Add Magma interface for orders and ideals of number fields

[mmasdeu]

This ticket adds functionality to convert orders and ideals of number fields from Sage to Magma and back.

[mmasdeu]

New commits:

​ffdad84

Added Magma interface for orders and ideals of number fields.

[vdelecroix]

There is a problem with the copy of the script directory on the server

sage: magma=Magma(...) # custom server config
sage: magma('1')
Traceback (most recent call last):
...
TypeError: Can't open package spec file ... for reading (No such file or directory)

The solution might be to create the directory remotely if it does not exist. Something like

os.system("ssh SERVE 'mkdir -p THE_GOOD_DIR'")

[mmasdeu]

This ticket is independent of #20388... It won't work unless Magma is installed locally. Once #20388 is merged this should be rebased, I guess...

[vdelecroix]

Indeed, #20388 is merged in the last beta and I was able to use magma.

However

sage: K.<a> = NumberField(x^3 + 2)
sage: I = K.ideal(5)
sage: I._magma_init_(magma)
Traceback (most recent call last):
...
TypeError: Error evaluating Magma code.
IN:_sage_[3]:=SageCreateWithNames(PolynomialRing(_sage_ref1),["x"]);
OUT:
In file "/home/delecroi/tmp/data//sage/basic.m", line 104, column 6:
>>   if IsPrimeField(X) then
        ^
Runtime error: Undefined reference 'IsPrimeField' in package "/home/delecroi/tmp/data//sage/basic.m"

[chapoton]

ok, for me, with m4gm4 version Magma V2.22-3