Changeset 8b6880 in git

Timestamp:

Nov 26, 2022, 2:22:39 PM (17 months ago)

Author:

Oleksandr Iena <o.g.yena@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

07fefd7e1818a24a256b720bb0c7021058b855b9

Parents:

b3594cbd522dbba3563a80c89f0e99a9eb523ec2

git-author:

Oleksandr Iena <o.g.yena@gmail.com>2022-11-26 14:22:39+01:00

git-committer:

Oleksandr Iena <o.g.yena@gmail.com>2022-11-28 22:47:47+01:00

Message:

Bug fix symNsym: fix and some comments corrected

* The procedure symNsym is not really used in the library, it was however added as a comfort feature.
* The main motivation for having the procedure is to have a possibility to represent a symmetric polynomial in terms of the elementary symmetric polynomials.
* It can be discussed whether the remainder feature is reasonable at all, the current code should give a formally correct answer.

File:

• Singular/LIB/chern.lib (modified) (4 diffs)

Singular/LIB/chern.lib

@@ -177 +177 @@
           as well a non-symmetric remainder
 EXAMPLE:  example symNsym; shows an example
-NOTE:     constants are not considered symmetric
+NOTE:     constants are considered symmetric
 "
 {
@@ -215 +215 @@
   list l=symm(list(A@(1..nV) )); // symmetric functions in A@(i)
   intvec v=leadexp(f), 0; // the exponent of the leading monomial
+  int exponent;
+  // We proceed as if the initial polynomial were symmetric.
+  // Under this assumption the leading monomial will always be of the form
+  // A@(1)^n1 * A@(2)^n2 * ... * A@(nV)^nnV, n1 >= n2 >= ... >= nnV.
+  // Everything which contradicts this assumption is considered as a part of the remainder.
   while(v[N1]!=0)
   {
     mon=leadcoef(f); // leading coefficient of f
     monc=mon;
-    for(i=1; v[N1+i-1]!=0 ;i++ )
-    {
-      mon = mon*c@(i)^( v[N1+i-1]-v[N1+i] );
-      monc = monc*l[i]^( v[N1+i-1]-v[N1+i] ); // has the same leading coefficient as f
-    }
-    rez1=rez1+mon; // add a monomial
-    f=f-monc; // subtract the monomial
+    for(i=1; i<=nV && mon !=0 ;i++ )
+    {
+      exponent = v[N1+i-1]-v[N1+i];
+      if( exponent >=0 ) // symmetric case
+      {
+        mon = mon*c@(i)^exponent;
+        monc = monc*l[i]^exponent; // has the same leading coefficient as f
+      }
+      else // not the symmetric case
+      {
+        mon=0;
+        monc=0;
+      }
+    }
+    if(mon==0) // not the symmetric case
+    {
+      rez2=rez2+lead(f);
+      f=f-lead(f);
+    }
+    else // symmetric case
+    {
+      rez1=rez1+mon; // add a monomial
+      f=f-monc; // subtract the monomial
+    }
     v=leadexp(f), 0;
   }
@@ -245 +267 @@
   list l=c(1..3);
   // The symmetric part of f = 3x2 + 3y2 + 3z2 + 7xyz + y
-  // in terms of the elemenatary symmetric functions c(1), c(2), c(3)
+  // in terms of the elementary symmetric functions c(1), c(2), c(3)
   // and the remainder
   poly f = 3x2 + 3y2 + 3z2 + 7xyz + y;
   print( symNsym(f, l) );
-  // Take a symmetrix polynomial in variables x and z
+  // Take a symmetric polynomial in variables x and z
   f=x2+xz+z2;
   // Express it in terms of the elementary the symmetric functions
@@ -2479 +2501 @@
   print( cProj(1) );
 
-  // the coefficients of the total Chern class of the complex projective line
+  // the coefficients of the total Chern class of the complex projective plane
   print( cProj(2) );
 
-  // the coefficients of the total Chern class of the complex projective line
+  // the coefficients of the total Chern class of the complex projective space
+  // of dimension three
   print( cProj(3) );
 }