no_minpoly");
 //------------------------- choose symmetric basis -------------------------
   ideal symBasis = maxideal(k);
@@ -1116 +1115 @@
 
 //------------------------- create ring container for symmetric power basis-
-  execute("ring @@@EXT_POWER_RING_NAME=(0),("+S+"(1.."+string(n)+")),dp;");
+  ring @@@EXT_POWER_RING_NAME = create_ring(0,"("+S+"(1.."+string(n)+"))","dp","no_minpoly");
 
 //------------------------- choose exterior basis -------------------------

Singular/LIB/modwalk.lib

@@ -481 +481 @@
    ideal xI = args[1];
    ring xR = basering;
-   execute("ring yR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";");
+   ring yR = create_ring(ringlist(xR)[1], "("+varstr(xR)+")", ord_str, "no_minpoly");
    ideal yI = fetch(xR,xI);
    ideal yresult = fetch(xR,result);

Singular/LIB/mprimdec.lib

@@ -283 +283 @@
 
       @U[size(@U)]=")";           // we compute the extractor (w.r.t. @U)
-      execute("ring RAU="+charstr(basering)+",("+@A+@U+",(C,dp("+string(szA)+"),dp);");
+      ring RAU = create_ring(ringlist(basering)[1],"("+@A+@U,"(C,dp("+string(szA)+"),dp)","no_minpoly");
       module @N=std(imap(BAS,@N));
                                   // this is also a standard basis in (R[U])[A]
@@ -670 +670 @@
   }
   @U[size(@U)]=")";             // we compute the extractor (w.r.t. @U)
-  execute("ring RAU="+charstr(basering)+",("+@A+@U+",(C,dp("+string(szA)+"),dp);");
+  ring RAU = create_ring(ringlist(basering)[1],"("+@A+@U,"(C,dp("+string(szA)+"),dp)","no_minpoly");
   module @N=std(imap(BAS,@N));  // this is also a standard basis in (R[U])[A]
   @A[size(@A)]=")";
@@ -773 +773 @@
      }
   }
-  execute("ring PRing="+string(char(basering))+",("+strg+varstr(basering)+"),dp");
+  ring PRing = create_ring(ringlist(basering)[1],"("+strg+varstr(basering)+")","dp","no_minpoly");
   ideal @a=ideal(imap(LBAS,@i),imap(LBAS,@j));
   poly @p=lcm(@a);
@@ -1494 +1494 @@
        newva[size(newva)]=")";
        newma[size(newma)]=";";
-       execute("ring @deirf=("+charstr(BAS)+"),("+newva+",(C,lp);");
+       ring @deirf = create_ring(ringlist(BAS)[1],"("+newva,"(C,lp)","no_minpoly");
        execute("map @kappa=BAS,"+newma);
        ideal @j = @kappa(ann);
@@ -1551 +1551 @@
     for (@k2=1;@k2<=szIndep;@k2++)
     {
-      execute("ring RAU=("+charstr(basering)+"),("+indep[@k1][@k2][1]+","+indep[@k1][@k2][2]+"),"+indep[@k1][@k2][3]+";");
+      ring RAU = create_ring(ringlist(basering)[1],"("+indep[@k1][@k2][1]+","+indep[@k1][@k2][2]+")","indep[@k1][@k2][3]","no_minpoly");
       module @N=std(imap(BAS,@N)); // the standard basis in (R[U])[A]
       execute("ring Rloc=("+charstr(basering)+","+indep[@k1][@k2][2]+"),("+indep[@k1][@k2][1]+"),(C,dp);");
@@ -2153 +2153 @@
    if(ordstr(basering)[1,2]!="dp")
    {
-      execute("ring @Phelp=("+charstr(@P)+"),("+varstr(@P)+"),(C,dp);");
+      ring @Phelp = create_ring(ringlist(@P)[1],"("+varstr(@P)+")","(C,dp)","no_minpoly");
       module inew=std(imap(@P,id));
       ideal  @h=imap(@P,h1);

Singular/LIB/normal.lib

@@ -2417 +2417 @@
    poly p=I[1];
 
-   execute("ring S=("+charstr(R)+"),(x,y,t),dp;");
+   ring S = create_ring(ringlist(R)[1],"(x,y,t)","dp","no_minpoly");
    ideal L=maxideal(1);
-   execute("ring C=("+charstr(R)+"),(x,y),ds;");
+   ring C = create_ring(ringlist(R)[1], "(x,y)", "ds", "no_minpoly");
    ideal I;
-   execute("ring A=("+charstr(R)+"),(x,t),dp;");
+   ring A = create_ring(ringlist(R)[1], "(x,t)", "dp", "no_minpoly");
    map phi=S,1,x,t;
    map psi=S,x,1,t;
    poly g,h;
    ideal I,I1;
-   execute("ring B=("+charstr(R)+"),(x,t),ds;");
-
+   ring B = create_ring(ringlist(R)[1], "(x,t)", "ds", "no_minpoly");
    setring S;
    if(o)
@@ -2505 +2504 @@
       "singularities at (x,y,1):";"";
    }
-   execute("ring newR=("+charstr(R)+"),(x,y),dp;");
+   ring newR = create_ring(ringlist(R)[1], "(x,y)", "dp", "no_minpoly");
    //the singularities at the affine part
    map sigma=S,var(1),var(2),1;
@@ -2720 +2719 @@
       }
 
