Changeset 7af4ad9 in git

Timestamp:

Jan 7, 2001, 4:21:46 PM (23 years ago)

Author:

Gert-Martin Greuel <greuel@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

1adaa7cccf071b7264e7d562e31ff2fbcf28bda0

Parents:

90611c96f29bf20282ba8567dc61e6aa0533155e

Message:

* GMG: Kosmetik


git-svn-id: file:///usr/local/Singular/svn/trunk@5022 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

Singular/LIB

Files:

• gaussman.lib (modified) (4 diffs)
• matrix.lib (modified) (11 diffs)

Singular/LIB/gaussman.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: gaussman.lib,v 1.20 2000-12-24 15:39:11 mschulze Exp $";
+version="$Id: gaussman.lib,v 1.21 2001-01-07 15:21:09 greuel Exp $";
 category="Singularities";
 
@@ -147 +147 @@
 RETURN:
 @format
-  if mode=0:
-    matrix M: exp(-2*pi*i*M) is a monodromy matrix of f
-  if mode=1:
-    ideal e: exp(-2*pi*i*e) is the spectrum of the monodromy of f
+          if mode=0:
+             matrix M: exp(-2*pi*i*M) is a monodromy matrix of f
+          if mode=1:
+             ideal e: exp(-2*pi*i*e) is the spectrum of the monodromy of f
 @end format
 SEE ALSO: monodromy.lib, jordan.lib
@@ -371 +371 @@
 
 proc vfiltration(poly f,list #)
-"USAGE:    vfiltration(f[,mode]); poly f, int mode[=1]
-ASSUME:   basering has local ordering, f has isolated singularity at 0
-RETURN:
-@format
-  list l:
-  if mode=0 or mode=1:
-    ideal l[1]: spectral numbers in increasing order
-    intvec l[2]:
-      int l[2][i]: multiplicity of spectral number l[1][i]
-  if mode=1:
-    list l[3]:
-      module l[3][i]: vector space basis of l[1][i]-th graded part
-                      of the V-filtration on H''/H' in terms of l[4]
-    ideal l[4]: monomial vector space basis of H''/H'
-    ideal l[5]: standard basis of the Jacobian ideal
-@end format
-NOTE:     H' and H'' denote the Brieskorn lattices
+"USAGE:    vfiltration(f[,mode]); poly f, int mode[default=1]
+ASSUME:   local ordering, f isolated singularity at 0
+RETURN:   list l:
+@format           
+          list l:
+          if mode=0 or mode=1:
+            l[1]: ideal, spectral numbers in increasing order
+            l[2]: intvec
+                  l[2][i]: int, multiplicity of spectral number l[1][i]
+          if mode=1 :
+            l[3]: list
+                  l[3][i]: module, vector space basis of l[1][i]-th graded 
+                           part of the V-filtration on H''/H' in terms of l[4]
+            l[4]: ideal, monomial vector space basis of H''/H'
+            l[5]: ideal, standard basis of Jacobian ideal
+          @end format
+NOTE:     H' and H'' denote Brieskorn lattices
 SEE ALSO: spectrum.lib
 KEYWORDS: singularities; Gauss-Manin connection; spectrum;
@@ -749 +749 @@
 
 proc vfiltjacalg(list l)
-"USAGE:   vfiltjacalg(vfiltration(f)); poly f
-ASSUME:  basering has local ordering, f has isolated singularity at 0
-RETURN:
-@format
-  list l:
-    ideal l[1]: spectral numbers of the V-filtration
-                on the Jacobian algebra in increasing order
-    intvec l[2]:
-      int l[2][i]: multiplicity of spectral number l[1][i]
-    list l[3]:
-      module l[3][i]: vector space basis of the l[1][i]-th graded part 
-                      of the V-filtration on the Jacobian algebra
-                      in terms of l[4]
-    ideal l[4]: monomial vector space basis of the Jacobian algebra
-    ideal l[5]: standard basis of the Jacobian ideal
+"USAGE:   vfiltjacalg(vfiltration(f));
+ASSUME:  local ordering, f isolated singularity at 0
+RETURN:  
+@format  
+         list l:
+           l[1]: ideal, spectral numbers of the V-filtration on the 
+                 Jacobian algebra in increasing order
+           l[2]: intvec
+               l[2][i]: int, multiplicity of spectral number l[1][i]
+           l[3]: list
+               l[3][i]: module, vector space basis of l[1][i]-th graded part 
+                        of the V-filtration on the Jacobian algebra in terms
+                        of l[4]
+           l[4]: ideal, monomial vector space basis of the Jacobian algebra
+           l[5]: ideal, standard basis of Jacobian ideal
 @end format
 EXAMPLE: example vfiltjacalg; shows an example

