# how to calcualte the basis of quotient module over the steenrod algebra in Sage

A(2) is steenrod algebra generated by sq1, sq2,sq4 with Adem relations, we knew A(2) has dimension 64, how to calculate the basis like quotient algebra A(2)/A(2){sq1} and A(2)/A(2){sq1,sq2sq3} and A(2)/A(2){sq1, sq7,sq3sq7+sq4sq6} in Sage? Thanks !

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Quotients like this are not well implemented in Sage, and in particular, there is no simple way to compute a basis. Examples of ways in which the implementation is not great:

sage: A2 = SteenrodAlgebra(profile=(3,2,1))
sage: s1 = A2.Sq(1)
sage: I = A2.ideal(s1)
sage: I
Twosided Ideal (Sq(1)) of sub-Hopf algebra of mod 2 Steenrod algebra, milnor basis, profile function [3, 2, 1]
sage: s1 in I
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)

....

NotImplementedError:
sage: R = A2.quotient(I)
sage: R(s1) == 0
False

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