OK, I tried the following:

S.<i,x,y> = PolynomialRing(QQ,order='lex')
I = ideal(i^2+1,(1+i)*x+y,x+(1-i)*y-(1-i))
G = I.groebner_basis()
G

would give me

[i - x - 1, x^2 + 2*x + 2, y - 2]

which are the results. But I am confused; why I can't get the result when I try 
to get a polynomial ring in the field of complex numbers implemented by sage? 
Also,
does adding i**2+1=0 really extend the rational numbers to complex number field?

Best Regards,


On Monday, February 17, 2014 12:14:25 PM UTC-5, john_perry_usm wrote:
>
> ACK! Make sure I=sqrt(-1) first!
>
> john perry
>
> On Monday, February 17, 2014 10:37:30 AM UTC-6, sahi...@gmail.com wrote:
>>
>> Hi:
>>
>> I am trying to obtain solution of a system of polynomial equations with 
>> complex coefficients without success. For example, when I try 
>>
>> S.<x,y> = PolynomialRing(CC,order='lex')
>> I = ideal((1+i)*x+y,x+(1-i)*y-(1-i))
>> G = I.groebner_basis()
>>
>> I see this error:
>>
>> AttributeError: 'Ideal_generic' object has no attribute 'groebner_basis'
>>
>> I tried another ideal and I am getting the same error. What am I doing 
>> wrong? 
>> Any help would be well appreciated.
>>
>> Best Regards,
>>
>>
>>  

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