===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/kanExport0.c,v
retrieving revision 1.9
retrieving revision 1.36
diff -u -p -r1.9 -r1.36
--- OpenXM/src/kan96xx/Kan/kanExport0.c	2002/09/08 10:49:49	1.9
+++ OpenXM/src/kan96xx/Kan/kanExport0.c	2004/09/16 02:22:03	1.36
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/kan96xx/Kan/kanExport0.c,v 1.8 2002/02/24 10:27:18 takayama Exp $  */
+/* $OpenXM: OpenXM/src/kan96xx/Kan/kanExport0.c,v 1.35 2004/09/15 06:40:26 takayama Exp $  */
 #include <stdio.h>
 #include "datatype.h"
 #include "stackm.h"
@@ -19,6 +19,7 @@ int SerialCurrent = -1;  /* Current Serial number of t
 
 int ReverseOutputOrder = 1;  
 int WarningNoVectorVariable = 1;
+extern int QuoteMode;
 
 /** :arithmetic **/
 struct object KooAdd(ob1,ob2)
@@ -142,7 +143,11 @@ struct object KooAdd(ob1,ob2)
     
 
   default:
-    warningKan("KooAdd() has not supported yet these objects.\n");
+    if (QuoteMode) {
+      rob = addTree(ob1,ob2);
+    }else{
+      warningKan("KooAdd() has not supported yet these objects.\n");
+    }
     break;
   }
   return(rob);
@@ -270,7 +275,11 @@ struct object KooSub(ob1,ob2)
     break;
 
   default:
-    warningKan("KooSub() has not supported yet these objects.\n");
+    if (QuoteMode) {
+      rob = minusTree(ob1,ob2);
+    }else{
+      warningKan("KooSub() has not supported yet these objects.\n");
+    }
     break;
   }
   return(rob);
@@ -412,7 +421,11 @@ struct object KooMult(ob1,ob2)
     break;
 
   default:
-    warningKan("KooMult() has not supported yet these objects.\n");
+    if (QuoteMode) {
+      rob = timesTree(ob1,ob2);
+    }else{
+      warningKan("KooMult() has not supported yet these objects.\n");
+    }
     break;
   }
   return(rob);
@@ -451,7 +464,11 @@ struct object KoNegate(obj)
     break;
 
   default:
-    warningKan("KoNegate() has not supported yet these objects.\n");
+    if (QuoteMode) {
+      rob = unaryminusTree(obj);
+    }else{
+      warningKan("KoNegate() has not supported yet these objects.\n");
+    }
     break;
   }
   return(rob);
@@ -653,7 +670,11 @@ struct object KooDiv(ob1,ob2)
 
