I think you also might find http://flask.sagenb.org/home/pub/82/ usefull. 
It's a worksheet created by Simon King which explains how to make new sage 
classes.

Le jeudi 29 mars 2012 00:14:43 UTC+2, Mark Shimozono a écrit :
>
> Suppose I want to create a custom subclass of a polynomial ring. 
> From which class should it inherit? It should not care so much about 
> the 
> eventual base ring. 
>
> I'm a sage development newbie. 
> Where can I read about the class hierarchy for sage polynomials? 
> I'm a little confused at the organizational principle behind the 
> following output. 
>
> sage: R = PolynomialRing(QQ,['x']) 
> sage: R.__class__ 
> <class 
> 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category'> 
>
>
> sage: R.an_element().__class__ 
> <type 
> 'sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint'> 
>
>
> sage: S = PolynomialRing(QQ,['x','y']) 
> sage: S.__class__ 
> <type 
> 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'>
>  
>
>
> sage: S.an_element().__class__ 
> <type 
> 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'> 
>
>
> --Mark 
>

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