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2020-03-12 15:44:28 +0100 asked a question ... `pushforward` method is not properly implemented.

When I run a script stored in a file test.sage as follows:

Fqm.<a> = GF(2^16)
Frob = Fqm.frobenius_endomorphism()
P.<z> = Fqm['z', Frob]

And then load this in sage with sage: load("test.sage"), everything is fine. But then when I load it a second time in the same instance of sage with sage: load("test.sage"), I get the following error message:

None fails to convert into the map's domain Finite Field in a of size 2^16, but a `pushforward` method is not properly implemented.

For field sizes smaller than 2^16 it seems to work without problems but as soon as I make the field 2^16 or larger this error occurs on a second call of the script. Placing a reset() function at the beginning of the script also does not help. Only closing sage completely and then loading the script again. Is this a bug or am I doing something wrong? I'm using the newest sage version 9.0.

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2018-05-31 02:15:36 +0100 asked a question span of vectors over an extension field but with coefficients from the base field

Hi all,

Assume I have a vector space with coefficients from a finite extension field. How can I make the sub space spanned by vectors over that extension field but with coefficients from the base field? When I do something like this:

sage: F = GF(2)
sage: FF.<a> = F.extension(4)
sage: VS = VectorSpace(FF, 6)
sage: span([VS.random_element() for i in range(3)], F)

I get an error that "is not compatble with base_ring". But if I would replace VS with VS = FreeModule(ZZ, 6) it works. But that is not what I want. Are there any solutions?

2018-05-31 02:15:36 +0100 asked a question span of vectors over an extension field but with coefficients from the base field

Hi all,

Assume I have a vector space with coefficients from a finite extension field. How can I make the sub space spanned by vectors over that extension field but with coefficients from the base field? When I do something like this:

F = GF(2) FF.= F.extension(4) VS = VectorSpace(FF, 6)

span([VS.random_element() for i in range(3)], F) I get an error that "is not compatble with base_ring". But if I would replace VS with VS = FreeModule(ZZ, 6) it works. But that is not what I want. Are there any solutions?