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5

1

$begingroup$

When I try to define this simple function

getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

I get an error:

SeriesData: Coefficient specification coeff_ in SeriesData[_,_,coeff_,_,_,_] is not a list.

Can someone explain what's wrong with this? My understanding was that SetDelayed shouldn't complain about such things because until I actually evaluate an expression containing getCoeff it shouldn't try to evaluate Part[coeff,2].

There is no error thrown for the similar function

f[g[_, _, x_, _, _, _]] := x[[2]]

and furthermore getCoeff works as expected:

getCoeff@Series[E^([Pi] x), {x, 0, 3}]

outputs $pi$.

I know the "right" way to manipulate SeriesData, I'd just like to understand this case for its own sake.

series-expansion assignment

share|improve this question

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Use unevaluated: getCoeff[Unevaluated[SeriesData[_, _, coeff_, _, _, _]]] := coeff[[2]]; Then getCoeff@Series[E^([Pi] x), {x, 0, 3}] = [Pi].
  $endgroup$
  – Shredderroy
  8 hours ago
  

  
  
  
  

add a comment
 | 

5

1

$begingroup$

When I try to define this simple function

getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

I get an error:

SeriesData: Coefficient specification coeff_ in SeriesData[_,_,coeff_,_,_,_] is not a list.

Can someone explain what's wrong with this? My understanding was that SetDelayed shouldn't complain about such things because until I actually evaluate an expression containing getCoeff it shouldn't try to evaluate Part[coeff,2].

There is no error thrown for the similar function

f[g[_, _, x_, _, _, _]] := x[[2]]

and furthermore getCoeff works as expected:

getCoeff@Series[E^([Pi] x), {x, 0, 3}]

outputs $pi$.

I know the "right" way to manipulate SeriesData, I'd just like to understand this case for its own sake.

series-expansion assignment

share|improve this question

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Use unevaluated: getCoeff[Unevaluated[SeriesData[_, _, coeff_, _, _, _]]] := coeff[[2]]; Then getCoeff@Series[E^([Pi] x), {x, 0, 3}] = [Pi].
  $endgroup$
  – Shredderroy
  8 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

When I try to define this simple function

getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

I get an error:

SeriesData: Coefficient specification coeff_ in SeriesData[_,_,coeff_,_,_,_] is not a list.

Can someone explain what's wrong with this? My understanding was that SetDelayed shouldn't complain about such things because until I actually evaluate an expression containing getCoeff it shouldn't try to evaluate Part[coeff,2].

There is no error thrown for the similar function

f[g[_, _, x_, _, _, _]] := x[[2]]

and furthermore getCoeff works as expected:

getCoeff@Series[E^([Pi] x), {x, 0, 3}]

outputs $pi$.

I know the "right" way to manipulate SeriesData, I'd just like to understand this case for its own sake.

series-expansion assignment

share|improve this question

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

$endgroup$

getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]

SeriesData: Coefficient specification coeff_ in SeriesData[_,_,coeff_,_,_,_] is not a list.

f[g[_, _, x_, _, _, _]] := x[[2]]

getCoeff@Series[E^([Pi] x), {x, 0, 3}]

share|improve this question

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

share|improve this question

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

asked 8 hours ago

DiffycueDiffycue

28111 silver badge66 bronze badges

1 Answer
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5

$begingroup$

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)

HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)



(* prevent only evaluation of the first argument (equivalent in this case) *)

getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)

share|improve this answer

answered 7 hours ago

Lukas LangLukas Lang

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5

$begingroup$

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)

HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)



(* prevent only evaluation of the first argument (equivalent in this case) *)

getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)

share|improve this answer

answered 7 hours ago

Lukas LangLukas Lang

9,82911 gold badge1313 silver badges3636 bronze badges

$endgroup$

add a comment
 | 

5

$begingroup$

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)

HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)



(* prevent only evaluation of the first argument (equivalent in this case) *)

getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)

share|improve this answer

answered 7 hours ago

Lukas LangLukas Lang

9,82911 gold badge1313 silver badges3636 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

This is due to the special behavior of SetDelayed (:=) with regards to the first argument (see e.g. this question): The arguments of the l.h.s. are evaluated by SetDelayed, which causes the error you are seeing - after all, SeriesData[_, _, coeff_, _, _, _] is not a valid SeriesData construct. This is what HoldPattern is designed for: It prevents evaluation of its argument (like Hold), but is invisible to the pattern matcher. The solution is therefore simply:

(* prevent the l.h.s. from being evaluated *)

HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)



(* prevent only evaluation of the first argument (equivalent in this case) *)

getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)

share|improve this answer

answered 7 hours ago

Lukas LangLukas Lang

9,82911 gold badge1313 silver badges3636 bronze badges

$endgroup$

(* prevent the l.h.s. from being evaluated *)

HoldPattern@getCoeff[SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)



(* prevent only evaluation of the first argument (equivalent in this case) *)

getCoeff[HoldPattern@SeriesData[_, _, coeff_, _, _, _]] := coeff[[2]]



getCoeff@Series[E^(π x), {x, 0, 3}]

(* π *)

share|improve this answer

answered 7 hours ago

Lukas LangLukas Lang

9,82911 gold badge1313 silver badges3636 bronze badges

answered 7 hours ago

Lukas LangLukas Lang

9,82911 gold badge1313 silver badges3636 bronze badges

answered 7 hours ago

Lukas LangLukas Lang

9,82911 gold badge1313 silver badges3636 bronze badges