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

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Diff for /OpenXM/src/k097/lib/minimal/cohom.k between version 1.1 and 1.5

-version 1.1, 2000/05/03 06:42:07
+version 1.5, 2000/11/19 10:48:48
 Line 1
 Line 1
 Line 1
- /* $OpenXM$ */
+ /* $OpenXM: OpenXM/src/k097/lib/minimal/cohom.k,v 1.4 2000/11/19 05:50:30 takayama Exp $ */
+ /* k0 interface functions for cohom.sm1 */
  def Boundp(a) {
     local b;
     sm1("[(parse) [(/) ",a," ( load tag 0 eq
 Line 27  def sm1_deRham(a,b) {
 Line 27  def sm1_deRham(a,b) {
 Line 27  def sm1_deRham(a,b) {
    }
    sm1("[", aa,bb, " ]  deRham /FunctionValue set ");
  }
+ HelpAdd(["sm1_deRham",
+ ["sm1_deRham(f,v) computes the dimension of the deRham cohomology groups",
+  "of C^n - V(f)",
+  "This function does not use (-w,w)-minimal free resolution.",
+   "Example:  sm1_deRham(\"x^3-y^2\",\"x,y\");"
+ ]]);
  def Weyl(v,w,p) {
-Line 45  def Weyl(v,w,p) {
+Line 51  def Weyl(v,w,p) {
 Line 45  def Weyl(v,w,p) {
 Line 51  def Weyl(v,w,p) {
    sm1(" define_ring_variables ");
    return(a);
  }
+ HelpAdd(["Weyl",
+ [ "Weyl(v,w) defines the Weyl algebra (the ring of differential operators)",
+   "with the weight vector w.",
+   "Example:  Weyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); "
+ ]]);
+ /* (  and  ) must match  in HelpAdd. */
  def sm1_pmat(a) {
    sm1(a," pmat ");
-Line 85  def sm1_syz(A,V,W) {
+Line 97  def sm1_syz(A,V,W) {
 Line 85  def sm1_syz(A,V,W) {
 Line 97  def sm1_syz(A,V,W) {
    sm1(P," syz /FunctionValue set");
  }
  /*
+   cf.  Kernel()
    sm1_syz([x*Dx,y*Dy],[x,y]):
    We want to syz_h, too.
    Step 1: Control by global variable ?  syz ==> syz_generic
-Line 185  def ex2_9() {
+Line 198  def ex2_9() {
 Line 185  def ex2_9() {
 Line 198  def ex2_9() {
    return(a);
  }
+ def to_int0(A) {
+    local i,c,n,r;
+    if (IsArray(A)) {
+      n = Length(A);
+      r = NewArray(n);
+      for (i=0; i<n; i++) {
+        r[i] = to_int0(A[i]);
+      }
+      return(r);
+    } else if (IsInteger(A)) {
+      return(IntegerToSm1Integer(A));
+    } else {
+      return(A);
+    }
+ }
+ HelpAdd(["Translate.to_int0",
+  ["to_int0(a) :  as same as sm1_push_int0."]]);
+ def GKZ(A,B) {
+   /* we need sm1_rat_to_p in a future. */
+   local c;
+   c = to_int0([A,B]);
+   sm1(c," gkz /FunctionValue set ");
+ }
+ HelpAdd(["GKZ.GKZ",
+   ["GKZ(a,b) returns the GKZ systems associated to the matrix a and the vector b",
+    "The answer is given by strings.",
+    "Example: GKZ([[1,1,1,1],[0,1,3,4]],[0,2]);"]]);
+ def ToricIdeal(A) {
+   /* we need sm1_rat_to_p in a future. */
+   local c,B,i,n,pp;
+   n = Length(A);
+   B = NewArray(n);
+   for (i=0; i<n; i++) {B[i] = 0;}
+   c = to_int0([A,B]);
+   sm1(c," gkz 0 get /pp set ");
+   for (i=0; i<n; i++) { pp = Rest(pp); }
+   return(pp);
+ }
+ HelpAdd(["ToricIdeal",
+   ["ToricIdeal(a) returns the affine toric ideal associated to the matrix a",
+    "The answer is given by a list of strings.",
+    "Example: ToricIdeal([[1,1,1,1],[0,1,3,4]]);"]]);
+ def Rest(a) {
+   sm1(a," rest /FunctionValue set ");
+ }
+ HelpAdd(["Rest",
+ ["Rest(a), list a; "]]);
+ def Annfs(f,v) {
+   local fs;
+   fs = ToString(f);
+   sm1(" [fs v] annfs /FunctionValue set ");
+ }
+ HelpAdd(["Annfs",
+ ["Annfs(f,v) computes the annihilating ideal of f^r and the Bernstein-Sato",
+  "  polynomial b(s) of f",
+  "Return value: [Ann(f^r), r, b(s)] where r is the minimal integral root of",
+  "              b(s) = 0.",
+  "Example:  Annfs(x^2+y^2,\"x,y\"): "
+ ]]);

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