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Diff for /OpenXM/src/k097/help.k between version 1.1.1.1 and 1.8

version 1.1.1.1, 1999/10/08 02:12:15 version 1.8, 2001/01/05 11:14:25
Line 1 
Line 1 
   /* $OpenXM: OpenXM/src/k097/help.k,v 1.7 2001/01/04 12:29:31 takayama Exp $ */
 if (K00_verbose)  if (K00_verbose)
   Println("help.k (help.ccc).  8/6, 1996 --- 8/7, 1996. 3/6, 1997 --- 12/21, 1997.");    Println("help.k:  8/6, 1996 --- 8/7, 1996. 3/6, 1997 --- 12/21, 1997.");
   
 def help(x) {  def help(x) {
   if (Length(Arglist) < 1) {    if (Length(Arglist) < 1) {
Line 168  HelpAdd(["Poly",
Line 168  HelpAdd(["Poly",
  "Poly(name) returns the polynomial name in the current ring   "Poly(name) returns the polynomial name in the current ring
   (string name)."]);    (string name)."]);
 HelpAdd(["PolyR",  HelpAdd(["PolyR",
  "PolyR(name,r) returns the polynomial name in the ring r   ["PolyR(name,r) returns the polynomial name in the ring r
  (string name, ring r).   (string name, ring r).",
  Ex. r = RingD(\"x,y\"); y = PolyR(\"y\",r); "]);   "Ex. r = RingD(\"x,y\"); y = PolyR(\"y\",r); "]]);
 HelpAdd(["RingD",  HelpAdd(["RingD",
  ["RingD(names) defines a new ring (string names).",   ["RingD(names) defines a new ring (string names).",
   "RingD(names,weight_vector) defines a new ring with the weight vector",    "RingD(names,weight_vector) defines a new ring with the weight vector",
Line 185  ascii code is ascii_code (integer ascii_code)."]);
Line 185  ascii code is ascii_code (integer ascii_code)."]);
 HelpAdd(["ToString","ToString(obj) transforms the <<obj>> to a string."]);  HelpAdd(["ToString","ToString(obj) transforms the <<obj>> to a string."]);
 HelpAdd(["Numerator","Numerator(f) returns the numerator of <<f>> (rational f)."]);  HelpAdd(["Numerator","Numerator(f) returns the numerator of <<f>> (rational f)."]);
 HelpAdd(["Denominator","Denominator(f) returns the denominator of <<f>> (rational f)."]);  HelpAdd(["Denominator","Denominator(f) returns the denominator of <<f>> (rational f)."]);
 HelpAdd(["Replace","Replace(f,rule) (polynomial f, array rule).  HelpAdd(["Replace",
            Ex. Replace( (x+y)^3, [[x,Poly(\"1\")]])"]);    ["Replace(f,rule) (polynomial f, array rule).  ",
      "Ex. Replace( (x+y)^3, [[x,Poly(\"1\")]])"]]);
 HelpAdd(["SetRingVariables",  HelpAdd(["SetRingVariables",
  "SetRingVariables()   "SetRingVariables()
   Set the generators of the current ring as global variables.    Set the generators of the current ring as global variables.
Line 195  HelpAdd(["Append","Append([f1,...,fn],g) returns the l
Line 196  HelpAdd(["Append","Append([f1,...,fn],g) returns the l
 HelpAdd(["Join",  HelpAdd(["Join",
  "Join([f1,...,fn],[g1,...,gm]) returns the list   "Join([f1,...,fn],[g1,...,gm]) returns the list
   [f1,...,fn,g1,...,gm]"]);    [f1,...,fn,g1,...,gm]"]);
 HelpAdd(["Indexed",  
  "Indexed(name,i) returns the string name[i]  
   (string name, integer i)"]);  
   
 HelpAdd(["-ReservedName1",  HelpAdd(["!ReservedNames",
  ["The names k00*, K00*, sm1* , arg1,arg2,arg3,arg4,....," ,   ["The names k00*, K00*, sm1* , arg1,arg2,arg3,arg4,....," ,
   "Helplist, Arglist, FunctionValue,",    "Helplist, Arglist, FunctionValue,",
   "@@@*, db.*, k.*, tmp002*, tmp00* are used for system functions."]]);    "@@@*, db.*, k.*, tmp002*, tmp00* are used for system functions."]]);
Line 222  HelpAdd(["Init_w",
Line 220  HelpAdd(["Init_w",
   "to the variables <<vars>> (array of polynomials).",    "to the variables <<vars>> (array of polynomials).",
   "Example: Init_w(x^2+y^2+x,[x,y],[1,1]):"]]);    "Example: Init_w(x^2+y^2+x,[x,y],[1,1]):"]]);
   