 
   default:
-    warningKan("KooDiv() has not supported yet these objects.\n");
+    if (QuoteMode) {
+      rob = divideTree(ob1,ob2);
+    }else{
+      warningKan("KooDiv() has not supported yet these objects.\n");
+    }
     break;
   }
   return(rob);
@@ -666,8 +687,16 @@ KooEqualQ(obj1,obj2)
 {
   struct object ob;
   int i;
+  extern int Verbose;
   if (obj1.tag != obj2.tag) {
     warningKan("KooEqualQ(ob1,ob2): the datatypes of ob1 and ob2  are not same. Returns false (0).\n");
+	if (Verbose & 0x10) {
+	  fprintf(stderr,"obj1(tag:%d)=",obj1.tag);
+	  printObject(obj1,0,stderr);
+	  fprintf(stderr,", obj2(tag:%d)=",obj2.tag);
+	  printObject(obj2,0,stderr);
+	  fprintf(stderr,"\n"); fflush(stderr);
+	}
     return(0);
   }
   switch(obj1.tag) {
@@ -776,6 +805,21 @@ struct object KooGreater(obj1,obj2)
     if ( KopDouble(obj1) > KopDouble(obj2) ) return(KpoInteger(1));
     else return(KpoInteger(0));
     break;
+  case Sarray:
+  {
+    int i,m1,m2;
+    struct object rr;
+    m1 = getoaSize(obj1); m2 = getoaSize(obj2);
+    for (i=0; i< (m1>m2?m2:m1); i++) {
+      rr=KooGreater(getoa(obj1,i),getoa(obj2,i));
+      if (KopInteger(rr) == 1) return rr;
+      rr=KooGreater(getoa(obj2,i),getoa(obj1,i));
+      if (KopInteger(rr) == 1) return KpoInteger(0);
+    }
+    if (m1 > m2) return KpoInteger(1);
+    else return KpoInteger(0);
+  }
+  break;
   default:
     errorKan1("%s\n","KooGreater() has not supported these objects yet.");
     break;
@@ -817,6 +861,21 @@ struct object KooLess(obj1,obj2)
     if ( KopDouble(obj1) < KopDouble(obj2) ) return(KpoInteger(1));
     else return(KpoInteger(0));
     break;
+  case Sarray:
+  {
+    int i,m1,m2;
+    struct object rr;
+    m1 = getoaSize(obj1); m2 = getoaSize(obj2);
+    for (i=0; i< (m1>m2?m2:m1); i++) {
+      rr=KooLess(getoa(obj1,i),getoa(obj2,i));
+      if (KopInteger(rr) == 1) return rr;
+      rr=KooLess(getoa(obj2,i),getoa(obj1,i));
+      if (KopInteger(rr) == 1) return KpoInteger(0);
+    }
+    if (m1 < m2) return KpoInteger(1);
+    else return KpoInteger(0);
+  }
+  break;
   default:
     errorKan1("%s\n","KooLess() has not supported these objects yet.");
     break;
@@ -868,6 +927,10 @@ struct object KdataConversion(obj,key)
       return(rob);
     }else if (strcmp(key,"poly") == 0) {
       rob = KpoPOLY(ZERO);
+      return rob;
+    }else if (strcmp(key,"array") == 0) {
+      rob = newObjectArray(0);
+      return rob;
     }else{
       warningKan("Sorry. The data conversion from null to this data type has not supported yet.\n");
     }
@@ -893,8 +956,7 @@ struct object KdataConversion(obj,key)
       strcpy(rob.lc.str,intstr);
       return(rob);
     }else if (strcmp(key,"universalNumber")==0) {
-      rob.tag = SuniversalNumber;
-      rob.lc.universalNumber = intToCoeff(obj.lc.ival,&SmallRing);
+      rob = KintToUniversalNumber(obj.lc.ival);
       return(rob);
     }else if (strcmp(key,"double") == 0) {
       rob = KpoDouble((double) (obj.lc.ival));
@@ -965,7 +1027,7 @@ struct object KdataConversion(obj,key)
     if (strcmp(key,"array") == 0) {
       return(rob);
     }else if (strcmp(key,"list") == 0) {
-      rob = *( arrayToList(obj) );
+      rob = KarrayToList(obj);
       return(rob);
     }else if (strcmp(key,"arrayOfPOLY")==0) {
       rob = KpoArrayOfPOLY(arrayToArrayOfPOLY(obj));
@@ -980,11 +1042,19 @@ struct object KdataConversion(obj,key)
       rob = NullObject;
       return(rob);
     }else {
-      warningKan("Sorry. This type of data conversion has not supported yet.\n");
+	  { /* Automatically maps the elements. */
+		int n,i;
+		n = getoaSize(obj);
+		rob = newObjectArray(n);
+		for (i=0; i<n; i++) {
+		  putoa(rob,i,KdataConversion(getoa(obj,i),key));
+		}
+		return(rob);
+	  }
     }
     break;
   case Spoly:
-    if (strcmp(key,"poly")==0) {
+    if ((strcmp(key,"poly")==0) || (strcmp(key,"numerator")==0)) {
       rob = obj;
       return(rob);
     }else if (strcmp(key,"integer")==0) {
@@ -1050,12 +1120,13 @@ struct object KdataConversion(obj,key)
     break;
   case Slist:
     if (strcmp(key,"array") == 0) {
-      rob = listToArray(&obj);
+      rob = KlistToArray(obj);
       return(rob);
     }
     break;
   case SuniversalNumber:
-    if (strcmp(key,"universalNumber")==0) {
+    if ((strcmp(key,"universalNumber")==0) || (strcmp(key,"numerator")==0)) {
+      rob = obj;
       return(rob);
     }else if (strcmp(key,"integer")==0) {
       rob = KpoInteger(coeffToInt(obj.lc.universalNumber));
@@ -1073,6 +1144,9 @@ struct object KdataConversion(obj,key)
     }else if (strcmp(key,"double") == 0) {
       rob = KpoDouble( toDouble0(obj) );
       return(rob);
+    }else if (strcmp(key,"denominator") == 0) {
+      rob = KintToUniversalNumber(1);
+      return(rob);
     }else{
       warningKan("Sorry. This type of data conversion of universalNumber has not supported yet.\n");
     }
@@ -1137,6 +1211,9 @@ struct object KdataConversion(obj,key)
     if (strcmp(key,"orderMatrix")==0) {
       rob = oGetOrderMatrix(KopRingp(obj));
       return(rob);
+    }else if (strcmp(key,"oxRingStructure")==0) {
+      rob = oRingToOXringStructure(KopRingp(obj));
+      return(rob);
     }else{
       warningKan("Sorryl This type of data conversion of ringp has not supported yet.\n");
     }
@@ -1146,7 +1223,24 @@ struct object KdataConversion(obj,key)
   }
   return(NullObject);
 }
-    
+
+/* cf. macro to_int32 */
+struct object Kto_int32(struct object ob) {
+  int n,i;
+  struct object otmp;
+  struct object rob;
+  if (ob.tag == SuniversalNumber) return KdataConversion(ob,"integer");
+  if (ob.tag == Sarray) {
+	n = getoaSize(ob);
+	rob = newObjectArray(n);
+	for (i=0; i<n; i++) {
+	  otmp = Kto_int32(getoa(ob,i));
+	  putoa(rob,i,otmp);
+	}
+	return rob;
+  }
+  return ob;
+}    
 /* conversion functions between primitive data and objects.
    If it's not time critical, it is recommended to use these functions */
 struct object KpoInteger(k)
@@ -1200,6 +1294,24 @@ struct object KpoRingp(ringp)
   return(obj);
 }
 
