Changeset c57a83e in git

Timestamp:

Mar 5, 2010, 11:36:12 PM (13 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')

Children:

73809b3238e9c892b9499243f1d22f8a468631a8

Parents:

1f190d7136840b518cb253adbb3225c11420b6ea

Message:

*levandov: doc improvements

git-svn-id: file:///usr/local/Singular/svn/trunk@12608 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/involut.lib (modified) (4 diffs)

Singular/LIB/involut.lib

@@ -7 +7 @@
 @*        Viktor Levandovskyy,  levandov@mathematik.uni-kl.de
 
-THEORY: Involution is an anti-isomorphism of a noncommutative algebra with the
- property that applied an involution twice, one gets an identity. Involution is linear with respect to the ground field. In this library we compute linear involutions, distinguishing the case of a diagonal matrix (such involutions are called homothetic) and a general one.
+THEORY: Involution is an anti-isomorphism of a non-commutative K-algebra 
+@* with the property that applied an involution twice, one gets an identity. 
+@* Involution is linear with respect to the ground field. In this library we compute 
+@* linear involutions, distinguishing the case of a diagonal matrix (such involutions 
+@* are called homothetic) and a general one. Also, linear automorphisms of different
+@* order can be computed.
 
 SUPPORT: Forschungsschwerpunkt 'Mathematik und Praxis' (Project of Dr. E. Zerz
@@ -19 +23 @@
 findInvo();          computes linear involutions on a basering;
 findInvoDiag();     computes homothetic (diagonal) involutions on a basering;
-findAuto();          computes linear automorphisms of a basering;
+findAuto(n);          computes linear automorphisms of order n of a basering;
 ncdetection();        computes an ideal, presenting an involution map on some particular noncommutative algebras;
 involution(m,theta);  applies the involution to an object.
@@ -280 +284 @@
 RETURN:  object of the same type as m
 PURPOSE: applies the involution, presented by theta to the object m
-THEORY: for an involution theta and two polynomials a,b from the algebra, theta(ab) = theta(b) theta(a); theta is linear with respect to the ground field
+THEORY: for an involution theta and two polynomials a,b from the algebra, 
+@*  theta(ab) = theta(b) theta(a); theta is linear with respect to the ground field
 NOTE: This is generalized ''theta(m)'' for data types unsupported by ''map''.
 EXAMPLE: example involution; shows an example
@@ -687 +692 @@
 @*        L[i][1]  =  ideal; a Groebner Basis of an i-th associated prime,
 @*        L[i][2]  =  matrix, defining a linear map, with entries, reduced with respect to L[i][1]
-PURPOSE: compute the ideal of linear automorphisms of the basering, given by a matrix, n-th power of which gives identity (i.e. unipotent matrix)
-NOTE: if n=0, a matrix, defining an automorphism is not assumed to be unipotent but just non-degenerate. A nonzero parameter @code{@@p} is introduced as the value of the determinant of the matrix above.
-@* For convenience, the full ideal of relations @code{idJ} and the initial matrix with indeterminates @code{matD} are mutually exported in the output ring
+PURPOSE: compute the ideal of linear automorphisms of the basering, 
+@*  given by a matrix, n-th power of which gives identity (i.e. unipotent matrix)
+NOTE: if n=0, a matrix, defining an automorphism is not assumed to be unipotent 
+@* but just non-degenerate. A nonzero parameter @code{@@p} is introduced as the value of 
+@* the determinant of the matrix above.
+@* For convenience, the full ideal of relations @code{idJ} and the initial matrix with indeterminates 
+@* @code{matD} are mutually exported in the output ring
 SEE ALSO: findInvo
 EXAMPLE: example findAuto; shows examples