Singular/LIB/matrix.lib

@@ -1 +1 @@
 // GMG/BM, last modified: 8.10.98
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: matrix.lib,v 1.19 2001-01-06 00:41:54 greuel Exp $";
+version="$Id: matrix.lib,v 1.20 2001-01-07 15:21:46 greuel Exp $";
 category="Linear Algebra";
 info="
@@ -503 +503 @@
 
 proc gauss_col (matrix A, list #)
-"USAGE:   gauss_col(A[,e]); A matrix, e any type
+"USAGE:   gauss_col(A[,any]); A a matrix, any any type
 RETURN:  - a matrix B, if called with one argument; B is the complete column-
            reduced upper-triangular normal form of A if A is constant, 
@@ -509 +509 @@
            no division by polynomials).
 @*       - a list L of two matrices, if called with two arguments;  
-           L satidfies L[1] = A * L[2] with L[1] the column-reduced form of A
+           L satisfies L[1] = A * L[2] with L[1] the column-reduced form of A
            and L[2] the transformation matrix.
 NOTE:    * The procedure just applies interred to A with ordering (C,dp).
@@ -518 +518 @@
 @*       * Parameters are allowed. Hence, if the entries of A are parameters,
            B is the column-reduced form of A over the rational function field.
+SEE ALSO:  colred
 EXAMPLE: example gauss_col; shows an example
 "
@@ -526 +527 @@
    module M = A;
    intvec v = option(get);
+//------------------------ change ordering if necessary ----------------------
    if( ordstr(R) != "C,dp(nvars(R))" )
    {
@@ -532 +534 @@
      module M = A;
    }
+//------------------------------ start computation ---------------------------
    option(redSB);
    M = simplify(interred(M),1);
- /*
-   if (#[1] == 0)
-   {
-     M = simplify(std(M),1);
-   }
-   if (#[1] == 1)
-   {
-     M = simplify(interred(M),1);
-   }
- */
-   if (size(#) != 0)
-   {
-    module N = lift(A,M);
-   }
+   if(size(#) != 0) 
+   {
+      module N = lift(A,M);
+   }
+//--------------- reset ring and options and return --------------------------
    if ( u==1 )
    {
@@ -596 +590 @@
 
 proc gauss_row (matrix A, list #)
-"USAGE:  gauss_row(A); A matrix, e any type
+"USAGE:  gauss_row(A [,e]); A matrix, e any type
 RETURN: - a matrix B, if called with one argument; B is the complete row-
           reduced lower-triangular normal form of A if A is constant,
@@ -611 +605 @@
 @*      * Parameters are allowed. Hence, if the entries of A are parameters,
           B is the row-reduced form of A over the rational function field.
+SEE ALSO: rowred
 EXAMPLE: example gauss_row; shows an example
 "
@@ -633 +628 @@
    0, 0,  0, 0, 0,  0, 0, 2a;"";
    print(gauss_row(m));"";
-
    ring S=0,x,dp;
    matrix A[4][5] =  3, 1,1,-1,2,
@@ -766 +760 @@
            the row-reduced form of A and L[2] the transformation matrix
            (if rowred is called with two arguments).
-NOTE:    * This procedure is designed for teaching purposes only.
+NOTE:    * This procedure is designed for teaching purposes mainly.
 @*       * The straight forward Gaussian algorithm is implemented in the 
-           library (no standard basis computation), hence it is not very 
-           efficient. The transformation matrix is obtained by concatenating
-           a unit matrix to A, proc gauss_red should be faster.
+           library (no standard basis computation).
+           The transformation matrix is obtained by concatenating a unit 
+           matrix to A. proc gauss_row should be faster.
 @*       * It should only be used with exact coefficient field (there is no
            pivoting) over the polynomial ring (ordering lp or dp).
 @*       * Parameters are allowed. Hence, if the entries of A are parameters
            the computation takes place over the field of rational functions.
+SEE ALSO:  gauss_row
 EXAMPLE: example rowred; shows an example
 "
@@ -850 +845 @@
            the column-reduced form of A and L[2] the transformation matrix
            (if colred is called with two arguments).
-NOTE:    * This procedure is designed for teaching purposes only.
-@*       * It applies rowred to the transposed matrix, hence it is not very 
-           efficient (cf. rowred); proc gauss_col should be faster.
+NOTE:    * This procedure is designed for teaching purposes mainly.
+@*       * It applies rowred to the transposed matrix.
+           proc gauss_col should be faster.
 @*       * It should only be used with exact coefficient field (there is no
            pivoting) over the polynomial ring (ordering lp or dp).
 @*       * Parameters are allowed. Hence, if the entries of A are parameters
            the computation takes place over the field of rational functions.
+SEE ALSO:  gauss_col
 EXAMPLE: example colred; shows an example
 "