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function evaluation - I don't get it

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2

$begingroup$

this function returns Pi/4 for a[1,4]

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], an];
a[1, 4]

Out[...]= Pi/4

so the kernel knows that an evaluates to Pi/4

This function returns something that seems inconsistent with how it worked before

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], n/2 h w];
a[1, 4]

Out[...]= 4 Cos[an] Sin[an]

I get that Mathematica evaluation can seem non-intuitive but how this is as simple as it can get - comparing the 2 functions and their behaviors seems to show inconsistency: it knows that an=Pi/4, yet when an is used in simple algebraic expressions, an is returned unevaluated.

I must be missing something, but so far it eludes me.

EDIT:
after following user kglr's recommendation of reading the Trace I got the idea of moving the defn. of an outside of Module - that "fixes" things and gives me an actual answer but I am not yet quite sure why.

functions evaluation scoping

share|improve this question

edited 7 hours ago

Paul_A

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  inspect Trace[a[1, 4]] to see how an is processed.
  $endgroup$
  – kglr
  8 hours ago
  
  

  
  
  
  

add a comment | 

2

$begingroup$

this function returns Pi/4 for a[1,4]

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], an];
a[1, 4]

Out[...]= Pi/4

so the kernel knows that an evaluates to Pi/4

This function returns something that seems inconsistent with how it worked before

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], n/2 h w];
a[1, 4]

Out[...]= 4 Cos[an] Sin[an]

I get that Mathematica evaluation can seem non-intuitive but how this is as simple as it can get - comparing the 2 functions and their behaviors seems to show inconsistency: it knows that an=Pi/4, yet when an is used in simple algebraic expressions, an is returned unevaluated.

I must be missing something, but so far it eludes me.

EDIT:
after following user kglr's recommendation of reading the Trace I got the idea of moving the defn. of an outside of Module - that "fixes" things and gives me an actual answer but I am not yet quite sure why.

functions evaluation scoping

share|improve this question

edited 7 hours ago

Paul_A

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  inspect Trace[a[1, 4]] to see how an is processed.
  $endgroup$
  – kglr
  8 hours ago
  
  

  
  
  
  

add a comment | 

$begingroup$

this function returns Pi/4 for a[1,4]

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], an];
a[1, 4]

Out[...]= Pi/4

so the kernel knows that an evaluates to Pi/4

This function returns something that seems inconsistent with how it worked before

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], n/2 h w];
a[1, 4]

Out[...]= 4 Cos[an] Sin[an]

I get that Mathematica evaluation can seem non-intuitive but how this is as simple as it can get - comparing the 2 functions and their behaviors seems to show inconsistency: it knows that an=Pi/4, yet when an is used in simple algebraic expressions, an is returned unevaluated.

I must be missing something, but so far it eludes me.

EDIT:
after following user kglr's recommendation of reading the Trace I got the idea of moving the defn. of an outside of Module - that "fixes" things and gives me an actual answer but I am not yet quite sure why.

functions evaluation scoping

share|improve this question

edited 7 hours ago

Paul_A

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

$endgroup$

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], an];
a[1, 4]

Out[...]= Pi/4

In[...]:= a[r_, n_] := 
 Module[an = Pi/n, h = r Cos[an], w = 2 r Sin[an], n/2 h w];
a[1, 4]

Out[...]= 4 Cos[an] Sin[an]

share|improve this question

edited 7 hours ago

Paul_A

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

share|improve this question

edited 7 hours ago

Paul_A

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

asked 8 hours ago

Paul_APaul_A

19088 bronze badges

1 Answer
1

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5

$begingroup$

In a module, the local-variable declarations aren't executed one after the other, but rather independently. If you want to execute code sequentially, put it inside the module, not in the variable declaration:

a[r_, n_] := Module[an, h, w,
 an = Pi/n;
 h = r Cos[an];
 w = 2 r Sin[an];
 n/2 h w];
a[1, 4]
(* 2 *)

share|improve this answer

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges

$endgroup$

add a comment | 

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5

$begingroup$

In a module, the local-variable declarations aren't executed one after the other, but rather independently. If you want to execute code sequentially, put it inside the module, not in the variable declaration:

a[r_, n_] := Module[an, h, w,
 an = Pi/n;
 h = r Cos[an];
 w = 2 r Sin[an];
 n/2 h w];
a[1, 4]
(* 2 *)

share|improve this answer

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges

$endgroup$

add a comment | 

5

$begingroup$

In a module, the local-variable declarations aren't executed one after the other, but rather independently. If you want to execute code sequentially, put it inside the module, not in the variable declaration:

a[r_, n_] := Module[an, h, w,
 an = Pi/n;
 h = r Cos[an];
 w = 2 r Sin[an];
 n/2 h w];
a[1, 4]
(* 2 *)

share|improve this answer

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges

$endgroup$

add a comment | 

$begingroup$

In a module, the local-variable declarations aren't executed one after the other, but rather independently. If you want to execute code sequentially, put it inside the module, not in the variable declaration:

a[r_, n_] := Module[an, h, w,
 an = Pi/n;
 h = r Cos[an];
 w = 2 r Sin[an];
 n/2 h w];
a[1, 4]
(* 2 *)

share|improve this answer

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges

$endgroup$

a[r_, n_] := Module[an, h, w,
 an = Pi/n;
 h = r Cos[an];
 w = 2 r Sin[an];
 n/2 h w];
a[1, 4]
(* 2 *)

share|improve this answer

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges

answered 8 hours ago

RomanRoman

15.4k11 gold badge2121 silver badges5252 bronze badges