Changeset c87dbd in git

Timestamp:

Apr 20, 2007, 2:21:12 PM (16 years ago)

Author:

Hans Schönemann <hannes@…>

Branches:

(u'spielwiese', '828514cf6e480e4bafc26df99217bf2a1ed1ef45')

Children:

5411c83f97258af47096ddd35e1e76f1d12b9d3c

Parents:

adde988366fe79ac130279c9a15ff9741ba9b061

Message:

*hannes: optimizations


git-svn-id: file:///usr/local/Singular/svn/trunk@9985 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/alexpoly.lib (modified) (19 diffs)

Singular/LIB/alexpoly.lib

@@ -1 @@
-version="$Id: alexpoly.lib,v 1.15 2007-04-19 15:10:38 Singular Exp $";
+version="$Id: alexpoly.lib,v 1.16 2007-04-20 12:21:12 Singular Exp $";
 category="Singularities";
 info="
@@ -117 +117 @@
   /// separated on the first exceptional divisor. Otherwise split_graph should not be applied!
   ///////////////////////////////////////////////////////////////////////////////////////////////
-  /// If #[1]="tau", then totalmultiplicities is called for the use in tau_es - thus it returns
+  /// If #[1]="tau", then totalmultiplicities is called for the use in tau_es2 - thus it returns
   /// the prolonged resolutiongraphs of the branches, their multiplicity sequences and their
   /// contact matrix - sorted appropriately.
@@ -279 +279 @@
   }
   ///////////////////////////////////////////////////////////////////////////////
-  // Check, if the procedure is called from inside tau_es.
+  // Check, if the procedure is called from inside tau_es2.
   int check_tau;
   if (size(#)==1)
@@ -289 +289 @@
   }
   /////////////////////////////////////////////////////////////////////////////////
-  // The procedure tau_es expects the branches to be ordered according to their
+  // The procedure tau_es2 expects the branches to be ordered according to their
   // contact during the resolution process.
   /////////////////////////////////////////////////////////////////////////////////
@@ -305 +305 @@
   }
   ///////////////////////////////////////////////////////////////////////////////////
-  /// If the procedure is called from inside tau_es, the output will be the prolonged
+  /// If the procedure is called from inside tau_es2, the output will be the prolonged
   /// resolutiongraphs of the branches, their multiplicity sequences and their contact matrix.
   if (check_tau==1)
@@ -2123 +2123 @@
 "USAGE:    delete_row(M,i); M intmat, i int
 RETURN:   intmat, which is derived from M by removing the ith row
-NOTE:     This procedure is only for internal use; it is called in move_row and tau_es.
+NOTE:     This procedure is only for internal use; it is called in move_row and tau_es2.
 "
 {
@@ -2185 +2185 @@
 "USAGE:    find_last_non_one (v,k); intvec v, int k
 RETURN:   int i, the last index i>=k such that v[i]!=1, or k-1 if no such i exists.
-NOTE:     This procedure is only for internal use; it is called in tau_es.
+NOTE:     This procedure is only for internal use; it is called in tau_es2.
 "
 {
@@ -2206 +2206 @@
 "USAGE:    intmat_minus_one(M);  intmat M
 RETURN:   intmat, all non-zero entries of M deminuished by 1.
-NOTE:     This procedure is only for internal use; it is called in tau_es.
+NOTE:     This procedure is only for internal use; it is called in tau_es2.
 "
 {
@@ -2228 +2228 @@
          or the output of @code{hnexpansion(f[,\"ess\"])}, or the list @code{hne} in
          the ring created by @code{hnexpansion(f[,\"ess\"])}, or the output of
-         @code{develop(f)} resp. of @code{extdevelop(f,n)}, or a list containing 
-         the contact matrix and a list of integer vectors with the characteristic exponents 
+         @code{develop(f)} resp. of @code{extdevelop(f,n)}, or a list containing
+         the contact matrix and a list of integer vectors with the characteristic exponents
          of the branches of a plane curve singularity, or an integer vector containing the
-         characteristic exponents of an irreducible plane curve singularity, or the resolution 
+         characteristic exponents of an irreducible plane curve singularity, or the resolution
          graph of a plane curve singularity (i.e. the output of resolutiongraph or
          the first entry in the output of totalmultiplicities).
-RETURN:  list, of three integer matrices. The first one is the proximity matrix of 
-         the plane curve defined by the INPUT, i.e. the entry i,j is 1 if the 
-         infinitely near point corresponding to row i is proximate to the infinitely 
-         near point corresponding to row j. The second integer matrix is the incidence matrix of the 
-         resolution graph of the plane curve. The entry on the diagonal in row i is -s-1 
-         if s is the number of points proximate to the infinitely near point corresponding 