+struct object KpoUniversalNumber(u)
+     struct coeff *u;
+{
+  struct object obj;
+  obj.tag = SuniversalNumber;
+  obj.lc.universalNumber = u;
+  return(obj);
+}
+struct object KintToUniversalNumber(n)
+	 int n;
+{
+  struct object rob;
+  extern struct ring SmallRing;
+  rob.tag = SuniversalNumber;
+  rob.lc.universalNumber = intToCoeff(n,&SmallRing);
+  return(rob);
+}
+
 /*** conversion 2. Data conversions on arrays and matrices. ****/
 struct object arrayOfPOLYToArray(aa)
      struct arrayOfPOLY *aa;
@@ -1496,7 +1608,8 @@ int KsetUpRing(ob1,ob2,ob3,ob4,ob5)
       outputVars[i] = i;
     }
   }
-  
+
+  ob4 = Kto_int32(ob4); /* order matrix */
   oasize = getoaSize(ob4);
   order = (int *)sGC_malloc(sizeof(int)*((2*n)*oasize+1));
   if (order == (int *)NULL) errorKan1("%s\n","No memory.");
@@ -1538,6 +1651,11 @@ int KsetUpRing(ob1,ob2,ob3,ob4,ob5)
   newRingp->gbListTower = NULL;
   newRingp->outputOrder = outputVars;
   newRingp->weightedHomogenization = 0;
+  newRingp->degreeShiftSize = 0;
+  newRingp->degreeShiftN = 0;
+  newRingp->degreeShift = NULL;
+  newRingp->partialEcart = 0;
+  newRingp->partialEcartGlobalVarX = NULL;
 
