Changeset 73e5a2 in git

Timestamp:

Feb 13, 2009, 10:37:20 PM (15 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

61d32c91fe3976149b9b30938476f2c3c1257eee

Parents:

59f78ae5a870b7808ef48f59619f0aabf5305d9a

Message:

*levandov: doc changes, new function lpMult


git-svn-id: file:///usr/local/Singular/svn/trunk@11399 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

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

Singular/LIB/freegb.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: freegb.lib,v 1.15 2009-01-14 16:07:04 Singular Exp $";
+version="$Id: freegb.lib,v 1.16 2009-02-13 21:37:20 levandov Exp $";
 category="Noncommutative";
 info="
-LIBRARY: freegb.lib   Twosided Noncommutative Groebner bases in Free Algebras
+LIBRARY: freegb.lib   Twosided Noncommutative Groebner bases in Free Algebras via Letterplace
 AUTHOR: Viktor Levandovskyy,     levandov@math.rwth-aachen.de
+
+THEORY: See chapter 'Letterplace' in the Singular Manual.
 
 PROCEDURES:
@@ -12 +14 @@
 AUXILIARY PROCEDURES:
 
+lpMult(f,g);        letterplace multiplication of letterplace polynomials
 lp2lstr(K, s);      convert letter-place ideal to a list of modules
 lst2str(L[, n]);     convert a list (of modules) into polynomials in free algebra
@@ -19 +22 @@
 Serre(A,z);          compute the ideal of Serre's relations associated to a generalized Cartan matrix A
 isVar(p);             check whether p is a power of a single variable
+adem(i,j);            compute the ideal of Adem relations for i<2j in char 0
 
 SEE ALSO: Letterplace
@@ -38 +42 @@
   example freegbasis;
     "AUXILIARY PROCEDURES: ";
+  example lpMult;
   example lp2lstr;
   example lst2str;
@@ -1458 +1463 @@
 proc adem(int i, int j)
 "USAGE:  adem(i,j); i,j int
-RETURN:  ideal
+RETURN:  ring and exports ideal
 ASSUME: there are at least i+j variables in the basering
 PURPOSE: compute the ideal of Adem relations for i<2j in characteristic 0
+@*  the ideal is exported under the name AdemRel in the output ring
 EXAMPLE: example adem; shows examples
 "
@@ -1478 +1484 @@
   n = binomial(j-1,i);
   q = n*s(i+j)*s(0);
-  printf("k=0, term=%s",q);
+  //  printf("k=0, term=%s",q);
   p = p + q;
   for (k=1; k<= ii; k++)
@@ -1484 +1490 @@
     n = binomial(j-k-1,i-2*k);
     q = n*s(i+j-k)*s(k);;
-    printf("k=%s, term=%s",k,q);
+    //    printf("k=%s, term=%s",k,q);
     p = p + q;
   }
@@ -1531 +1537 @@
   // Adem rels modulo 2 are interesting
 
-//static
-proc stringpoly2lplace(string s)
+static proc stringpoly2lplace(string s)
 {
   // decomposes sentence into terms
@@ -1706 +1711 @@
 }
 
-//static
-proc sent2lplace(string s)
+static proc sent2lplace(string s)
 {
   // SENTence of words TO LetterPLACE
@@ -1776 +1780 @@
 }
 
-proc str2lplace(string s)
+static proc str2lplace(string s)
 {
   // converts a word (monomial) with coeff into letter-place
@@ -1966 +1970 @@
 "USAGE:  Liebr(a,b[,N]); a,b letterplace polynomials, N an optional integer
 RETURN:  poly
+ASSUME: basering has a letterplace ring structure, like the one returned by freegbRing
+@*   Moreover, the variables 'uptodeg' (degree bound of the letterplace ring) and 'lV' (number of
+blocks of variables of the letterplace ring ) must be defined
 PURPOSE: compute the Lie bracket [a,b] = ab - ba between letterplace polynomials
 NOTE: if N>1 is specified, then the left normed bracket [a,[...[a,b]]]] is computed.
@@ -1971 +1978 @@
 "
 {
+
+  if (lpAssumeViolation())
+  {
+    ERROR("Either 'uptodeg' or 'lV' global variables are not set!");
+  }
   // alias ppLiebr;
   //if int N is given compute [a,[...[a,b]]]] left normed bracket
@@ -2007 +2019 @@
   Liebr(a,b);
   Liebr(x(1),y(1),2);
+  kill uptodeg, lV;
 }
 
@@ -2026 +2039 @@
   // shifts a monomial a by i
   // calls pLPshift(p,sh,uptodeg,lVblock);
+  if (deg(a) + i > uptodeg)
+  {
+    ERROR("degree bound violated by the shift!");
+  }
   return(system("stest",a,i,uptodeg,lV));
 }
@@ -2051 +2068 @@
   poly p = mmLiebr(a(1),b(1));
   poly p = Liebr(a(1),b(1));
+  kill uptodeg, lV;
 }
 
@@ -2113 +2131 @@
   ideal I = Serre(A,1); I = simplify(I,1+2+8);
   I;
+  kill uptodeg, lV;
 }
 
@@ -2242 +2261 @@
 }
 
-proc strList2poly(list L)
+static proc strList2poly(list L)
 {
   //  list L comes from sent2lplace (which takes a poly on the input)
@@ -2282 +2301 @@
 }
 
-proc file2lplace(string fname)
+static proc file2lplace(string fname)
 "USAGE:  file2lplace(fnm);  fnm a string
 RETURN:  ideal
@@ -2383 +2402 @@
 // reduction/ Normalform? needs kernel stuff
 
+proc lpMult(poly f, poly g)
+"USAGE:  lpMult(f,g); f,g letterplace polynomials
+RETURN:  poly
+ASSUME: basering has a letterplace ring structure, like the one returned by freegbRing
+@*   Moreover, the variables 'uptodeg' (degree bound of the letterplace ring) and 'lV' (number of
+blocks of variables of the letterplace ring ) must be defined
+PURPOSE: compute the letterplace form of f*g
+EXAMPLE: example lpMult; shows examples
+"
+{
+  if (lpAssumeViolation())
+  {
+    ERROR("Either 'uptodeg' or 'lV' global variables are not set!");
+  }
+  int sf = deg(f);
+  int sg = deg(g);
+  if (sf+sg > uptodeg)
+  {
+    ERROR("degree bound violated by the product!");
+  }
+  //  if (sf>1) { sf = sf -1; }
+  poly v = f*pshift(g,sf);
+  return(v);
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  // define a ring in letterplace form as follows:
+  ring r = 0,(x(1),y(1),x(2),y(2),x(3),y(3),x(4),y(4)),dp; 
+  poly a = x(1)*y(2); poly b = y(1);
+  int uptodeg=4; int lV=2;
+  export uptodeg; export lV;
+  lpMult(b,a);
+  lpMult(a,b);
+  kill uptodeg, lV;
+}
+
+static proc lpAssumeViolation()
+{
+  // checks whether the global vars
+  // uptodeg and lV are defined
+  // returns Boolean : yes/no [for assume violation]
+  int i = ( defined(uptodeg) && (defined(lV)) );
+  return ( !i );
+}