Changeset c57a83e in git
 Timestamp:
 Mar 5, 2010, 11:36:12 PM (13 years ago)
 Branches:
 (u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')
 Children:
 73809b3238e9c892b9499243f1d22f8a468631a8
 Parents:
 1f190d7136840b518cb253adbb3225c11420b6ea
 File:

 1 edited
Legend:
 Unmodified
 Added
 Removed

Singular/LIB/involut.lib
r1f190d7 rc57a83e 7 7 @* Viktor Levandovskyy, levandov@mathematik.unikl.de 8 8 9 THEORY: Involution is an antiisomorphism of a noncommutative algebra with the 10 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. 9 THEORY: Involution is an antiisomorphism of a noncommutative Kalgebra 10 @* with the property that applied an involution twice, one gets an identity. 11 @* Involution is linear with respect to the ground field. In this library we compute 12 @* linear involutions, distinguishing the case of a diagonal matrix (such involutions 13 @* are called homothetic) and a general one. Also, linear automorphisms of different 14 @* order can be computed. 11 15 12 16 SUPPORT: Forschungsschwerpunkt 'Mathematik und Praxis' (Project of Dr. E. Zerz … … 19 23 findInvo(); computes linear involutions on a basering; 20 24 findInvoDiag(); computes homothetic (diagonal) involutions on a basering; 21 findAuto( ); computes linear automorphismsof a basering;25 findAuto(n); computes linear automorphisms of order n of a basering; 22 26 ncdetection(); computes an ideal, presenting an involution map on some particular noncommutative algebras; 23 27 involution(m,theta); applies the involution to an object. … … 280 284 RETURN: object of the same type as m 281 285 PURPOSE: applies the involution, presented by theta to the object m 282 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 286 THEORY: for an involution theta and two polynomials a,b from the algebra, 287 @* theta(ab) = theta(b) theta(a); theta is linear with respect to the ground field 283 288 NOTE: This is generalized ''theta(m)'' for data types unsupported by ''map''. 284 289 EXAMPLE: example involution; shows an example … … 687 692 @* L[i][1] = ideal; a Groebner Basis of an ith associated prime, 688 693 @* L[i][2] = matrix, defining a linear map, with entries, reduced with respect to L[i][1] 689 PURPOSE: compute the ideal of linear automorphisms of the basering, given by a matrix, nth power of which gives identity (i.e. unipotent matrix) 690 NOTE: if n=0, a matrix, defining an automorphism is not assumed to be unipotent but just nondegenerate. A nonzero parameter @code{@@p} is introduced as the value of the determinant of the matrix above. 691 @* For convenience, the full ideal of relations @code{idJ} and the initial matrix with indeterminates @code{matD} are mutually exported in the output ring 694 PURPOSE: compute the ideal of linear automorphisms of the basering, 695 @* given by a matrix, nth power of which gives identity (i.e. unipotent matrix) 696 NOTE: if n=0, a matrix, defining an automorphism is not assumed to be unipotent 697 @* but just nondegenerate. A nonzero parameter @code{@@p} is introduced as the value of 698 @* the determinant of the matrix above. 699 @* For convenience, the full ideal of relations @code{idJ} and the initial matrix with indeterminates 700 @* @code{matD} are mutually exported in the output ring 692 701 SEE ALSO: findInvo 693 702 EXAMPLE: example findAuto; shows examples
Note: See TracChangeset
for help on using the changeset viewer.