field extensions in python

edit

You can define a field extenion at the sage prompt with

QC.<j>; = QQ.extension(x^2+1)

however this same line in a python script yields a syntax error

def mytest(): 
    QC.<j> = QQ.extension(x^2+1);
    return

Traceback (most recent call last):
...
def mytest(): QC.<j> = QQ.extension(x**_sage_const_2 +_sage_const_1 ); return
                 ^
SyntaxError: invalid syntax

Note:syntax error point to < character

eval also fails

eval('QC.<j> = QQ.extension(x^2+1)')

Traceback (most recent call last):
....    
QC.<j> = QQ.extension(x^2+1)
   ^
SyntaxError: invalid syntax

I also have similar problems with defining Quaternion Algebras in python

HQ.<q1,q2,q3> = QuaternionAlgebra(QC,-1,-1)

so why does QC.<j> = QQ.extension(x^2+1) work at the sage prompt and not in python or with eval(string)

Thanks, Steve