   if (ob5.tag != Sarray || (getoaSize(ob5) % 2) != 0) {
     errorKan1("%s\n","[(keyword) value (keyword) value ....] should be given.");
@@ -1588,7 +1706,68 @@ int KsetUpRing(ob1,ob2,ob3,ob4,ob5)
         if (getoa(ob5,i+1).tag != Sinteger) {
           errorKan1("%s\n","A integer should be given. (weightedHomogenization)");
         }
-		newRingp->weightedHomogenization = KopInteger(getoa(ob5,i+1));
+        newRingp->weightedHomogenization = KopInteger(getoa(ob5,i+1));
+      } else if (strcmp(KopString(getoa(ob5,i)),"degreeShift") == 0) {
+        if (getoa(ob5,i+1).tag != Sarray) {
+          errorKan1("%s\n","An array of array should be given. (degreeShift)");
+        }
+        {
+          struct object ods;
+          struct object ods2;
+          int dssize,k,j,nn;
+          ods=getoa(ob5,i+1);
+          if ((getoaSize(ods) < 1) || (getoa(ods,0).tag != Sarray)) {
+            errorKan1("%s\n", "An array of array should be given. (degreeShift)");
+          }
+          nn = getoaSize(ods);
+          dssize = getoaSize(getoa(ods,0));
+          newRingp->degreeShiftSize = dssize;
+          newRingp->degreeShiftN = nn;
+          newRingp->degreeShift = (int *) sGC_malloc(sizeof(int)*(dssize*nn+1));
+          if (newRingp->degreeShift == NULL) errorKan1("%s\n","No more memory.");
+          for (j=0; j<nn; j++) {
+            ods2 = getoa(ods,j);
+            for (k=0; k<dssize; k++) {
+              if (getoa(ods2,k).tag == SuniversalNumber) {
+                (newRingp->degreeShift)[j*dssize+k] = coeffToInt(getoa(ods2,k).lc.universalNumber);
+              }else{
+                (newRingp->degreeShift)[j*dssize+k] = KopInteger(getoa(ods2,k));
+              }
+            }
+          }
+        }
+      } else if (strcmp(KopString(getoa(ob5,i)),"partialEcartGlobalVarX") == 0) {
+        if (getoa(ob5,i+1).tag != Sarray) {
+          errorKan1("%s\n","An array of array should be given. (partialEcart)");
+        }
+        {
+          struct object odv;
+          struct object ovv;
+          int k,j,nn;
+          char *vname;
+          odv=getoa(ob5,i+1);
+          nn = getoaSize(odv);
+          newRingp->partialEcart = nn;
+          newRingp->partialEcartGlobalVarX = (int *) sGC_malloc(sizeof(int)*nn+1);
+          if (newRingp->partialEcartGlobalVarX == NULL) errorKan1("%s\n","No more memory.");
+          for (j=0; j<nn; j++)
+            (newRingp->partialEcartGlobalVarX)[j] = -1;
+          for (j=0; j<nn; j++) {
+            ovv = getoa(odv,j);
+            if (ovv.tag != Sdollar) errorKan1("%s\n","partialEcartGlobalVarX: string is expected.");
+            vname = KopString(ovv);
+            for (k=0; k<n; k++) {
+              if (strcmp(vname,xvars[k]) == 0) {
+                (newRingp->partialEcartGlobalVarX)[j] = k; break;
+              }else{
+                if (k == n-1) errorKan1("%s\n","partialEcartGlobalVarX: no such variable.");
+              }
+            }
+          }
+        }
+
+        switch_function("grade","module1v");
+        /* Warning: grading is changed to module1v!! */
       } else {
         errorKan1("%s\n","Unknown keyword to set_up_ring@");
       }
@@ -2028,7 +2207,47 @@ int KtoArgvbyCurryBrace(str,argv,limit)
   return(argc);
 }
 
