Changeset bca5a64 in git

Timestamp:

Feb 13, 2019, 1:27:58 AM (5 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '9ea349771971bc025429e7c2f664c4ed01240724')

Children:

e54cd64f6533b4c1a5b125b3abb3b22b94e98f34

Parents:

705501e9c1243b90d049bde35cba1c383fb97724

Message:

doc-related fixes

Location:

Singular/LIB

Files:

• ncfactor.lib (modified) (2 diffs)
• ncrat.lib (modified) (4 diffs)

Singular/LIB/ncfactor.lib

@@ -25 +25 @@
   facShift(h);               Factorization in the n'th shift algebra
   facFirstShift(h);          Factorization in the first shift algebra
+  homogfacNthWeyl(h);        Homogeneous factorization in the n'th Weyl algebra
   homogfacNthQWeyl(h);       Homogeneous factorization in the n'th Q-Weyl algebra
   homogfacFirstQWeyl(h);     Homogeneous factorization in the first Q-Weyl algebra
@@ -5257 +5258 @@
 //////////////////////////////////////////////////
 
-static proc homogfacNthWeyl(poly h)
+proc homogfacNthWeyl(poly h)
 "USAGE: homogfacNthWeyl(h); h is a homogeneous polynomial in the
  nth Weyl algebra with respect to the -1,1-grading

Singular/LIB/ncrat.lib

@@ -3 +3 @@
 category="Noncommutative";
 info="
-LIBRARY:      ncrat.lib Framework for working with nc rational functions
+LIBRARY:      ncrat.lib Framework for working with non-commutative rational functions
 
 AUTHOR:       Ricardo Schnur, email: ricardo.schnur@math.uni-sb.de
 
-SUPPORT:      This project is funded by the SFB-TRR 195
+SUPPORT:      This project has been funded by the SFB-TRR 195
   'Symbolic Tools in Mathematics and their Application'.
 
 OVERVIEW:     This library provides a framework for working with
   non-commutative rational functions (or rather, expressions)
-  and their representations
+  and their linearized representations
 
 REFERENCES:   T. Mai: On the analytic theory of non-commutative
@@ -21 +21 @@
    rational functions; formal linear representations; minimal representations
 
+NOTE: an almost self-explaining introduction to the posibilities of the framework
+can be achieved by running the example for the procedure ncrepGetRegularMinimal.
+   
 PROCEDURES:
   ncInit(list);                 Set up framework, list contains nc variables
@@ -2808 +2811 @@
   "EXAMPLE: (Hua's identity)";
   echo = 2;
+  // We want to prove the Hua's identity, telling that for two
+  // invertible elements x,y from a division ring, one has
+  // inv(x+x*inv(y)*x)+inv(x+y) = inv(x)
+  // where inv(t) stands for the two-sided inverse of t
   ncInit(list("x", "y"));
   ncrat f = ncratFromString("inv(x+x*inv(y)*x)+inv(x+y)-inv(x)");
@@ -2816 +2823 @@
   ncrepDim(s);
   print(s);
+  // since s represents the zero element, Hua's identity holds.
 }