Changeset f9c3c3 in git for Singular/LIB/surfacesignature.lib

Timestamp:

Sep 24, 2010, 5:16:44 PM (14 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

731e4dff10fbf61f908cbb628058b4252455f60b

Parents:

7ef5b62b7463b2574e24d6d9b80966ea720ba93b

Message:

format

git-svn-id: file:///usr/local/Singular/svn/trunk@13279 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

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

Singular/LIB/surfacesignature.lib

@@ +1 @@
+//
 version="$Id$";
 category="Singularities";
 info="
-LIBRARY:  signaturesurfsing.lib       signature of surface singularity
+LIBRARY:  surfacesignature.lib       signature of surface singularity
 
 AUTHORS:  Gerhard Pfister             pfister@mathematik.uni-kl.de
 @*        Muhammad Ahsan Banyamin     ahsanbanyamin@gmail.com
-@*        Stefan Steidel              steidel@mathematik.uni-kl.de 
-
-OVERVIEW: 
+@*        Stefan Steidel              steidel@mathematik.uni-kl.de
+
+OVERVIEW:
 
   A library for computing the signature of irreducible surface singularity.
-  The signature of a surface singularity is defined in [Durfee, A.: The 
-  Signature of Smoothings of Complex Surface Singularities, Math. Ann., 232, 
-  85-98 (1978)]. The algorithm we use has been proposed in [Nemethi, A.: The 
-  signature of f(x,y)+z^N, Proceedings of Singularity Conference (C.T.C. Wall's 
-  60th birthday meeting), Liverpool 1996, London Math.Soc. LN 263(1999), 
+  The signature of a surface singularity is defined in [Durfee, A.: The
+  Signature of Smoothings of Complex Surface Singularities, Math. Ann., 232,
+  85-98 (1978)]. The algorithm we use has been proposed in [Nemethi, A.: The
+  signature of f(x,y)+z^N, Proceedings of Singularity Conference (C.T.C. Wall's
+  60th birthday meeting), Liverpool 1996, London Math.Soc. LN 263(1999),
   131-149].
 
@@ -31 +32 @@
 
 static proc exponentSequence(poly f)
-//=== computes the sequence a_1,...,a_s of exponents as described in [Nemethi] 
+//=== computes the sequence a_1,...,a_s of exponents as described in [Nemethi]
 //=== using the Puiseux pairs (m_1, n_1),...,(m_s, n_s) of f:
-//===  - a_1 = m_1, 
+//===  - a_1 = m_1,
 //===  - a_i = m_i - n_i * (m_[i-1] - n_[i-1] * a_[i-1]).
 //===
@@ -45 +46 @@
    list puiseuxPairs = invariants(f);
    setring R;
-   
+
    intvec M = puiseuxPairs[1][3];
    intvec N = puiseuxPairs[1][4];
-   
+
    int i;
    int a = M[1];
@@ -57 +58 @@
       A[size(A)+1] = a;
    }
-  
+
    return(list(A,N));
 }
@@ -76 +77 @@
    int a_temp, t, k1, k2, k3, s_t, sigma;
    number s;
-   
+
    if(a1 > a2) { a_temp = a1; a1 = a2; a2 = a_temp; }
    if(a2 > a3) { a_temp = a2; a2 = a3; a3 = a_temp; }
    if(a1 > a2) { a_temp = a1; a1 = a2; a2 = a_temp; }
-   
+
    for(t = 0; t <= 2; t++)
    {
@@ -99 +100 @@
                   else
                   {
-                     break; 
+                     break;
                   }
                }
@@ -128 +129 @@
    list L = exponentSequence(f);
    int s = size(L[2]);
-   
+
    if(s == 1)
    {
       return(brieskornSign(L[1][1], L[2][1], N));
    }
-   
+
    prod = 1;
    sigma = brieskornSign(L[1][s], L[2][s], N);
@@ -142 +143 @@
       sigma = sigma + d * brieskornSign(L[1][i], L[2][i], N/d);
    }
-   
+
    return(sigma);
 }
@@ -191 +192 @@
 
