Changeset 7f3ad4 in git for Singular/LIB/matrix.lib

Timestamp:

Jan 14, 2009, 5:07:05 PM (15 years ago)

Author:

Hans Schönemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

0721816437af5ddabc83aa203a12d9b58b42a33c

Parents:

95edd5641377e851d4a1d4e986853687991d0895

Message:

*hannes: format


git-svn-id: file:///usr/local/Singular/svn/trunk@11306 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

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

Singular/LIB/matrix.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: matrix.lib,v 1.45 2008-12-08 14:31:46 motsak Exp $";
+version="$Id: matrix.lib,v 1.46 2009-01-14 16:07:05 Singular Exp $";
 category="Linear Algebra";
 info="
@@ -30 +30 @@
  rowred(A[,any]);       reduction of matrix A with elementary row-operations
  colred(A[,any]);       reduction of matrix A with elementary col-operations
- linear_relations(E);   find linear relations between homogeneous vectors 
+ linear_relations(E);   find linear relations between homogeneous vectors
  rm_unitrow(A);         remove unit rows and associated columns of A
  rm_unitcol(A);         remove unit columns and associated rows of A
@@ -37 +37 @@
  exteriorBasis(n,k[,s]); basis of k-th exterior power of n-dim v.space
  symmetricPower(A,k);   k-th symmetric power of a module/matrix A
- exteriorPower(A,k);    k-th exterior power of a module/matrix A 
+ exteriorPower(A,k);    k-th exterior power of a module/matrix A
           (parameters in square brackets [] are optional)
 ";
@@ -910 +910 @@
 "USAGE:   linear_relations(M);
          M: a module
-ASSUME:  All non-zero entries of M are homogeneous polynomials of the same 
-         positife degree. The base field must be an exact field (not real 
+ASSUME:  All non-zero entries of M are homogeneous polynomials of the same
+         positife degree. The base field must be an exact field (not real
          or complex).
          It is not checked whether these assumptions hold.
@@ -957 +957 @@
   pmat(REL);
   pmat(M*REL);
-}  
+}
 
 //////////////////////////////////////////////////////////////////////////////
@@ -1078 +1078 @@
 proc symmetricBasis(int n, int k, list #)
 "USAGE:    symmetricBasis(n, k[,s]); n int, k int, s string
-RETURN:   ring, poynomial ring containing the ideal \"symBasis\", 
+RETURN:   ring, poynomial ring containing the ideal \"symBasis\",
           being a basis of the k-th symmetric power of an n-dim vector space.
-NOTE:     The output polynomial ring has characteristics 0 and n variables 
+NOTE:     The output polynomial ring has characteristics 0 and n variables
           named \"S(i)\", where the base variable name S is either given by the
           optional string argument(which must not contain brackets) or equal to
@@ -1099 +1099 @@
     if( (find(S, "(") + find(S, ")")) > 0 )
     {
-      ERROR("Wrong optional argument: must be a string without brackets"); 
+      ERROR("Wrong optional argument: must be a string without brackets");
     }
   }
@@ -1117 +1117 @@
 
