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3

You can use a conditional replacement rule to set any power of x higher than 1 to zero: simp[expr_, x_] := ExpandAll[expr] /. {Power[x, a_] /; a > 1 -> 0} simp[(1/x - 3 x + 4 - x)^4, x] simp[(1 - x)^2, x] (* -416 + 1/x^4 + 16/x^3 + 80/x^2 + 64/x - 256 x *) (* 1 - 2 x *) Of course, the easy way to do it would be to just take the Series and convert ...


1

The AddInputAlias function in the Notation package solves this problem. To use the example input alias created below, simply type Esc apply Esc. << Notation`; AddInputAlias[ParsedBoxWrapper[ RowBox[{"\[Placeholder]", " ", OverscriptBox["\[LongRightArrow]", RowBox[{" ", "Apply", " "}]], " ", "\[Placeholder]", " "}]], "apply"]


3

As noted by Rahul, one can always fall back on using the Rodrigues rotation formula if need be: rodrigues[th_, axis_?VectorQ] := With[{om = -LeviCivitaTensor[3].Normalize[axis]}, IdentityMatrix[3] + om Sin[th] + 2 MatrixPower[om, 2] Sin[th/2]^2]



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