List of valid integer numpy.dtype values that are compatible with this finite field. Creating an array with an unsupported dtype will raise a TypeError exception.

For finite fields whose elements cannot be represented with numpy.int64, the only valid data type is numpy.object_.

Examples¶

For small finite fields, all integer data types are acceptable, with the exception of numpy.uint64. This is because all arithmetic is done using numpy.int64.

In [1]: GF = galois.GF(31); GF.dtypes
Out[1]: 
[numpy.uint8,
 numpy.uint16,
 numpy.uint32,
 numpy.int8,
 numpy.int16,
 numpy.int32,
 numpy.int64]

Some data types are too small for certain finite fields, such as numpy.int16 for \(\mathrm{GF}(7^5)\).

In [2]: GF = galois.GF(7**5); GF.dtypes
Out[2]: [numpy.uint16, numpy.uint32, numpy.int16, numpy.int32, numpy.int64]

Large fields must use numpy.object_ which uses Python int for its unlimited size.

In [3]: GF = galois.GF(2**100); GF.dtypes
Out[3]: [numpy.object_]

In [4]: GF = galois.GF(36893488147419103183); GF.dtypes
Out[4]: [numpy.object_]