+struct object KstringToArgv(struct object ob) {
+  struct object rob;
+  char *s;
+  int n,wc,i,inblank;
+  char **argv;
+  if (ob.tag != Sdollar)
+    errorKan1("%s\n","KstringToArgv(): the argument must be a string.");
+  n = strlen(KopString(ob));
+  s = (char *) sGC_malloc(sizeof(char)*(n+2));
+  if (s == NULL) errorKan1("%s\n","KstringToArgv(): No memory.");
+  strcpy(s,KopString(ob));
+  inblank = 1;  wc = 0; 
+  for (i=0; i<n; i++) {
+    if (inblank && (s[i] > ' ')) {
+      wc++; inblank = 0;
+    }else if ((!inblank) && (s[i] <= ' ')) {
+      inblank = 1;
+    }
+  }
+  argv = (char **) sGC_malloc(sizeof(char *)*(wc+2));
+  argv[0] = NULL;
+  inblank = 1;  wc = 0; 
+  for (i=0; i<n; i++) {
+    if (inblank && (s[i] > ' ')) {
+      argv[wc] = &(s[i]); argv[wc+1]=NULL;
+      wc++; inblank = 0;
+    }else if ((inblank == 0) && (s[i] <= ' ')) {
+      inblank = 1; s[i] = 0;
+    }else if (inblank && (s[i] <= ' ')) {
+      s[i] = 0;
+    }
+  }
 
+  rob = newObjectArray(wc);
+  for (i=0; i<wc; i++) {
+    putoa(rob,i,KpoString(argv[i]));
+    /* printf("%s\n",argv[i]); */
+  }
+  return(rob);
+}
+
 static void checkDuplicateName(xvars,dvars,n)
      char *xvars[];
      char *dvars[];
@@ -2050,6 +2269,16 @@ static void checkDuplicateName(xvars,dvars,n)
   }
 }
 
+struct object KooPower(struct object ob1,struct object ob2) {
+  struct object rob;
+  /* Bug. It has not yet been implemented. */
+  if (QuoteMode) {
+    rob = powerTree(ob1,ob2);
+  }else{
+    warningKan("KooDiv2() has not supported yet these objects.\n");
+  }
+  return(rob);
+}
 
 
 
@@ -2112,7 +2341,11 @@ struct object KooDiv2(ob1,ob2)
     break;
 
   default:
-    warningKan("KooDiv2() has not supported yet these objects.\n");
+    if (QuoteMode) {
+      rob = divideTree(ob1,ob2);
+    }else{
+      warningKan("KooDiv2() has not supported yet these objects.\n");
+    }
     break;
   }
   return(rob);
@@ -2168,6 +2401,7 @@ struct object KgbExtension(struct object obj)
   POLY f;
   int m,i;
   struct pairOfPOLY pf;
+  struct coeff *cont;
 
