This calculator uses the Adem relations to express elements of the mod 2 Steenrod algebra in terms of the Serre-Cartan basis.
To evaluate (for example) Sq2Sq7+Sq9, use input format: 2 7 + 9
Currently this is the only input format supported, i.e. input must be a single Steenrod square, a product of squares, or a sum of products of squares - no parenthesization allowed.
Output is in the same format.

Result:

Compiled to Javascript from Racket (a Scheme dialect) using Whalesong.

N.B.: This entire page (aside from the N.B. that you're currently reading) was created by Alex Kruckman. If you've appreciated it, write him to say thanks!

I wrote the app above for a fun programming diversion during my first semester of graduate school. Since many people have found it useful, it is still being hosted here. But I would like to advertise the existence of a Sage package for computations in the Steenrod algebra, which is much more flexible than my simple calculator. Full documentation is here.

For example, the following Sage code expresses Sq2Sq7+Sq9 in terms of the Serre-Cartan basis in the mod 2 Steenrod algebra.
``` A = SteenrodAlgebra(basis="serre-cartan") A.Sq(2)*A.Sq(7)+A.Sq(9) ```

Sage can handle the mod p Steenrod algebras too. The following code expresses P1 β P3 in terms of the Serre-Cartan basis in the mod 7 Steenrod algebra. Note that `Q(0)` represents the Bockstein operation β.
``` A = SteenrodAlgebra(7,basis="serre-cartan") A.P(1)*A.Q(0)*A.P(3) ```

Try it in your browser on SageMathCell.