Changeset 6ad6d7 in git for Singular/LIB/ellipticcovers.lib

Timestamp:

Dec 18, 2013, 6:42:50 PM (10 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

1129351bca33bc8786735f0f6b3ef6e938ff6352

Parents:

b5bb857a49ad6ba995c35f60c39498abec0f46fc

Message:

fix: format, sum->lsum in ellipticcovers.lib

File:

• Singular/LIB/ellipticcovers.lib (modified) (21 diffs, 1 prop)

Singular/LIB/ellipticcovers.lib

@@ -13 +13 @@
 We implement a formula for computing the number of covers of elliptic curves.
 It has beed obtained by proving mirror symmetry
-for arbitrary genus by tropical methods in [BBM]. A Feynman graph of genus 
-g is a trivalent, connected graph of genus g (with 2g-2 vertices 
-and 3g-3 edges). The branch type b=(b_1,...,b_(3g-3)) of a stable map is the 
+for arbitrary genus by tropical methods in [BBM]. A Feynman graph of genus
+g is a trivalent, connected graph of genus g (with 2g-2 vertices
+and 3g-3 edges). The branch type b=(b_1,...,b_(3g-3)) of a stable map is the
 multiplicity of the the edge i over a fixed base point.
 
-Given a Feynman graph G and a branch type b, we obtain the number 
+Given a Feynman graph G and a branch type b, we obtain the number
 N_(G,b) of stable maps of branch type b from a genus g curve of topological type G
-to the elliptic curve by computing a path integral 
+to the elliptic curve by computing a path integral
 over a rational function. The path integral is computed as a residue.
 
@@ -37 +37 @@
 
 KEYWORDS:
-
 tropical geometry; mirror symmetry; tropical mirror symmetry; Gromov-Witten invariants; elliptic curves; propagator; Feynman graph; path integral
 
@@ -52 +51 @@
 computeConstant(number, number)           constant coefficient in the Laurent series expansion of a rational function in a given variable
 evalutateIntegral(number, list)           path integral for a given propagator and ordered sequence of variables
-gromovWitten(number)                      sum of path integrals for a given propagator over all orderings of the variables, or 
+gromovWitten(number)                      sum of path integrals for a given propagator over all orderings of the variables, or
                                           Gromov Witten invariant for a given graph and a fixed branch type, or
                                           list of Gromov Witten invariants for a given graph and all branch types
@@ -60 +59 @@
 partitions(int, int)                      partitions of an integer into a fixed number of summands
 permute(list)                             all permutations of a list
-sum(list)                                 sum of the elements of a list
+lsum(list)                                sum of the elements of a list
 
 ";
@@ -196 +195 @@
          product of propagator(list(v[i],w[i]),b[i]) over all edges i with multiplicity b[i] over the base point
          and vertices v[i] and w[i].
-      
-KEYWORDS: propagator; elliptic curve
+
+KEYWORDS: elliptic curve
 EXAMPLE:  example propagator; shows an example
 "
@@ -231 +230 @@
 { "EXAMPLE:"; echo=2;
   ring R=(0,x1,x2,x3,x4),(q1,q2,q3,q4,q5,q6),dp;
-  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4))); 
+  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4)));
   propagator(list(x1,x2),0);
   propagator(list(x1,x2),2);
@@ -246 +245 @@
 RETURN:  number, the constant coefficient of the Laurent series of f in the variable x.
 THEORY:  Computes the constant coefficient of the Laurent series by iterative differentiation.
-      
+
 KEYWORDS: Laurent series
 EXAMPLE:  example computeConstant; shows an example
@@ -272 +271 @@
 { "EXAMPLE:"; echo=2;
   ring R=(0,x1,x2,x3,x4),(q1,q2,q3,q4,q5,q6),dp;
-  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4))); 
+  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4)));
   number P = propagator(G,list(1,1,1,0,0,0));
   computeConstant(P,x2);
@@ -287 +286 @@
 
          In the setting of covers of elliptic curves this is the path integral over the
-         propagator divided by the product of all variables (corresponding to the vertices) 
+         propagator divided by the product of all variables (corresponding to the vertices)
          computed as a residue.
-      
+
 KEYWORDS: residue; Laurent series
 EXAMPLE:  example evaluateIntegral; shows an example
@@ -302 +301 @@
 { "EXAMPLE:"; echo=2;
   ring R=(0,x1,x2,x3,x4),(q1,q2,q3,q4,q5,q6),dp;
-  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4))); 
+  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4)));
   number p = propagator(G,list(0,2,1,0,0,1));
   evaluateIntegral(p,list(x1,x3,x4,x2));
@@ -315 +314 @@
 
          This will eventually be deleted and become a more efficient kernel function.
-      
+
 KEYWORDS: permutations
 EXAMPLE:  example permute; shows an example
@@ -350 +349 @@
 