-      execute("ring B=("+charstr(S)+"),a,dp;");
+      ring B = create_ring(ringlist(R)[1], "(a)", "dp", "no_minpoly");
       map beta=S,a,a;
       poly p=beta(p);
 
-      execute("ring C=("+charstr(S)+",a),(x,y),ds;");
+      list L1 = char(S), list("a"), list(list("lp", intvec(1))), ideal(0);
+      ring C = create_ring(L1, "(x,y)", "ds");  
       minpoly=number(imap(B,p));
 

Singular/LIB/poly.lib

@@ -730 +730 @@
   if (attrib(br,"global")==1)
   {
-    execute("ring R=("+charstr(br)+"),(@x(1..n),@z),dp;");
+    ring R = create_ring(ringlist(br)[1],"(@x(1..n),@z)","dp","no_minpoly");
   }
   else

Singular/LIB/primdec.lib

@@ -2564 +2564 @@
 
   indep=maxIndependSet(j);
-
-  execute("ring gnir1 = ("+charstr(basering)+"),("+indep[1][1]+"),("
-                              +indep[1][2]+");");
+  ring gnir1 = create_ring(ringlist(basering)[1],"("+indep[1][1]+")","("+indep[1][2]+")","no_minpoly");
   if(homo==1)
   {
@@ -3112 +3110 @@
       newva[size(newva)]=")";
       newma[size(newma)]=";";
-      execute("ring @deirf=("+charstr(gnir)+"),("+newva+",lp;");
+      ring @deirf = create_ring(ringlist(gnir)[1],"("+newva,"lp","no_minpoly");
       execute("map @kappa=gnir,"+newma);
       ideal @j= @kappa(@j);
@@ -3337 +3335 @@
         @j=fetch(@P,i);
       }
-      execute("ring gnir1 = ("+charstr(basering)+"),("+indep[@m][1]+"),("
-                              +indep[@m][2]+");");
+      ring gnir1 = create_ring(ringlist(basering)[1],"("+indep[@m][1]+")","("+indep[@m][2]+")","no_minpoly");
       execute("map phi=gnir,"+@va+";");
       op=option(get);
@@ -3646 +3643 @@
         {
           @va=string(maxideal(1));
-          execute("ring gnir1 = ("+charstr(basering)+"),("+
-                      restindep[@m][1]+"),(" +restindep[@m][2]+");");
+          ring gnir1 = create_ring(ringlist(basering)[1],"("+restindep[@m][1]+")","("+restindep[@m][2]+")","no_minpoly");
           execute("map phi=gnir,"+@va+";");
           op=option(get);
@@ -4614 +4610 @@
   def oldring=basering;
   string n=system("neworder",PS);
-  execute("ring r=("+charstr(oldring)+"),("+n+"),dp;");
+  ring r = create_ring(ringlist(oldring)[1],"("+n+")","dp","no_minpoly");
   ideal PS=imap(oldring,PS);
   matrix m=char_series(PS);  // We compute an irreducible
@@ -4629 +4625 @@
     for(i=1;i<nvars(oldring);i++) { n=n+","+string(var(i)); }
     kill r;
-    execute("ring r=("+charstr(oldring)+"),("+n+"),dp;");
+    ring r = create_ring(ringlist(oldring)[1],"("+n+")","dp","no_minpoly");
     ideal PS=imap(oldring,PS);
     matrix m=char_series(PS);
@@ -5272 +5268 @@
 
       U[size(U)]=")";           // we compute the extractor of I (w.r.t. U)
-      execute("ring RAU=("+charstr(basering)+"),("+A+U+",(dp("+string(a)+"),dp);");
+      ring RAU = create_ring(ringlist(basering)[1],"("+A+U,"(dp("+string(a)+"),dp)","no_minpoly");
       ideal I=imap(R,SI);
       //I=std(I,hv);            // the standard basis in (R[U])[A]
@@ -6763 +6759 @@
       @va = string(maxideal(1));
 