   if (obj.tag != Sarray) errorKan1("%s\n","KgbExtension(): The argument must be an array.");
   size = getoaSize(obj);
@@ -2247,6 +2481,13 @@ struct object KgbExtension(struct object obj)
       errorKan1("%s\n","The datatype of the argument mismatch: [(isConstant) polynomial] gbext");
     }
     return(KpoInteger(isConstant(KopPOLY(obj1))));
+  }else if (strcmp(key,"isConstantAll")==0) {
+    if (size != 2) errorKan1("%s\n","[(isConstantAll) poly ] gbext bool");
+    obj1 = getoa(obj,1);
+    if (obj1.tag != Spoly) {
+      errorKan1("%s\n","The datatype of the argument mismatch: [(isConstantAll) polynomial] gbext");
+    }
+    return(KpoInteger(isConstantAll(KopPOLY(obj1))));
   }else if (strcmp(key,"schreyerSkelton") == 0) {
     if (size != 2) errorKan1("%s\n","[(schreyerSkelton) array_of_poly ] gbext array");
     obj1 = getoa(obj,1);
@@ -2281,6 +2522,37 @@ struct object KgbExtension(struct object obj)
     obj1 = getoa(obj,1);
     if (obj1.tag != Spoly) errorKan1("%s\n","[(isOrdered) poly] gbext poly");
     return(KisOrdered(obj1));
+  }else if (strcmp(key,"reduceContent")==0) {
+    if (size != 2) errorKan1("%s\n","[(reduceContent)  poly1 ] gbext.");
+    obj1 = getoa(obj,1);
+    if (obj1.tag != Spoly)
+      errorKan1("%s\n","[(reduceContent)  poly1 ] gbext.");
+    f1 = KopPOLY(obj1);
+    rob = newObjectArray(2);
+    f1 = reduceContentOfPoly(f1,&cont);
+    putoa(rob,0,KpoPOLY(f1));
+    if (f1 == POLYNULL) {
+      putoa(rob,1,KpoPOLY(f1));
+    }else{
+      putoa(rob,1,KpoPOLY(newCell(cont,newMonomial(f1->m->ringp))));
+    }
+  }else if (strcmp(key,"ord_ws_all")==0) {
+    if (size != 3) errorKan1("%s\n","[(ord_ws_all) fv wv] gbext");
+    obj1 = getoa(obj,1);
+    obj2 = getoa(obj,2);
+    rob  = KordWsAll(obj1,obj2);
+  }else if (strcmp(key,"exponents")==0) {
+    if (size == 3) {
+      obj1 = getoa(obj,1);
+      obj2 = getoa(obj,2);
+      rob  = KgetExponents(obj1,obj2);
+    }else if (size == 2) {
+      obj1 = getoa(obj,1);
+      obj2 = KpoInteger(2);
+      rob  = KgetExponents(obj1,obj2);
+    }else{
+      errorKan1("%s\n","[(exponents) f type] gbext");
+    }
   }else {
     errorKan1("%s\n","gbext : unknown tag.");
   }
@@ -2316,6 +2588,12 @@ struct object KmpzExtension(struct object obj)
     if (size != 3) errorKan1("%s\n","[(gcd)  universalNumber universalNumber] mpzext.");
     obj1 = getoa(obj,1);
     obj2 = getoa(obj,2);
+    if (obj1.tag != SuniversalNumber) {
+      obj1 = KdataConversion(obj1,"universalNumber");
+	}
+    if (obj2.tag != SuniversalNumber) {
+      obj2 = KdataConversion(obj2,"universalNumber");
+	}
     if (obj1.tag != SuniversalNumber || obj2.tag != SuniversalNumber)
       errorKan1("%s\n","[(gcd)  universalNumber universalNumber] mpzext.");
     if (! is_this_coeff_MP_INT(obj1.lc.universalNumber) ||
@@ -2332,6 +2610,12 @@ struct object KmpzExtension(struct object obj)
     if (size != 3) errorKan1("%s\n","[(tdiv_qr)  universalNumber universalNumber] mpzext.");
     obj1 = getoa(obj,1);
     obj2 = getoa(obj,2);
+    if (obj1.tag != SuniversalNumber) {
+      obj1 = KdataConversion(obj1,"universalNumber");
+	}
+    if (obj2.tag != SuniversalNumber) {
+      obj2 = KdataConversion(obj2,"universalNumber");
+	}
     if (obj1.tag != SuniversalNumber || obj2.tag != SuniversalNumber)
       errorKan1("%s\n","[(tdiv_qr)  universalNumber universalNumber] mpzext.");
     if (! is_this_coeff_MP_INT(obj1.lc.universalNumber) ||
@@ -2390,6 +2674,9 @@ struct object KmpzExtension(struct object obj)
     /*  One arg functions  */
     if (size != 2) errorKan1("%s\n","[key num] mpzext");
     obj1 = getoa(obj,1);
+    if (obj1.tag != SuniversalNumber) {
+      obj1 = KdataConversion(obj1,"universalNumber");
+	}
     if (obj1.tag != SuniversalNumber)
       errorKan1("%s\n","[key num] mpzext : num must be a universalNumber.");
     if (! is_this_coeff_MP_INT(obj1.lc.universalNumber))
@@ -2411,6 +2698,12 @@ struct object KmpzExtension(struct object obj)
     if (size != 3) errorKan1("%s\n","[key  num1 num2] mpzext.");
     obj1 = getoa(obj,1);
     obj2 = getoa(obj,2);
+    if (obj1.tag != SuniversalNumber) {
+      obj1 = KdataConversion(obj1,"universalNumber");
+	}
+    if (obj2.tag != SuniversalNumber) {
+      obj2 = KdataConversion(obj2,"universalNumber");
+	}
     if (obj1.tag != SuniversalNumber || obj2.tag != SuniversalNumber)
       errorKan1("%s\n","[key num1 num2] mpzext.");
     if (! is_this_coeff_MP_INT(obj1.lc.universalNumber) ||
@@ -2442,6 +2735,15 @@ struct object KmpzExtension(struct object obj)
     /* three args */
     if (size != 4) errorKan1("%s\n","[key num1 num2 num3] mpzext");
     obj1 = getoa(obj,1); obj2 = getoa(obj,2); obj3 = getoa(obj,3);
+    if (obj1.tag != SuniversalNumber) {
+      obj1 = KdataConversion(obj1,"universalNumber");
+	}
+    if (obj2.tag != SuniversalNumber) {
+      obj2 = KdataConversion(obj2,"universalNumber");
+	}
+    if (obj3.tag != SuniversalNumber) {
+      obj3 = KdataConversion(obj3,"universalNumber");
+	}
     if (obj1.tag != SuniversalNumber ||
         obj2.tag != SuniversalNumber ||
         obj3.tag != SuniversalNumber ) {
@@ -2460,6 +2762,28 @@ struct object KmpzExtension(struct object obj)
     mpz_powm(r1,f,g,h);
     rob.tag = SuniversalNumber;
     rob.lc.universalNumber = mpintToCoeff(r1,SmallRingp);
+  } else if (strcmp(key,"lcm")==0) {
+    if (size != 3) errorKan1("%s\n","[(lcm)  universalNumber universalNumber] mpzext.");
+    obj1 = getoa(obj,1);
+    obj2 = getoa(obj,2);
+    if (obj1.tag != SuniversalNumber) {
+      obj1 = KdataConversion(obj1,"universalNumber");
+	}
+    if (obj2.tag != SuniversalNumber) {
+      obj2 = KdataConversion(obj2,"universalNumber");
+	}
+    if (obj1.tag != SuniversalNumber || obj2.tag != SuniversalNumber)
+      errorKan1("%s\n","[lcm num1 num2] mpzext.");
+    if (! is_this_coeff_MP_INT(obj1.lc.universalNumber) ||
+        ! is_this_coeff_MP_INT(obj2.lc.universalNumber)) {
+      errorKan1("%s\n","[(lcm)  universalNumber universalNumber] mpzext.");
+    }
+    f = coeff_to_MP_INT(obj1.lc.universalNumber);
+    g = coeff_to_MP_INT(obj2.lc.universalNumber);
+    r1 = newMP_INT();
+    mpz_lcm(r1,f,g);
+    rob.tag = SuniversalNumber;
+    rob.lc.universalNumber = mpintToCoeff(r1,SmallRingp); 
   }else {
     errorKan1("%s\n","mpzExtension(): Unknown tag.");
   }
@@ -2666,8 +2990,85 @@ struct object KdefaultPolyRing(struct object ob) {
 }
   
