## 4.23 vector

Vectors are elements of a free module over the basering with basis `gen(1)`, `gen(2)`, ... . Like polynomials they can only be defined or accessed with respect to the basering. Each vector belongs to a free module of rank equal to the biggest index of a generator with non-zero coefficient. Since generators with zero coefficients need not be written any vector may be considered also as an element of a free module of higher rank. (E.g., if `f` and `g` are polynomials then `f*gen(1)+g*gen(3)+gen(4)` may also be written as `[f,0,g,1]` or as `[f,0,g,1,0]`.) Note that the elements of a vector have to be surrounded by square brackets (`[` , `]`) (cf. Representation of mathematical objects).

> 4.23.1 vector declarations |  |
> 4.23.2 vector expressions |  |
> 4.23.3 vector operations |  |
> 4.23.4 vector related functions |  |

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