This is a Steenrod calculator. A Steenrod square is input like "Sq5" or "P5". The Milnor primitives are written like "Q2". The Bockstein is written as "b". The Milnor basis elements are denoted like "Sq(0,1)" or "P(0, 1)".
In order to multiply two elements you MUST include a "*" between them, for instance "Sq4*Sq2*Sq1". You can use parentheses for grouping as in "(Q2 + Sq7)*Sq2". Input can be an arbitrary homogenous arithmetic expression using +, -, *, and parentheses in these generators. Scalars are denoted like "2*P2". "P1*P1*2", or "-P1*P1" or "P1*P1*-1" are all valid notations.
For convenience, we also allow the notation "A(2 2 2 2)" for $Sq^2 Sq^2 Sq^2 Sq^2$ and "A(1 b 1)" for $P^1 \beta P^1$. The letter "A" here stands for "admissible", though of course the sequences involved are not admissible. We also allow "M(0 0 2)" as an alternate notation for "P(0, 0, 2)" or "Sq(0,0,2)".