 HelpAdd(["RingDonIndexedVariables",  
  ["RingDonIndexedVariables(name,n) defines and returns the ring of",  
   "homogenized differential operators",  
   "Q<h, name[0], ..., name[n-1], Dname[0], ..., Dname[n-1]>",  
   "where <<name>> is a string and <<n>> is an integer.",  
   "Note that this function defines global variables",  
   "h, name[0], ..., name[n-1], Dname[0], ..., Dname[n-1].",  
   "Example: RingDonIndexedVariables(\"x\",3).",  
   "RingDonIndexedVariables(name,n,w) defines and returns the ring of",  
   "homogenized differential operators with the ordering defined by ",  
   "the weight vector <<w>> (array)",  
   "Example: RingDonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);  
   
 HelpAdd(["Groebner",  HelpAdd(["Groebner",
  ["Groebner(input) returns Groebner basis of the left module (or ideal)",   ["Groebner(input) returns Groebner basis of the left module (or ideal)",
Line 270  HelpAdd(["IsString",
Line 256  HelpAdd(["IsString",
 ["IsString(obj) returns true if << obj >> is a string (object obj).",  ["IsString(obj) returns true if << obj >> is a string (object obj).",
  "Example:  if (IsString(\"abc\")) Println(\"Hello\"); ;"]]);   "Example:  if (IsString(\"abc\")) Println(\"Hello\"); ;"]]);
   
   HelpAdd(["IsRing",
   ["IsRing(obj) returns true if << obj >> is a ring (object obj)."
   ]]);
   
   
 HelpAdd(["IsSm1Integer",  HelpAdd(["IsSm1Integer",
 ["IsSm1Integer(obj) returns true if << obj >> is an integer of sm1(object obj)."]]);  ["IsSm1Integer(obj) returns true if << obj >> is an integer of sm1(object obj)."]]);
   
Line 331  def RingPoly(vList,weightMatrix,pp) {
Line 321  def RingPoly(vList,weightMatrix,pp) {
     sm1("[", vList,      sm1("[", vList,
         "ring_of_polynomials ( ) elimination_order 0 ] define_ring          "ring_of_polynomials ( ) elimination_order 0 ] define_ring
          /tmp set ");           /tmp set ");
       SetRingVariables();
     return(tmp);      return(tmp);
   } else ;    } else ;
   if (argsize == 2) {    if (argsize == 2) {
Line 351  def RingPoly(vList,weightMatrix,pp) {
Line 342  def RingPoly(vList,weightMatrix,pp) {
     }      }
     new0[i] = newtmp;      new0[i] = newtmp;
   }    }
     SetRingVariables();
   ringpp =    ringpp =
   sm1("[", vList,    sm1("[", vList,
       "ring_of_polynomials ", new0, " weight_vector", pp, " ] define_ring");        "ring_of_polynomials ", new0, " weight_vector", pp, " ] define_ring");
Line 366  def IsSm1Integer(ob) {
Line 358  def IsSm1Integer(ob) {
   sm1(ob , " isInteger /FunctionValue set ");    sm1(ob , " isInteger /FunctionValue set ");
 }  }
   
   def IsRing(ob) {
     sm1(ob , " isRing /FunctionValue set ");
   }
   
   
 def CancelNumber(rn) {  def CancelNumber(rn) {
   local tmp;    local tmp;
   sm1(" [(cancel) ",rn," ] mpzext /tmp set ");    sm1(" [(cancel) ",rn," ] mpzext /tmp set ");
Line 374  def CancelNumber(rn) {
Line 370  def CancelNumber(rn) {
   sm1(" tmp (denominator) dc (1).. eq { /FunctionValue tmp (numerator) dc def} { /FunctionValue tmp def } ifelse ");    sm1(" tmp (denominator) dc (1).. eq { /FunctionValue tmp (numerator) dc def} { /FunctionValue tmp def } ifelse ");
 }  }
   
