===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v
retrieving revision 1.28
retrieving revision 1.31
diff -u -p -r1.28 -r1.31
--- OpenXM/src/k097/lib/minimal/minimal.k	2000/08/21 07:45:22	1.28
+++ OpenXM/src/k097/lib/minimal/minimal.k	2000/12/10 03:12:20	1.31
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.27 2000/08/16 22:38:52 takayama Exp $ */
+/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.30 2000/11/19 05:50:30 takayama Exp $ */
 #define DEBUG 1 
 Sordinary = false;
 /* If you run this program on openxm version 1.1.2 (FreeBSD),
@@ -44,13 +44,25 @@ def Sprint2(s) {
      
 */
 
+/* We cannot use load command in the if statement. */
+load("lib/minimal/cohom.k");
 
-load("cohom.k");
 def load_tower() {
+  local ppp;
   if (Boundp("k0-tower.sm1.loaded")) {
   }else{
-    sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
-    sm1(" [(parse) (new.sm1) pushfile ] extension ");
+    if (Tag(GetPathName("k0-tower.sm1")) == 0) {
+      ppp = GetPathName("lib/minimal/k0-tower.sm1");
+      sm1(" [(parse) ppp pushfile ] extension ");
+    }else{
+      sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
+    }
+    if (Tag(GetPathName("new.sm1")) == 0) {
+      ppp = GetPathName("lib/minimal/new.sm1");
+      sm1(" [(parse) ppp pushfile ] extension ");
+    }else{
+      sm1(" [(parse) (new.sm1) pushfile ] extension ");
+    }
     sm1(" /k0-tower.sm1.loaded 1 def ");
   }
   sm1(" oxNoX ");
@@ -145,6 +157,28 @@ 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 +199,6 @@ def test1() {
 }
 
   
-
 def Sweyl(v,w) {
   /* extern WeightOfSweyl ; */
   local ww,i,n;
@@ -1564,4 +1597,32 @@ 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]);"
+]]);
+
+
+