23 Row Vectors

A row vector is a vector (see IsVector) that is also a homogeneous list. Typical examples are lists of integers, lists of finite field elements of the same characteristic, lists of polynomials from a common polynomial ring, and matrices.

The additive operations of the vector must thus be compatible with that for lists, implying that the list entries are the coefficients of the vector with respect to some basis.

Note that not all row vectors admit a scalar product via *; for example, matrices are row vectors but the matrix product is defined in a different way. For the installation of a scalar product of row vectors, the entries of the vector must be ring elements; note that the default method expects the row vectors to lie in IsRingElementList, and this category may not be implied by IsRingElement for all entries of the row vector (see the comment for IsVector in IsVector).

Note that methods for special types of row vectors really must be installed with the requirement IsRowVector, since IsVector may lead to a rank of the method below that of the default method for row vectors (see file vecmat.gi).

gap> IsRowVector([1,2,3]);
true

Because row vectors are just a special case of lists, all operations and functions for lists are applicable to row vectors as well (see chapter Lists). This especially includes accessing elements of a row vector (see List Elements), changing elements of a mutable row vector (see List Assignment), and comparing row vectors (see Comparisons of Lists).

Note that, unless your algorithms specifically require you to be able to change entries of your vectors, it is generally better and faster to work with immutable row vectors. See section Mutability and Copyability for more details.

Sections

1. Operators for Row Vectors
2. Row Vectors over Finite Fields
3. Coefficient List Arithmetic
4. Shifting and Trimming Coefficient Lists
5. Functions for Coding Theory
6. Vectors as coefficients of polynomials

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