          This may eventually be deleted and become a more efficient kernel function.
-      
+
 KEYWORDS: partitions
 EXAMPLE:  example partitions; shows an example
@@ -384 +383 @@
          - the invariant N_(G,d)*|Aut(G)| where d is the degree of the covering, or @*
 
-         - the number N_(G,b) of coverings with source G and target an elliptic curves with branch type a over a 
+         - the number N_(G,b) of coverings with source G and target an elliptic curves with branch type a over a
          fixed base point (that is, the i-th edge passes over the base point with multiplicity b[i]).@*
-      
+
 KEYWORDS: Gromov-Witten invariants; elliptic curves; coverings; Hurwitz numbers
 EXAMPLE:  example gromovWitten; shows an example
@@ -420 +419 @@
        //print(string(j)+" / "+string(size(pa))+"    "+string(pa[j])+"     "+string(re[j])+"      "+string(sum(re))+"     "+string(ti));
       }
-     return(sum(re));
+     return(lsum(re));
      }
   }
@@ -427 +426 @@
 { "EXAMPLE:"; echo=2;
   ring R=(0,x1,x2,x3,x4),(q1,q2,q3,q4,q5,q6),dp;
-  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4))); 
+  graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4)));
   number P = propagator(G,list(0,2,1,0,0,1));
   gromovWitten(P);
@@ -439 +438 @@
 "USAGE:  computeGromovWitten(G, d, st, en [, vb] ); G graph, d int, st int, en  int, optional: vb int@*
 ASSUME:  G is a Feynman graph, d a non-negative integer, st specified the start- and en the end partition
-         in the list pa = partition(d). Specifying a positive optional integer vb leads to intermediate printout.@* 
+         in the list pa = partition(d). Specifying a positive optional integer vb leads to intermediate printout.@*
          We assume that the coefficient ring has one rational variable for each vertex of G.@*
 RETURN:  list L, where L[i] is gromovWitten(G,pa[i]) and all others are zero.
 THEORY:  This function does essentially the same as the function gromovWitten, but is designed for handling complicated examples.
          Eventually it will also run in parallel.@*
-      
+
 KEYWORDS: Gromov-Witten invariants; elliptic curves; coverings; Hurwitz numbers
 EXAMPLE:  example computeGromovWitten; shows an example
@@ -463 +462 @@
        re[j]=gromovWitten(propagator(P,pa[j]));
        ti=timer-ti;
-       if (vb>0){print(string(j)+" / "+string(size(pa))+"    "+string(pa[j])+"     "+string(re[j])+"      "+string(sum(re))+"     "+string(ti));}
+       if (vb>0){print(string(j)+" / "+string(size(pa))+"    "+string(pa[j])+"     "+string(re[j])+"      "+string(lsum(re))+"     "+string(ti));}
       } else {re[j]=s;}
      }
@@ -473 +472 @@
   ring R=(0,x1,x2,x3,x4),(q1,q2,q3,q4,q5,q6),dp;
   graph G = makeGraph(list(1,2,3,4),list(list(1,3),list(1,2),list(1,2),list(2,4),list(3,4),list(3,4)));
-  partitions(6,2); 
+  partitions(6,2);
   computeGromovWitten(G,2,3,7);
   computeGromovWitten(G,2,3,7,1);
@@ -479 +478 @@
 
 
-proc sum(list L)
-"USAGE:  sum(L); L list@*
-ASSUME:  L is a list of things with the binary operator + defined.@* 
+proc lsum(list L)
+"USAGE:  lsum(L); L list@*
+ASSUME:  L is a list of things with the binary operator + defined.@*
 RETURN:  The sum of the elements of L.
-THEORY:  Sums the elements of a list. 
+THEORY:  Sums the elements of a list.
 
          Eventually this will be deleted and become a more efficient kernel function.@*
-      
-KEYWORDS: sum
-EXAMPLE:  example sum; shows an example
+
+EXAMPLE:  example lsum; shows an example
 "
 {
@@ -499 +497 @@
 { "EXAMPLE:"; echo=2;
   list L = 1,2,3,4,5;
-  sum(L);
+  lsum(L);
 }
 
@@ -507 +505 @@
 "USAGE:  generatingFunction(G, d); G graph, d int@*
 ASSUME:  G is a Feynman graph, d a non-negative integer. The basering has one polynomial variable for each
-         edge, and the coefficient ring has one rational variable for each vertex.@* 
+         edge, and the coefficient ring has one rational variable for each vertex.@*
 RETURN:  poly.
 THEORY:  This function compute the multivariate generating function of all Gromov-Witten invariants up to
          degree d, that is, the sum of all gromovWitten(G,b)*q^b.@*
-      
+
 KEYWORDS: generating function; Gromov-Witten invariants; elliptic curves; coverings; Hurwitz numbers
 EXAMPLE:  example generatingFunction; shows an example