Piecewise function inside If statement or another Piecewise function breaks outputs

Question

I have a calculation that outputs a piecewise function that has as its cases a list of expressions. An example (3 cases with each a list of 4 expressions) is below:

pw[x_,y_]:=Piecewise[{{{a1,b1,c1,d1},x>5y},{{a2,b2,c2,d2},x<3y}},{a3,b3,c3,d3}]

I need to remove the first expression (a1 or a2 or a3) before use in further calculation, so I apply the following Delete operations.

pw2[x_,y_]:=pw[x,y]//Delete[#,Table[{1,i,1,1},{i,1,Length[#[[1]]]}]]&//Delete[#,{2,1}]&
pw2[w,v] (*evaluates correctly*)
pw2[1,2] (*fails because it is no longer piecewise when evaluated*)

The above pw2[w,v] gives the desired output, but I would like the function to handle both symbolic inputs and numbers, but pw2[1,2] fails since the deletions are not being applied to a piecewise function.

While I might be able to use Hold or Block. I thought this case should be simple enough to be handled separately without imposing a hold on large parts of the calculation.

Attempted Fix 1: If statement

(*Try if statement to handle when inputs are symbolic and when they are numbers*)
pw3[x_,y_]:=If[VectorQ[{x,y}], pw[x,y]//Delete[#,1]&, pw2[x,y]]
pw3[w,v] (*fails for some reason related to the conditions of the piecewise functions being erased?*)
pw3[1,2] (*works as desired*)

The If statement approach seems to break the piecewise function. Why does this happen in a seemingly innocuous If statement? I had encountered similar errors with Piecewise when testing the Delete in pw2.

I though this might just be because If is a programmic construct, so I should use a mathematical construct.

Attempted Fix 2: Piecewise function

(*Try piecewise function to handle cases*)
pw4[x_,y_]:=Piecewise[{{pw[x,y]//Delete[#,1]&,VectorQ[{x,y}]}},{pw2[x,y]}]
pw4[w,v] (*fails as in pw3*)
pw4[1,2] (*works as desired*)

This has the same errors as in the If statement case.

What is happening in piecewise that causes the above to fail?

score 3 · Answer 1 · answered Jan 03 '20 at 17:40

Inject x and y after the deletions are done on p[.,.]:

ClearAll[pw2]
pw2[x_, y_] := (pw[\[FormalX], \[FormalY]] // 
     Delete[#, Table[{1, i, 1, 1}, {i, 1, Length[#[[1]]]}]] & // 
    Delete[#, {2, 1}] &) /. {\[FormalX] -> x, \[FormalY] -> y}

pw2[w, v]

pw2[1, 2]

{b2, c2, d2}

An alternative way to get the same result:

ClearAll[pw23]
pw3[x_, y_] := Replace[pw[x, y], {a_, b_, c_, d_} :> {b, c, d}, All]

pw3[w, v]

pw3[1, 2]

{b2, c2, d2}

Piecewise function inside If statement or another Piecewise function breaks outputs

1 Answers1