   
+struct object Krest(struct object ob) {
+  struct object rob;
+  struct object *op;
+  int n,i;
+  if (ob.tag == Sarray) {
+    n = getoaSize(ob);
+    if (n == 0) return ob;
+    rob = newObjectArray(n-1);
+    for (i=1; i<n; i++) {
+      putoa(rob,i-1,getoa(ob,i));
+    }
+    return rob;
+  }else if ((ob.tag == Slist) || (ob.tag == Snull)) {
+    return Kcdr(ob);
+  }else{
+    errorKan1("%s\n","Krest(ob): ob must be an array or a list.");
+  }
+}
+struct object Kjoin(struct object ob1, struct object ob2) {
+  struct object rob;
+  int n1,n2,i;
+  if ((ob1.tag == Sarray) &&  (ob2.tag == Sarray)) {
+    n1 = getoaSize(ob1); n2 = getoaSize(ob2);
+    rob = newObjectArray(n1+n2);
+    for (i=0; i<n1; i++) {
+      putoa(rob,i,getoa(ob1,i));
+    }
+    for (i=n1; i<n1+n2; i++) {
+      putoa(rob,i,getoa(ob2,i-n1));
+    }
+    return rob;
+  }else if ((ob1.tag == Slist) || (ob1.tag == Snull)) {
+	if ((ob2.tag == Slist) || (ob2.tag == Snull)) {
+	  return KvJoin(ob1,ob2);
+	}else{
+	  errorKan1("%s\n","Kjoin: both argument must be a list.");
+	}
+  }else{
+    errorKan1("%s\n","Kjoin: arguments must be arrays.");
+  }
+}
   
