OpenXM/src/k097/lib/minimal/minimal.k - diff

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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.20 and 1.21

-version 1.20, 2000/07/31 02:25:34
+version 1.21, 2000/08/01 03:42:35
 Line 1
 Line 1
 Line 1
- /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.19 2000/07/31 01:21:41 takayama Exp $ */
+ /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.20 2000/07/31 02:25:34 takayama Exp $ */
  #define DEBUG 1
  Sordinary = false;
  /* If you run this program on openxm version 1.1.2 (FreeBSD),
 Line 34  def load_tower() {
 Line 34  def load_tower() {
 Line 34  def load_tower() {
    if (Boundp("k0-tower.sm1.loaded")) {
    }else{
      sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
+     sm1(" [(parse) (new.sm1) pushfile ] extension ");
      sm1(" /k0-tower.sm1.loaded 1 def ");
    }
    sm1(" oxNoX ");
-Line 50  def Sgroebner(f) {
+Line 51  def Sgroebner(f) {
 Line 50  def Sgroebner(f) {
 Line 51  def Sgroebner(f) {
     sm1(" [f] groebner /FunctionValue set");
  }
+ def Sinvolutive(f,w) {
+   local g,m;
+   if (IsArray(f[0])) {
+     m = NewArray(Length(f[0]));
+   }else{
+     m = [0];
+   }
+   g = Sgroebner(f);
+   /* This is a temporary code. */
+   sm1(" g 0 get { w m init_w<m>} map /FunctionValue set ");
+ }
  def Error(s) {
    sm1(" s error ");
  }
-Line 83  def RingOf(f) {
+Line 97  def RingOf(f) {
 Line 83  def RingOf(f) {
 Line 97  def RingOf(f) {
    return(r);
  }
+ def Ord_w_m(f,w,m) {
+   sm1(" f  w  m ord_w<m> { (universalNumber) dc } map /FunctionValue set ");
+ }
+ HelpAdd(["Ord_w_m",
+ ["Ord_w_m(f,w,m) returns the order of f with respect to w with the shift m.",
+  "Note that the order of the ring and the weight w must be the same.",
+  "When f is zero, it returns -intInfinity = -999999999.",
+  "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+  "          Ord_w_m([x*Dx+1,Dx^2+x^5],[\"x\",-1,\"Dx\",1],[2,0]):"]]);
+ def Init_w_m(f,w,m) {
+   sm1(" f w m init_w<m> /FunctionValue set ");
+ }
+ HelpAdd(["Init_w_m",
+ ["Init_w_m(f,w,m) returns the initial of f with respect to w with the shift m.",
+  "Note that the order of the ring and the weight w must be the same.",
+  "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+  "          Init_w_m([x*Dx+1,Dx^2+x^5],[\"x\",-1,\"Dx\",1],[2,0]):"]]);
+ def Max(v) {
+   local i,t,n;
+   n = Length(v);
+   if (n == 0) return(null);
+   t = v[0];
+   for (i=0; i<n; i++) {
+     if (v[i] > t) { t = v[i];}
+   }
+   return(t);
+ }
+ HelpAdd(["Max",
+ ["Max(v) returns the maximal element in v."]]);
  /*  End of standard functions that should be moved to standard libraries. */
  def test0() {
    local f;
-Line 1345  HelpAdd(["IsExact_h",
+Line 1391  HelpAdd(["IsExact_h",
 Line 1345  HelpAdd(["IsExact_h",
 Line 1391  HelpAdd(["IsExact_h",
   "cf. ReParse"
  ]]);
+ def IsSameIdeal_h(ii,jj,v) {
+   local a;
+   v = ToString_array(v);
+   a = [ii,jj,v];
+   sm1(a," isSameIdeal_h /FunctionValue set ");
+ }
+ HelpAdd(["IsSameIdeal_h",
+ ["IsSameIdeal_h(ii,jj,var): bool",
+  "It checks the given ideals are the same or not in D<h> (homogenized Weyl algebra)",
+  "cf. ReParse"
+ ]]);
  def ReParse(a) {
    local c;
    if (IsArray(a)) {
-Line 1384  def ScheckIfSchreyer(s) {
+Line 1442  def ScheckIfSchreyer(s) {
 Line 1384  def ScheckIfSchreyer(s) {
 Line 1442  def ScheckIfSchreyer(s) {
    }
    /* More check will be necessary. */
    return(true);
- }
+ }
+ def SgetShift(mat,w,m) {
+   local omat;
+   sm1(" mat { w m ord_w<m> {(universalNumber) dc}map } map /omat set");
+   return(Map(omat,"Max"));
+ }
+ HelpAdd(["SgetShift",
+ ["SgetShift(mat,w,m) returns the shift vector of mat with respect to w with the shift m.",
+  "Note that the order of the ring and the weight w must be the same.",
+  "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+  "          SgetShift([[x*Dx+1,Dx^2+x^5],[Poly(\"0\"),x],[x,x]],[\"x\",-1,\"Dx\",1],[2,0]):"]]);
+ def SgetShifts(resmat,w) {
+   local i,n,ans,m0;
+   n = Length(resmat);
+   ans = NewArray(n);
+   m0 = NewArray(Length(resmat[0,0]));
+   ans[0] = m0;
+   for (i=0; i<n-1; i++) {
+     ans[i+1] = SgetShift(resmat[i],w,m0);
+     m0 = ans[i+1];
+   }
+   return(ans);
+ }
+ HelpAdd(["SgetShifts",
+ ["SgetShifts(resmat,w) returns the shift vectors of the resolution resmat",
+  " with respect to w with the shift m.",
+  "Note that the order of the ring and the weight w must be the same.",
+  "Zero row is not allowed.",
+  "Example:   a=Sannfs2(\"x^3-y^2\");",
+  "           b=a[0]; w = [\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1];",
+  "           Sweyl(\"x,y\",[w]); b = Reparse(b);",
+  "           SgetShifts(b,w):"]]);
+ def Sinit_w(resmat,w) {
+   local shifts,ans,n,i,m,mat,j;
+   shifts = SgetShifts(resmat,w);
+   n = Length(resmat);
+   ans = NewArray(n);
+   for (i=0; i<n; i++) {
+     m = shifts[i];
+     mat = ScopyArray(resmat[i]);
+     for (j=0; j<Length(mat); j++) {
+       mat[j] = Init_w_m(mat[j],w,m);
+     }
+     ans[i] = mat;
+   }
+   return(ans);
+ }
+ HelpAdd(["Sinit_w",
+ ["Sinit_w(resmat,w) returns the initial of the complex resmat with respect to the weight w.",
+  "Example:   a=Sannfs2(\"x^3-y^2\");",
+  "           b=a[0]; w = [\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1];",
+  "           Sweyl(\"x,y\",[w]); b = Reparse(b);",
+  "           c=Sinit_w(b,w); c:"
+ ]]);

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