Skip to main content

programming - Emulating Sequence with my own function



I just considered if/how one could implement Sequence in Mathematica if it were not predefined. It turned out that the following simple definition has in all my tests exactly the right behaviour:


myseq /: f_[x___, myseq[y___], z___] := f[x, y, z]

Now my question: Does this already correctly reproduce the full behaviour of Sequence, or is there something Sequence does but myseq doesn't which I missed in my tests?


Here's what I tested:


foo[myseq[a, b]]
(*
==> foo[a, b]
*)
Hold[mysec[a,b]]

(*
==> Hold[a, b]
*)
HoldComplete[myseq[a,b]]
(*
HoldComplete[myseq[a, b]]
*)
Hold[f[myseq[a,b]]]
(*
==> Hold[f[myseq[a, b]]]

*)
f[myseq[myseq[a,b],c,d],e,myseq[f,g,myseq[]]]
(*
==> f[a, b, c, d, e, f, g]
*)

Answer



Ok, my two cents. The answer seems to be - you can't. There are 3 "magic" symbols which are wired into the core evaluator much deeper than the rest: Evaluate, Unevaluated, and Sequence. You can't fully emulate any of those without essentially writing your own version of Mathematica evaluator on top of the built-in one.


For the record, I first read about it in the book of David Wagner, "Power programming with Mathematica - the Kernel", p.207. Which means - if this is correct, I take the credit, but if it is wrong, he is the one to blame :). But, seriously, there was nothing in my experience to contradict this. You may emulate some aspects of Sequence, but I would be very surprised if you could make a complete emulation (without writing your own evaluator on top of the system one).


Let me also add that, while it is hidden, you do use Sequence in your approach, since the y___ pattern is internally destructured as Sequence. Check this out:


ClearAll[myseq];

myseq /: f_[x___, myseq[y___], z___] := f[x, Head[Unevaluated[y]], z]

and now


f[1, myseq[], 5]


f[1, Sequence, 5]

Comments

Post a Comment

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more