Changeset 226747 in git for Singular

Timestamp:

May 23, 2005, 5:47:35 PM (19 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'd08f5f0bb3329b8ca19f23b74cb1473686415c3a')

Children:

cc0d57d9d94f7a92fa7fe69725dd33393317d485

Parents:

a29de753041f4926d05681d7672626f921ff8e6b

Message:

*levandov: return replaced, some typos corrected


git-svn-id: file:///usr/local/Singular/svn/trunk@8291 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/control.lib (modified) (14 diffs)

Singular/LIB/control.lib

@@ -1 @@
-version="$Id: control.lib,v 1.32 2005-05-23 15:36:46 levandov Exp $";
+version="$Id: control.lib,v 1.33 2005-05-23 15:47:35 levandov Exp $";
 category="System and Control Theory";
 info="
@@ -152 +152 @@
 proc rightKernel(matrix M)
 "USAGE:  rightKernel(M);   M a matrix
+RETURN:  module
 PURPOSE: computes the right kernel of matrix M (a module of all elements v such that Mv=0)
-RETURN:  module
 EXAMPLE: example rightKernel; shows an example
 "{
@@ -171 +171 @@
 proc leftKernel(matrix M)
 "USAGE:  leftKernel(M);   M a matrix
+RETURN:  module
 PURPOSE: computes left kernel of matrix M (a module of all elements v such that vM=0)
-RETURN:  module
 EXAMPLE:  example leftKernel; shows an example
 "
@@ -191 +191 @@
 proc leftInverse(module M)
 "USAGE:  leftInverse(M);  M a module
+RETURN:  module
 PURPOSE: computes such a matrix L, that LM = Id;
-RETURN:  module
 EXAMPLE: example leftInverse; shows an example
 NOTE: exists only in the case when M is free submodule
@@ -241 +241 @@
 proc rightInverse(module R)
 "USAGE:  rightInverse(M);  M a module
+RETURN:  module
 PURPOSE: computes such a matrix L, that ML = Id
-RETURN:  module
 EXAMPLE: example rightInverse; shows an example
 NOTE: exists only in the case when M is free submodule
@@ -397 +397 @@
 proc control(module R)
 "USAGE:  control(R);  R a module (R is the matrix of the system of equations to be investigated)
+RETURN:  list
 PURPOSE: compute the list of all the properties concerning controllability of the system (behavior), represented by the matrix R
-RETURN:  list
 EXAMPLE:  example control; shows an example
 "
@@ -438 +438 @@
 proc controlDim(module R)
 "USAGE:  controlDim(R); R a module (R is the matrix of the system of equations to be investigated)
+RETURN: list
 PURPOSE: computes list of all the properties concerning controllability of the system (behavior), represented by the  matrix R
-RETURN: list
 EXAMPLE:  example controlDim; shows an example
 NOTE: this procedure is analogous to 'control' but uses dimension calculations.This approach works for full row rank matrices only.
@@ -474 +474 @@
 proc colrank(module M)
 "USAGE: colrank(M); M a matrix/module
+RETURN: int
 PURPOSE: compute the column rank of M as of matrix
-RETURN: int
 NOTE: this procedure uses Bareiss algorithm 
-
-"
-{
+"{
   // NOte continued:
   // which might not terminate in some cases
@@ -579 +577 @@
 proc autonomDim(module R)
 "USAGE:  autonomDim(R);   R a module (R is a matrix of the system of equations which is to be investigated)
+RETURN: list
 PURPOSE: computes the list of all the properties concerning autonomy of the system (behavior), represented by the matrix R
-RETURN: list
 NOTE:  this procedure is analogous to 'autonom' but uses dimension calculations
 EXAMPLE:  example autonomDim; shows an example
@@ -614 +612 @@
 proc autonom(module R)
 "USAGE:  autonom(R);   R a module (R is a matrix of the system of equations which is to be investigated)
+RETURN:  list
 PURPOSE: find all the properties concerning autonomy of the system (behavior) represented by the  matrix R
-RETURN:  list
 EXAMPLE: example autonom; shows an example
 "
@@ -655 +653 @@
 proc genericity(matrix M)
 "USAGE:  genericity(M); M is a matrix/module
+RETURN:  list (of strings)
 PURPOSE: determine parametric expressions which have been assumed to be non-zero in the process of computing the Groebner basis
-RETURN:  list (of strings)
 NOTE: we strongly recommend to switch on the redSB and redTail options;
 @*    the procedure is effective with the lift procedure for modules with parameters
@@ -876 +874 @@
 proc canonize(list L)
 "USAGE:  canonize(L); L a list
+RETURN:  list
 PURPOSE: modules in the list are canonized by computing their reduced minimal (= unique up to constant factor w.r.t. the given ordering) Groebner bases
-RETURN:  list
 ASSUME:  L is the output of control/autonomy procedures
 EXAMPLE:  example canonize; shows an example
@@ -1364 +1362 @@
 proc findTorsion(module R, ideal TAnn)
 "USAGE:  findTorsion(R, I);   R an ideal/matrix/module, I an ideal
+RETURN:  module
 PURPOSE: computes the Groebner basis of the submodule of R, annihilated by I
-ETURN:  module
 NOTE: especially helpful, when I is the annihilator of the t(R) - the torsion submodule of R. In this case, the result is the explicit presentation of t(R) as
 the submodule of R
@@ -1407 +1405 @@
 proc controlExample(string s)
 "USAGE:  controlExample(s);   s a string
+RETURN:  ring
 PURPOSE: set up an example from the mini database by initalizing a ring and a module in a ring
-RETURN:  ring
 NOTE: in order to see the list of available examples, execute @code{controlExample(\"show\");}
 @* To use ab example, one has to do the following. Suppose one calls the ring, where the example will be activated, A. Then, by executing