Re: [sage-support] Finite Field Zage Logs Larger than 2^16

[Clement Pernet]

Hi,

For Givaro, there is no such limitation, the test-suite indeed tests the field 
GFqDom 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 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 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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[sage-support] 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.

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