-  
+struct object Kget(struct object ob1, struct object ob2) {
+  struct object rob;
+  struct object tob;
+  int i,j,size,n;
+  if (ob2.tag == Sinteger) {
+    i =ob2.lc.ival;
+  }else if (ob2.tag == SuniversalNumber) {
+    i = KopInteger(KdataConversion(ob2,"integer"));
+  }else if (ob2.tag == Sarray) {
+    n = getoaSize(ob2);
+    if (n == 0) return ob1;
+    rob = ob1;
+    for (i=0; i<n; i++) {
+      rob=Kget(rob,getoa(ob2,i));
+    }
+    return rob;
+  }
+  if (ob1.tag == Sarray) {
+    size = getoaSize(ob1);
+    if ((0 <= i) && (i<size)) {
+      return(getoa(ob1,i));
+    }else{
+      errorKan1("%s\n","Kget: Index is out of bound. (get)\n");
+    }
+  }else if (ob1.tag == Slist) {
+    rob = NullObject;
+    if (i < 0) errorKan1("%s\n","Kget: Index is negative. (get)"); 
+    for (j=0; j<i; j++) {
+      rob = Kcdr(ob1);
+      if ((ob1.tag == Snull) && (rob.tag == Snull)) {
+        errorKan1("%s\n","Kget: Index is out of bound. (get) cdr of null list.\n");
+      }
+      ob1 = rob;
+    }
+    return Kcar(ob1);
+  }else errorKan1("%s\n","Kget: argument must be an array or a list.");
+}
 
 /******************************************************************
      error handler
@@ -2681,6 +3082,7 @@ errorKan1(str,message)
   extern int GotoP;
   extern int ErrorMessageMode;
   char tmpc[1024];
+  cancelAlarm();
   if (ErrorMessageMode == 1 || ErrorMessageMode == 2) {
     sprintf(tmpc,"\nERROR(kanExport[0|1].c): ");
     if (strlen(message) < 900) {
@@ -2691,6 +3093,7 @@ errorKan1(str,message)
   if (ErrorMessageMode != 1) {
     fprintf(stderr,"\nERROR(kanExport[0|1].c): ");
     fprintf(stderr,str,message);
+    (void) traceShowStack(); traceClearStack();
   }
   /* fprintf(stderr,"Hello "); */
   if (GotoP) {
@@ -2706,6 +3109,7 @@ errorKan1(str,message)
   longjmp(EnvOfStackMachine,1);
 #endif
 }
+
 
 warningKan(str)
      char *str;