 static proc sumExcepDiv(intmat N, list M, int K, int n)
-//=== computes part of the formulae for eta(g,K), g defining an 
+//=== computes part of the formulae for eta(g,K), g defining an
 //=== isolated curve singularity
 //=== N the incidence matrix of the resolution graph of g
@@ -220 +221 @@
 
 static proc sumEdges(intmat N, list M, int K, int n)
-//=== computes part of the formulae for eta(g,K), g defining an 
+//=== computes part of the formulae for eta(g,K), g defining an
 //=== isolated curve singularity
 //=== N the incidence matrix of the resolution graph of g
@@ -275 +276 @@
             }
          }
-      }   
+      }
    }
    if(a==1)
@@ -309 +310 @@
 static proc etaSpec(list L, int N)
 //=== L spectral numbers
-//=== eta-invariant in terms of the spectral pairs of f 
+//=== eta-invariant in terms of the spectral pairs of f
 {
    int i;
    number e, h;
-   
+
    int n = ncols(L[1]);
-   
-   if((n mod 2) == 0)               
+
+   if((n mod 2) == 0)
    // 0 is not a spectral number, thus f is irreducible
    {
@@ -329 +330 @@
    {
       // sum of Hodge numbers in eta function
-      for(i = 1; i <= n; i++)                   
-      {
-         if((L[2][i] == 2)&&((denominator(leadcoef(N*L[1][i]))==1)||(denominator(leadcoef(N*L[1][i]))==-1))) 
-         { 
-            h = h + L[3][i]; 
-         }
-      }
-      
+      for(i = 1; i <= n; i++)
+      {
+         if((L[2][i] == 2)&&((denominator(leadcoef(N*L[1][i]))==1)||(denominator(leadcoef(N*L[1][i]))==-1)))
+         {
+            h = h + L[3][i];
+         }
+      }
+
       // summand coming from spectral number 0 in eta function
       h = h + L[3][(n+1)/2];
-      
+
       // sum coming from non-zero spectral numbers in eta function
       for(i = (n+3)/2; i <= n; i++)
@@ -347 +348 @@
             e = e + (1 - 2 * fracPart(N * number(L[1][i]))) * L[3][i];
          }
-      }    
+      }
       return(h + 2*e);
    }
@@ -369 +370 @@
       return(etaRes(L,N) - N*etaRes(L,1));
    }
-   
+
    if(#[1] == 1)
    {
       return(signatureP(N,f));
    }
-   
+
    if(#[1] == 2)
    {
@@ -380 +381 @@
       return(etaRes(L,N) - N*etaRes(L,1));
    }
-   
+
    if(#[1] == 3)
    {
@@ -416 +417 @@
 
 N = 5;
-f = x15-21x14+8x13y-6x13-16x12y+20x11y2-x12+8x11y-36x10y2    
-    +24x9y3+4x9y2-16x8y3+26x7y4-6x6y4+8x5y5+4x3y6-y8;      
-g = f^3 + x17y17;                                                
+f = x15-21x14+8x13y-6x13-16x12y+20x11y2-x12+8x11y-36x10y2
+    +24x9y3+4x9y2-16x8y3+26x7y4-6x6y4+8x5y5+4x3y6-y8;
+g = f^3 + x17y17;
 
 N = 6;
-f = y4+2x3y2+x6+x5y;                                             
+f = y4+2x3y2+x6+x5y;
 g1 = f^2 + x5y5;
 g2 = f^3 + x11y11;
@@ -431 +432 @@
 g2 = f^3 + x17y17;
 
-N = 6;     
+N = 6;
 // k0 = 30, k1 = 35, k2 = 71
 f = x71+6x65+15x59-630x52y6+20x53+6230x46y6+910x39y12+15x47
@@ -446 +447 @@
     -28x18y4+240x17y5-976x16y6+2208x15y7-2494x14y8+816x13y9+56x15y6
     -320x14y7+844x13y8-1216x12y9+440x11y10-70x12y8+240x11y9-344x10y10
-    +240x9y11+56x9y10-96x8y11+52x7y12-28x6y12+16x5y13+8x3y14-y16; 
+    +240x9y11+56x9y10-96x8y11+52x7y12-28x6y12+16x5y13+8x3y14-y16;