Hi there,
below a couple of quick comments:
> def coerce_ring_from_singular(r):
> cha=str(r.charstr())
> vars=str(r.varstr()).rsplit(',')
> ch=cha.partition(',')[0]
> if ch=='real':
> fiel=RR
> elif ch=='0':
> fiel=QQ
> elif ch=='complex':
> fiel=ComplexField()
> else:
> fiel=GF(sage_eval(ch))
> if ',' in cha and ch<>'complex' and ch<>'real':
I think you're probably looking for != here.
> generator=cha.partition(',')[2]
> fielx=PolynomialRing(fiel,generator)
> minpoly=r.ringlist()[1][4][1]
> minpoly=minpoly.sage_polystring()
> minpoly=sage_eval(minpoly,locals={generator:fielx.gen()})
Sorry for failing to mention that earlier, there is a function
called 'gens_dict' which gives you the right dictionary to pass to sage_eval:
sage: k.<a> = GF(2^8)
sage: k.gens_dict()
{'a': a}
sage: z = var('z'); K = NumberField(z^2 - 2,'s'); K
Number Field in s with defining polynomial z^2 - 2
sage: K.gens_dict()
{'s': s}
> if ch=='0':
> fiel=NumberField(minpoly,generator)
> else:
> fiel=fielx.quotient(fielx.ideal(minpoly))
This still doesn't work the right way for finite extension fields:
sage: k.<a> = GF(2^8)
sage: P.<x,y> = k[]
sage: P
Multivariate Polynomial Ring in x, y over Finite Field in a of size 2^8
sage: r = P._singular_()
sage: coerce_ring_from_singular(r)
Multivariate Polynomial Ring in x, y over Univariate Quotient Polynomial Ring
in abar over Finite Field of size 2 with modulus a^8 + a^4 + a^3 + a^2 + 1
> R=PolynomialRing(fiel,vars)
> return R
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
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