-      execute("ring gnir1 = (" + charstr(basering) + "), (" + indep[@m][1] + "),("
-                              + indep[@m][2] + ");");
+      ring gnir1 = create_ring(ringlist(basering)[1],"(" + indep[@m][1] + ")","(" + indep[@m][2] + ")","no_minpoly");
       execute("map phi = @P," + @va + ";");
       ideal @j = groebner(phi(I));
@@ -7325 +7320 @@
     string(timer-time));
 //---------------- compute characteristic polynomial of matrix --------------
-  execute("ring P1=("+charstr(R)+"),T,dp;");
+  ring P1 = create_ring(ringlist(R)[1],"T","dp","no_minpoly");
   matrix n=imap(R,n);
   time = timer;
@@ -7355 +7350 @@
 //Hence it is better to simultaneously reduce with I. For this we need a new
 //ring.
-    execute("ring P=("+charstr(R)+"),(T,"+varstr(R)+"),(dp(1),dp);");
+    ring P = create_ring(ringlist(R)[1],"(T,"+varstr(R)+")","(dp(1),dp)","no_minpoly");
     list rfac=imap(P1,fac);
     intvec ov=option(get);;
@@ -7652 +7647 @@
       newva[size(newva)]=")";
       newma[size(newma)]=";";
-      execute("ring @deirf=("+charstr(gnir)+"),("+newva+",lp;");
+      ring @deirf = create_ring(ringlist(gnir)[1],"("+newva,"lp","no_minpoly");
       execute("map @kappa=gnir,"+newma);
       ideal @j= @kappa(@j);
@@ -8043 +8038 @@
           {
              @va=string(maxideal(1));
-             execute("ring gnir1 = ("+charstr(basering)+"),("+
-                     restindep[@m][1]+"),(" +restindep[@m][2]+");");
+             ring gnir1 = create_ring(ringlist(basering)[1],"(" +restindep[@m][1]+")","(" +restindep[@m][2]+")","no_minpoly");
              execute("map phi=gnir,"+@va+";");
              op=option(get);
@@ -8387 +8381 @@
      //}
 //=======================
-     execute("ring gnir1 = ("+charstr(basering)+"),("+indepInfo[1]+"),("
-                              +indepInfo[2]+");");
+     ring gnir1 = create_ring(ringlist(basering)[1],"("+indepInfo[1]+")","(" +indepInfo[2]+")","no_minpoly");
      execute("map phi=gnir,"+@va+";");
      op=option(get);

Singular/LIB/primdecint.lib

@@ -1241 +1241 @@
    //=== K[i]/f; does not work in rings with integer! This should be replaced
    //=== later
-   execute("ring Rhelp=0,("+varstr(R)+"),dp;");
+   ring Rhelp = create_ring(0,"("+varstr(R)+")","dp","no_minpoly");
    ideal K=imap(R,K);
    poly f=imap(R,f);
@@ -1282 +1282 @@
    if (not attrib(I,"isSB") ) { print ("// ** I is no standard basis"); }
    def R=basering;
-   execute("ring Rhelp=0,("+varstr(R)+"),dp;");
+   ring Rhelp = create_ring(0,"("+varstr(R)+")","dp","no_minpoly");
    ideal I=imap(R,I);
    poly f=imap(R,f);

Singular/LIB/primitiv.lib

@@ -40 +40 @@
 {
  def altring=basering;
- execute("ring deglexring=("+charstr(altring)+"),("+varstr(altring)+"),dp;");
+ ring deglexring = create_ring(ringlist(altring)[1],"("+varstr(altring)+")","dp","no_minpoly");
  ideal j;
- execute("ring lexring=("+charstr(altring)+"),("+varstr(altring)+"),lp;");
+ ring lexring = create_ring(ringlist(altring)[1],"("+varstr(altring)+")","lp","no_minpoly");
  ideal i=fetch(altring,i);
 

Singular/LIB/schubert.lib

@@ -1907 +1907 @@
     variety P;
     P.dimension = n;
-    execute("ring r = 0, ("+h+"), wp(1);");
+    ring r = create_ring(0,"("+h+")","wp(1)","no_minpoly");
     setring r;
     P.baseRing = r;
@@ -1965 +1965 @@
     A.dimension = r - 1 + B.dimension;
     poly c = totalChernClass(S);
-    execute("ring P = 0, ("+z+"), wp(1);");
+    ring P = create_ring(0,"("+z+")","wp(1)","no_minpoly");
     def CR = P + R;
     setring CR;

Singular/LIB/teachstd.lib

@@ -757 +757 @@
   int ii;
   def bas = basering;
-  execute("ring  @r_locstd
-     =("+charstr(bas)+"),(local@t,"+varstr(bas)+"),(dp(1),dp);");
+  ring @r_locstd = create_ring(ringlist(bas)[1],"(local@t,"+varstr(bas)+")","(dp(1),dp)","no_minpoly");
   ideal id = imap(bas,id);
   ideal hid = homog(id,local@t);