   def DC_polynomial(obj) {
     return(DC(obj,"polynomial"));
   }
 def DC(obj,key) {  def DC(obj,key) {
     if (IsArray(obj) && key=="polynomial") {
       return(Map(obj,"DC_polynomial"));
     }
   if (key == "string") { return(ToString(obj)); }    if (key == "string") { return(ToString(obj)); }
   else if (key == "integer") { key = "universalNumber"; }    else if (key == "integer") { key = "universalNumber"; }
   else if (key == "sm1integer") { key = "integer"; }    else if (key == "sm1integer") { key = "integer"; }
Line 469  HelpAdd(["ReducedBase",
Line 471  HelpAdd(["ReducedBase",
  ["ReducedBase[base] prunes redundant elements in the Grobner basis <<base>> (array)."   ["ReducedBase[base] prunes redundant elements in the Grobner basis <<base>> (array)."
 ]]);  ]]);
   
 def IndexedVariables(name,size) {  
   local result,i,result2;  
   result = [ ];  
   for (i=0; i<size-1; i++) {  
     result = Append(result,Indexed(name,i));  
     result = Append(result,",");  
   }  
   if (size-1 >= 0) {  
     result = Append(result,Indexed(name,size-1));  
   }  
   result2 = Join(["{"],result);  
   result2 = Join(result2,["}"]);  
   return(AddString(result2));  
 }  
 HelpAdd(["IndexedVariables",  
 ["IndexedVariables(name,size) returns the string ",  
  " {name[0],name[1],...,name[size-1]} which can be used as inputs to ",  
  " the function RingD  (string name, integer size).",  
  " cf. RingDonIndexedVariables.",  
  " Ex. R = RingD(IndexedVariables(\"a\",3)); ",  
  "     h = Poly(\"h\");",  
  "     a = NewArray(3);",  
  "     for (i=0; i<3; i++) {a[i] = Poly(Indexed(\"a\",i));} ;"]]);  
   
   
 def RingDonIndexedVariables(vList, size, weightMatrix,pp) {  
   local myring,tmp,k00_i,argsize,vListD;  
   /* You cannot use these local varialbes as a name of global ring  
      variables. Change these names to names that start with k00_ */  
   argsize = Length(Arglist);  
   if (argsize == 1) {  
     Println("Error (IndexedRingD): ");  
     return(null);  
   }  
   if (argsize == 2) {  
     vListD = AddString(["D",vList]);  
     myring = RingD(IndexedVariables(vList,size));  
     SetRingVariables();  
     tmp = NewArray(size);  
     for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}  
     sm1(vList, " (literal) dc ", tmp, " def ");  
     tmp = NewArray(size);  
     for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}  
     sm1(vListD, " (literal) dc ", tmp, " def ");  
     if (SetRingVariables_Verbose) {  
       Print("Set the global variables ");  
       sm1("[(parse) ",vList," ] extension pop print ");  
       sm1("[(parse) ",vListD," ] extension pop print "); Ln();  
     }else {  
       sm1("[(parse) ",vList," ] extension pop  ");  
       sm1("[(parse) ",vListD," ] extension pop ");  
     }  
     return( myring );  
   }  
   if (argsize == 3 || argsize == 4) {  
    if (argsize == 3) { pp = 0; }  
    vListD = AddString(["D",vList]);  
    myring = RingD(IndexedVariables(vList,size),weightMatrix,pp);  
     SetRingVariables();  
     tmp = NewArray(size);  
     for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}  
     sm1(vList, " (literal) dc ", tmp, " def ");  
     tmp = NewArray(size);  
     for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}  
     sm1(vListD, " (literal) dc ", tmp, " def ");  
     if (SetRingVariables_Verbose) {  
       Print("Set the global variables ");  
       sm1("[(parse) ",vList," ] extension pop print ");  
       sm1("[(parse) ",vListD," ] extension pop print "); Ln();  
     } else {  
       sm1("[(parse) ",vList," ] extension pop  ");  
       sm1("[(parse) ",vListD," ] extension pop ");  
     }  
     return( myring );  
   }  
   return(-1);  
 }  
   
 def Ringp(f) {  def Ringp(f) {
   sm1(f, " (ring) dc /FunctionValue set ");    sm1(f, " (ring) dc /FunctionValue set ");
 }  }
Line 638  def ToDouble(f) {
Line 563  def ToDouble(f) {
 }  }
   
