===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v
retrieving revision 1.27
retrieving revision 1.32
diff -u -p -r1.27 -r1.32
--- OpenXM/src/k097/lib/minimal/minimal.k	2000/08/16 22:38:52	1.27
+++ OpenXM/src/k097/lib/minimal/minimal.k	2000/12/10 09:34:28	1.32
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.26 2000/08/10 02:59:08 takayama Exp $ */
+/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.31 2000/12/10 03:12:20 takayama Exp $ */
 #define DEBUG 1 
 Sordinary = false;
 /* If you run this program on openxm version 1.1.2 (FreeBSD),
@@ -44,18 +44,12 @@ def Sprint2(s) {
      
 */
 
+/* We cannot use load command in the if statement. */
+load("lib/minimal/cohom.k");
+Load_sm1(["k0-tower.sm1","lib/minimal/k0-tower.sm1"],"k0-tower.sm1.loaded");
+Load_sm1(["new.sm1","lib/minimal/new.sm1"],"new.sm1.loaded");
+sm1(" oxNoX ");
 
-load("cohom.k");
-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 ");
-}
-load_tower();
 SonAutoReduce = true;
 def Factor(f) {
    sm1(f, " fctr /FunctionValue set");
@@ -145,6 +139,28 @@ def Max(v) {
 HelpAdd(["Max",
 ["Max(v) returns the maximal element in v."]]);
 
+def Kernel(f) {
+  sm1(" [f] syz /FunctionValue set ");
+}
+def Syz(f) {
+  sm1(" [f] syz /FunctionValue set ");
+}
+HelpAdd(["Kernel",
+["Kernel(f) returns the syzygy of f.",
+ "Return value [b, c]: b is a set of generators of the syzygies of f",
+ "                   : c=[gb, backward transformation, syzygy without",
+ "                                                   dehomogenization",
+ "Example:  Weyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+ "          s=Kernel([x*Dx+1,Dx^2+x^5]); s[0]:"]]);
+/* cf. sm1_syz in cohom.k */
+def Gb(f) {
+  sm1(" [f] gb /FunctionValue set ");
+}
+HelpAdd(["Gb",
+["Gb(f) returns the Groebner basis of f.",
+ "cf. Kernel, Weyl."]]);
+
+
 /*  End of standard functions that should be moved to standard libraries. */
 def test0() {
   local f;
@@ -165,7 +181,6 @@ def test1() {
 }
 
   
-
 def Sweyl(v,w) {
   /* extern WeightOfSweyl ; */
   local ww,i,n;
@@ -1006,7 +1021,7 @@ def Sminimal(g,opt) {
   redundantTable = r[1];
   reducer = r[2];
   bettiTable = SbettiTable(redundantTable);
-  Sprintln2("Betti numbers are ------");
+  Sprintln2("BettiTable ------");
   if (Sverbose || Sverbose2) {sm1_pmat(bettiTable);}
   minRes = SnewArrayOfFormat(freeRes);
   seq = 0;
@@ -1070,9 +1085,9 @@ def Sminimal(g,opt) {
    Println("0: minimal resolution, 3: Schreyer resolution ");
    Println("------------ Resolution Summary  --------------");
    Print("Betti numbers : "); 
-   Println(Map(ansSminimal[0],"Length"));
+   Println(Join([Length(ansSminimal[0,0,0])],Map(ansSminimal[0],"Length")));
    Print("Betti numbers of the Schreyer frame: ");
-   Println(Map(ansSminimal[3],"Length"));
+   Println(Join([Length(ansSminimal[3,0,0])],Map(ansSminimal[3],"Length")));
    Println("-----------------------------------------------");
 
    sm1(" restoreEnvAfterResolution ");
@@ -1509,10 +1524,10 @@ HelpAdd(["SgetShift",
 def SgetShifts(resmat,w) {
   local i,n,ans,m0;
   n = Length(resmat);
-  ans = NewArray(n);
+  ans = NewArray(n+1);
   m0 = NewArray(Length(resmat[0,0]));
   ans[0] = m0;
-  for (i=0; i<n-1; i++) {
+  for (i=0; i<n; i++) {
     ans[i+1] = SgetShift(resmat[i],w,m0);
     m0 = ans[i+1];
   }
@@ -1564,4 +1579,32 @@ def SbettiTable(rtable) {
     ans[i] = pp;
   }
   return(ans);
-}
\ No newline at end of file
+}
+
+def BfRoots1(G,V) {
+   local bb,ans;
+   sm1(" /BFparlist [ ] def ");
+   if (IsString(V)) {
+      sm1(" [ V to_records pop ] /V set ");
+   }else {
+     sm1(" V { toString } map /V set ");  
+   }
+   sm1(" /BFvarlist V def ");
+  
+   sm1(" G flatten { toString } map  /G set ");
+   sm1(" G V bfm /bb set ");
+   if (IsSm1Integer(bb)) {
+     return([ ]);
+   }
+   sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
+   return([ans, bb]);
+}
+
+HelpAdd(["BfRoots1",
+["BfRoots1(g,v) returns the integral roots of g with respect to the weight",
+ "vector (1,1,...,1) and the b-function itself",
+ "Example:  BfRoots1([x*Dx-2, y*Dy-3],[x,y]);"
+]]);
+
+
+