-         to the ith row in the matrix. The third integer matrix is the incidence matrix of 
-         the Enriques diagram of the plane curve singularity, i.e. each row corresponds to 
+RETURN:  list, of three integer matrices. The first one is the proximity matrix of
+         the plane curve defined by the INPUT, i.e. the entry i,j is 1 if the
+         infinitely near point corresponding to row i is proximate to the infinitely
+         near point corresponding to row j. The second integer matrix is the incidence matrix of the
+         resolution graph of the plane curve. The entry on the diagonal in row i is -s-1
+         if s is the number of points proximate to the infinitely near point corresponding
+         to the ith row in the matrix. The third integer matrix is the incidence matrix of
+         the Enriques diagram of the plane curve singularity, i.e. each row corresponds to
          an infinitely near point in the minimal standard resolution, including the
          strict transforms of the branches, the diagonal element gives
@@ -2248 +2248 @@
          for other purposes as well it is better to calculate this first
          with the aid of @code{hnexpansion} and use it as input instead of
-         the polynomial itself. 
+         the polynomial itself.
          @*
-         If you are not sure whether the INPUT polynomial is reduced or not, use 
+         If you are not sure whether the INPUT polynomial is reduced or not, use
          @code{squarefree(INPUT)} as input instead.
          @*
-         If the input is a smooth curve, then the output will consist of 
+         If the input is a smooth curve, then the output will consist of
          three one-by-one zero matrices.
          @*
-         For the definitions of the computed objects see e.g. the book 
-         Eduardo Casas-Alvero, Singularities of Plane Curves.        
+         For the definitions of the computed objects see e.g. the book
+         Eduardo Casas-Alvero, Singularities of Plane Curves.
 SEE ALSO: develop, hnexpansion, totalmultiplicities, alexanderpolynomial
 EXAMPLE: example proximitymatrix;  shows an example
@@ -2267 +2267 @@
     intmat resgr=INPUT;
   }
-  else 
+  else
   {
     intmat resgr=totalmultiplicities(INPUT)[1];
@@ -2278 +2278 @@
   ////////  Calculate the proximity resolution graph ////////////
   int i,j;
-  int n=nrows(resgr); 
+  int n=nrows(resgr);
   intvec diag; // Diagonal of the Enriques diagram.
   int si; // number of points proximate to the point corresponding to the ith row
@@ -2295 +2295 @@
       resgr[i,i]=resgr[j,j]+1;
     }
-  }  
+  }
   // Set the weights in the resolution graph to the blowing up level in the resolution.
   for (i=1;i<=n;i++)
@@ -2301 +2301 @@
     resgr[i,i]=resgr[i,i]-1;
     diag[i]=resgr[i,i]; // The level of the corresponding infinitely near point.
-  }  
-  // Replace the weights in the resolution graph by 
+  }
+  // Replace the weights in the resolution graph by
   // -s-1, where s is the number of points which are proximate to the point.
   for (i=1;i<=n;i++)
   {
-    si=-1;  
+    si=-1;
     // Find the points of higher weight which are connected to the ith row.
     for (j=i+1;j<=n;j++)
@@ -2367 +2367 @@
 "
 {
-  for (int k=1;k<=ncols(M);k++)
-  {
-    M[j,k]=kj*M[j,k]+ki*M[i,k];
-  }
+  int k=ncols(M);
+  M[j,1..k]=kj*M[j,1..k]+ki*M[i,1..k];
   return(M);
 }
@@ -2393 +2391 @@
   {
     if (M[n,n]<0)
-    {    
+    {
       M=addmultiplrows(M,n,n,-1,0);
     }
@@ -2415 +2413 @@
 RETURN:      list, the first entry is an integer matrix containing the total
              multiplicities and the second entry is an integer matrix containing
-             the multiplicies of the resolution given by rg, where the zeros 
+             the multiplicies of the resolution given by rg, where the zeros
              corresponding to the strict transforms of the branches of the curve
              have been replaced by the (total) multiplicities of the infinitely near
@@ -2462 +2460 @@
 
 proc intmat_inverse (intmat M)
-"USAGE:      intmat_inverse(M); intmat M 
+"USAGE:      intmat_inverse(M); intmat M
 ASSUME:      M is a lower triangular integer matrix with diagonal entries 1 or -1
 RETURN:      intmat, the inverse of M
@@ -2472 +2470 @@
   int n=nrows(M);
   intmat U[n][n];
+  U=U+1;
   for (i=1;i<=n;i++)
   {
-    U[i,i]=1;
-  }
-  for (i=1;i<=n;i++)
-  {
     if (M[i,i]==-1)
-    {      
+    {
       M=addmultiplrows(M,i,i,-1,0);
       U=addmultiplrows(U,i,i,-1,0);
     }
     for (j=i+1;j<=n;j++)
-    {      
+    {
       U=addmultiplrows(U,i,j,-M[j,i],M[i,i]);
       M=addmultiplrows(M,i,j,-M[j,i],M[i,i]);
-    }  
+    }
   }
   return(U);