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 Results for DC.creator="A." AND DC.creator="Thiers" in section 1.2.7 of volume D   page 1 of 2 pages.
Introduction to the accompanying software Ten[chi]ar
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7, pp. 62-70 [ doi:10.1107/97809553602060000901 ]
... in complicated cases errors can be made. This is therefore a situation in which it is best to rely on computer ... is accompanied by two software packages. Here we shall give a short introduction to the Ten[chi]ar package that deals ... of point groups in the second module. The latter play a role when determining the number of independent elements of ...

Determination of tensor products and their decomposition
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.4.5, p. 68 [ doi:10.1107/97809553602060000901 ]
... decomposition 1.2.7.4.5. Determination of tensor products and their decomposition Given a character (for an irreducible representation from the character table, or ... integers satisfying . (2) For each such decomposition there is a term where , and p is the number of nonzero integers ... values (). (4) The sign of the term is for a symmetrized power and for an antisymmetrized power. (5) The ...

Determination of the vector representation
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.4.4, p. 68 [ doi:10.1107/97809553602060000901 ]
... the vector representation 1.2.7.4.4. Determination of the vector representation For a point group G, its isomorphism class and its character table are known. For each conjugacy class, a representative element is given as word where the 's correspond ... the letters by the generating matrices, one obtains as product a matrix for which the trace is the character of ...

Diagonalization of the action matrix and determination of the invariant tensor
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.4.3, pp. 67-68 [ doi:10.1107/97809553602060000901 ]
... element of the tensor space under the group G is a vector v that is left invariant under each generator: If ... are equal to zero. The corresponding rows of Q form a basis for the solution space. (See example further on.) References ...

Action of the generators of the point group G on the basis
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.4.2, p. 67 [ doi:10.1107/97809553602060000901 ]
... in principle non-commutative. This polynomial can be written as a sum of the monomials in the basis taking into account ... anti)symmetry of and . In this way, basis element (a monomial) is transformed to To each generator of G corresponds ... previous equation changes to The function Det(g) is just a one-dimensional representation of the group G. The determinant ...

Construction of a basis
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.4.1, p. 67 [ doi:10.1107/97809553602060000901 ]
Construction of a basis 1.2.7.4.1. Construction of a basis As a basis for a tensor space without permutation symmetry, one ...

Algorithms
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.4, pp. 67-70 [ doi:10.1107/97809553602060000901 ]
Algorithms 1.2.7.4. Algorithms 1.2.7.4.1. Construction of a basis | | As a basis for a tensor space without permutation symmetry, one may choose one ...

Characters
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.3, pp. 66-67 [ doi:10.1107/97809553602060000901 ]
... is selected in the main window by clicking `character'. A selection window opens in which a point group may be selected just as in the tensor ... organized according to dimension and geometric crystal class. Selection of a point group leads to the display of the character ...

Tensors
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.2, pp. 64-66 [ doi:10.1107/97809553602060000901 ]
... relations between the elements of tensors and pseudotensors invariant under a chosen point group and with specified permutation symmetry of the indices. Although the list of point groups provided in a database is limited to dimensions two and three, the program ... smaller than or equal to four. This is also not a restriction of the program, which works for arbitrary rank. ...

Overview
Ephra[iuml ]m, M., Janssen, T., Janner, A. and Thiers, A.  International Tables for Crystallography (2013). Vol. D, Section 1.2.7.1, pp. 62-64 [ doi:10.1107/97809553602060000901 ]
... in complicated cases errors can be made. This is therefore a situation in which it is best to rely on computer ... is accompanied by two software packages. Here we shall give a short introduction to the Ten[chi]ar package that deals ... of point groups in the second module. The latter play a role when determining the number of independent elements of ...

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