   
 def RingPonIndexedVariables(vList, size, weightMatrix) {  
   local myring,tmp,k00_i,argsize,vListD;  
   /* You cannot use these local varialbes as a name of global ring  
      variables. Change these names to names that start with k00_ */  
   argsize = Length(Arglist);  
   if (argsize == 1) {  
     Println("Error (RingPonIndexedVariables): ");  
     return(null);  
   }  
   if (argsize == 2) {  
     myring = RingPoly(IndexedVariables(vList,size));  
     SetRingVariables();  
     tmp = NewArray(size);  
     for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}  
     sm1(vList, " (literal) dc ", tmp, " def ");  
     if (SetRingVariables_Verbose) {  
      Print("Set the global variables ");  
      sm1("[(parse) ",vList," ] extension pop print "); Ln();  
     }else {  
      sm1("[(parse) ",vList," ] extension pop  ");  
     }  
     return( myring );  
   }  
   if (argsize == 3) {  
     myring = RingPoly(IndexedVariables(vList,size),weightMatrix);  
     SetRingVariables();  
     tmp = NewArray(size);  
     for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}  
     sm1(vList, " (literal) dc ", tmp, " def ");  
     if (SetRingVariables_Verbose) {  
       Print("Set the global variables ");  
       sm1("[(parse) ",vList," ] extension pop print "); Ln();  
     } else {  
       sm1("[(parse) ",vList," ] extension pop ");  
     }  
     return( myring );  
   }  
   return(-1);  
 }  
   
 HelpAdd(["RingPonIndexedVariables",  
  ["RingPonIndexedVariables(name,n) defines and returns the ring of",  
   "polynomials",  
   "Q<h, name[0], ..., name[n-1] >",  
   "where <<name>> is a string and <<n>> is an integer.",  
   "Note that this function defines global variables",  
   "h, name[0], ..., name[n-1].",  
   "Example: RingPonIndexedVariables(\"x\",3).",  
   "RingPonIndexedVariables(name,n,w) defines and returns the ring of",  
   "polynomials with the ordering defined by ",  
   "the weight vector <<w>> (array)",  
   "Example: RingPonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);  
   
   
 def Mod(f,n) {  def Mod(f,n) {
    if (IsPolynomial(f)) {     if (IsPolynomial(f)) {
      sm1("[(mod) ",f,n,"] gbext  /FunctionValue set ");       sm1("[(mod) ",f,n,"] gbext  /FunctionValue set ");
Line 727  HelpAdd(["IsConstant",
Line 599  HelpAdd(["IsConstant",
 Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");  Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");
   
 def Substitute(f,xx,g) {  def Substitute(f,xx,g) {
   local tmp, coeff0,ex,i,n,newex;    local tmp, coeff0,ex,i,n,newex,ans;
   if (IsInteger(f)) return(f);    if (IsInteger(f)) return(f);
     if (IsArray(f)) {
        n = Length(f);
        ans = NewVector(n);
        for (i=0; i<n; i++) {
          ans[i] = Substitute(f[i],xx,g);
        }
        return(ans);
     }
   if (! IsPolynomial(f)) {    if (! IsPolynomial(f)) {
     k00_error("Substitute","The first argument must be polynomial.");      k00_error("Substitute","The first argument must be polynomial.");
   }    }
Line 756  def Tag(f) {
Line 636  def Tag(f) {
   if (IsArray(f)) {    if (IsArray(f)) {
     return(Map(f,"Tag"));      return(Map(f,"Tag"));
   }else {    }else {
     ans = sm1(f," tag (universalNumber) dc ");      ans = sm1(f," etag (universalNumber) dc ");
     return(ans);      return(ans);
   }    }
 }  }
 HelpAdd(["Tag",  HelpAdd(["Tag",
 ["Tag(f) returns the datatype tags of f where",  ["Tag(f) returns the datatype tags of f where",
  "5: string,  9: polynomial, 15: integer(big-num), 16: rational, ",   "5: string,  9: polynomial, 15: integer(big-num), 16: rational, ",
  "17: object, 18:double.",   "18:double, 257: Error ",
  "Ex. Tag([Poly(\"0\"), 0]):"   "Ex. Tag([Poly(\"0\"), 0]):"
 ]]);  ]]);
   
   def Error(s) {
     sm1(" s error ");
   }
   HelpAdd(["Error",
   ["Error(s) causes an error and outputs a message s."]]);
   
 OutputPrompt ;  OutputPrompt ;
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