format

.gdbinit

@@ -10,7 +10,7 @@ break dPolyReportError
 define pp
   if $argc > 0
     print $arg0
-    if $arg0 != 0 
+    if $arg0 != 0
       print *$arg0
 
       if $argc == 2
@@ -21,14 +21,14 @@ define pp
     end
   end
 end
-     
+
 
 
 # print number coeffs
 define nn
   if $argc > 0
     print $arg0
-    if $arg0 != 0 
+    if $arg0 != 0
       print *$arg0
 
       if $argc == 2
@@ -39,4 +39,4 @@ define nn
     end
   end
 end
-     
+

IntegerProgramming/change_cost.hlp

@@ -1,141 +1,141 @@
 USAGE: change_cost [options] groebner_file new_cost_file
-            
-             
-           
+
+
+
 DESCRIPTION:
-             
+
 change_cost is a program for recomputing the reduced Groebner basis of
 a toric ideal with respect to a term ordering with modified
 weights. This can be used for varying the cost function in integer
 programming (see the help for solve_IP for more information).
 The program simply restarts Buchberger�s algorithm on an already
-computed toric ideal using the modified term ordering.               
-            
-                
-      
+computed toric ideal using the modified term ordering.
+
+
+
 FILE FORMAT:
-               
+
 The first input file has to be a GROEBNER file; the second input file
 should to be a NEW_COST file. For convenience, also MATRIX files are
 accepted as second input files. For their format see the help for the
-solve_IP or the toric_ideal program.  
-               
+solve_IP or the toric_ideal program.
+
 change_cost writes the new Groebner basis into a GROEBNER file named
 like the second input file with extensions replaced by
-          
+
 	.GB.<alg>
-              
+
 where GB stands for GROEBNER and <alg> is the abbreviation of the
-algorithm used for computing the input GROEBNER file (see the help for 
+algorithm used for computing the input GROEBNER file (see the help for
 solve_IP or toric_ideal for an explaination).
-               
+
 A GROEBNER file looks as follows:
-         
-         
-  GROEBNER 
-            
+
+
+  GROEBNER
+
   computed with algorithm:
   <algorithm name abbreviation>       (* abbreviations as above *)
-  from file(s):                       (* the following four lines are 
+  from file(s):                       (* the following four lines are
   <name of respective MATRIX file>       optional *)
-  computation time:                     
-  <computation time in seconds>          
-             
+  computation time:
+  <computation time in seconds>
+
   term ordering:
   elimination block
   <number of elimination variables>
   <LEX / DEG_LEX                      (* only if number of elimination
   / DEG_REV_LEX>                         variables >0 *)
   weighted block
   <number of weighted variables>
-  <W_LEX / W_REV_LEX                  (* number of weighted variables    
+  <W_LEX / W_REV_LEX                  (* number of weighted variables
   / W_DEG_LEX / W_DEG_REV_LEX>           should always be >0 *)
   <weight_vector>
-             
+
   size:
   <number of elements>
-          
+
   Groebner basis:
-  <basis elements>                   
-            
-  <settings for the Buchberger 
-   algorithm and compiler settings>  (* optional *)		
-            
-                  
+  <basis elements>
+
+  <settings for the Buchberger
+   algorithm and compiler settings>  (* optional *)
+
+
 The Groebner basis consists always of binomials of the form x^a - x^b
 where x^a and x^b are relatively prime. Such a binomial can be
-represented by the vector a-b. The basis elements in the GROEBNER file 
+represented by the vector a-b. The basis elements in the GROEBNER file
 are given by the coefficients of this vector representation.
 The settings for Buchberger�s algorithm and the compiler flags are
 produced when the GROEBNER file is generated by a call of solve_IP
 with the verbose output option
-          
-	-v, --verbose  
-             
+
+	-v, --verbose
+
 Example:
-         
-         
+
+
   GROEBNER
-         
+
   computed with algorithm:
   du
-        
-  term ordering:	
+
+  term ordering:
   elimination block:
   0
   weighted block:
   3
   W_LEX
   1 2 3
-           
+
   size:
   1
-              
+
   Groebner basis:
-  2 3 -2			    (*  x^2 * y^3 - z^2  *) 
-           
-               
+  2 3 -2			    (*  x^2 * y^3 - z^2  *)
+
+
 A NEW_COST file should look as follows:
-           
-            
-  NEW_COST              
-            
-  variables:			
-  <number of weighted variables>         
-              
+
+
+  NEW_COST
+
+  variables:
+  <number of weighted variables>
+
   cost vector:
-  <coefficients of the new weight vector>       
-               
-        
-                
-OPTIONS: 
-          
+  <coefficients of the new weight vector>
+
+
+
+OPTIONS:
+
  -p         <number>      percentage of new generators to cause an
-                          autoreduction during Buchberger�s algorithm; 
+                          autoreduction during Buchberger�s algorithm;
                           <number> may be an arbitrary float, a
                           negative value allows no intermediate
                           autoreductions
-			  default is 
-                          -p 12.0  
-                
+			  default is
+                          -p 12.0
+
  -S [RP] [M] [B] [M] [2]  criteria to use in Buchberger�s algorithm
                           for discarding unneccessary S-pairs
              RP           relatively prime leading terms
              M            Gebauer-Moeller criterion M
              F            Gebauer-Moeller criterion F
              B            Gebauer-Moeller criterion B
              2            Buchberger�s second criterion
-			  default is 
-                          -S RP M B 		
-             
- -v,          
---verbose                 verbose output mode; writes the settings for 
+			  default is
+                          -S RP M B
+
+ -v,
+--verbose                 verbose output mode; writes the settings for
                           Buchberger�s algorithm and the compiler
-                          flags into the output GROEBNER file 
-             
--V <number>, 
+                          flags into the output GROEBNER file
+
+-V <number>,
 --version <number>        version of Buchberger�s algorithm to use;
                           <number> may be 1, 1a, 2 or 3
 			  default is
-                          -V 1	
-                  
+                          -V 1
+