 // basis of the 3-rd symmetricPower of a 4-dim vector space:
-def R = symmetricBasis(4, 3, "@e"); setring R; 
+def R = symmetricBasis(4, 3, "@e"); setring R;
 R;  // container ring:
 symBasis; // symmetric basis:
@@ -1126 +1126 @@
 proc exteriorBasis(int n, int k, list #)
 "USAGE:    exteriorBasis(n, k[,s]); n int, k int, s string
-RETURN:   qring, an exterior algebra containing the ideal \"extBasis\", 
+RETURN:   qring, an exterior algebra containing the ideal \"extBasis\",
           being a basis of the k-th exterior power of an n-dim vector space.
-NOTE:     The output polynomial ring has characteristics 0 and n variables 
+NOTE:     The output polynomial ring has characteristics 0 and n variables
           named \"S(i)\", where the base variable name S is either given by the
           optional string argument(which must not contain brackets) or equal to
@@ -1147 +1147 @@
     if( (find(S, "(") + find(S, ")")) > 0 )
     {
-      ERROR("Wrong optional argument: must be a string without brackets"); 
+      ERROR("Wrong optional argument: must be a string without brackets");
     }
   }
@@ -1165 +1165 @@
 { "EXAMPLE:"; echo = 2;
 // basis of the 3-rd symmetricPower of a 4-dim vector space:
-def r = exteriorBasis(4, 3, "@e"); setring r; 
+def r = exteriorBasis(4, 3, "@e"); setring r;
 r; // container ring:
 extBasis; // exterior basis:
@@ -1194 +1194 @@
       rings Tn is source- and Tm is image-ring with bases
           resp. Ink and Imk.
-      M = max dim of Image, N - dim. of source      
+      M = max dim of Image, N - dim. of source
 SEE ALSO: symmetricPower, exteriorPower"
 {
@@ -1206 +1206 @@
 
 //------------------------- compute matrix of single images ------------------
-  def Rm = save + Tm;  setring Rm; 
+  def Rm = save + Tm;  setring Rm;
   dbprint(p-2, "Temporary Working Ring", Rm);
 
@@ -1228 +1228 @@
 //------------------------- compute image ---------------------
   // apply S^k(A): Tn -> Rm  to Source basis vectors Ink:
-  map TMap = Tn, B; 
-
-  ideal C = NF(TMap(Ink), std(0)); 
+  map TMap = Tn, B;
+
+  ideal C = NF(TMap(Ink), std(0));
   dbprint(p-1, "Image Matrix: ", C);
 
@@ -1273 +1273 @@
 "USAGE:    symmetricPower(A, k); A module, k int
 RETURN:   module: the k-th symmetric power of A
-NOTE:     the chosen bases and most of intermediate data will be shown if 
+NOTE:     the chosen bases and most of intermediate data will be shown if
           printlevel is big enough
 SEE ALSO: exteriorPower
@@ -1303 +1303 @@
 
 //------------------------- compute and return S^k(A) in chosen bases --
-  setring save;  
+  setring save;
 
   return(mapPower(p, A, k, Tn, Tm));
@@ -1332 +1332 @@
 "USAGE:    exteriorPower(A, k); A module, k int
 RETURN:   module: the k-th exterior power of A
-NOTE:     the chosen bases and most of intermediate data will be shown if 
+NOTE:     the chosen bases and most of intermediate data will be shown if
           printlevel is big enough. Last rows will be invisible if zero.
 SEE ALSO: symmetricPower
@@ -1366 +1366 @@
 example
 { "EXAMPLE:"; echo = 2;
-  ring r = (0),(a, b, c, d, e, f), dp; 
+  ring r = (0),(a, b, c, d, e, f), dp;
   r; "base ring:";
 
-  module B = a*gen(1) + c*gen(2) + e*gen(3), 
-             b*gen(1) + d*gen(2) + f*gen(3), 
+  module B = a*gen(1) + c*gen(2) + e*gen(3),
+             b*gen(1) + d*gen(2) + f*gen(3),
                         e*gen(1) + f*gen(3);
 
   print(B);
-  print(exteriorPower(B, 2)); 
-  print(exteriorPower(B, 3)); 
+  print(exteriorPower(B, 2));
+  print(exteriorPower(B, 3));
 
   def g = SuperCommutative(); setring g; g;
@@ -1384 +1384 @@
   print(exteriorPower(A, 2));
 
-  module B = a*gen(1) + c*gen(2) + e*gen(3), 
-             b*gen(1) + d*gen(2) + f*gen(3), 
+  module B = a*gen(1) + c*gen(2) + e*gen(3),
+             b*gen(1) + d*gen(2) + f*gen(3),
                         e*gen(1) + f*gen(3);
   print(B);