Finite Field Zage Logs Larger than 2^16

[Eric Zhu]

It is possible to get element_givaro.py to create finite fields using zech logs for order larger than 2^16? The memory shouldn't be an issue.

[Clement Pernet]

Hi,

For Givaro, there is no such limitation, the test-suite indeed tests the field GFqDom<int64_t> with
the 22 bits cardinality 4194301.
Note that there is a misleading error in the class, where maxCardinality() returns 65536.
This is reported in https://github.com/linbox-team/givaro/issues/121
Fortunately, this is not enforced at construction

Now from the SageMath point of view, element_givaro also restricts the cardinality to 65536.
One reason for that is that it uses GfqDom<int> which in most archs is 32 bits and therefore limits
cardinality to 65536 (one need to be able to store a product of 2 elements in an int).

For SageMath to be able to use GFqDom with larger cardinalities, one should switch to
GFqDom<int64_t> which may slow down small fields. So ideally one should have 2 classes, one over
int32_t and the other one over int64_t.
Maybe using a templated systems as done for matrix_modn_dense with float and double would help
factor out code.

Clément

Le 18/06/2019 à 20:18, Eric Zhu a écrit :
> It is possible to get element_givaro.py to create finite fields using zech logs for order larger
> than 2^16? The memory shouldn't be an issue.
>

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