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MathGroup Archive 1992

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  • To: mathgroup at yoda.physics.unc.edu
  • From: rvk at blink.att.com
  • Date: Tue, 27 Oct 92 14:58:38 EST

thanks to the more than two dozen people who responded to my
inquiry about converting a series to a function.  a few people
asked me to pass on any responses.  I'm attaching a few represetative
ones.

-r. kline
rvk at blink.att.com

==========================================================================

In[10]:= f = (Normal[Series[Sin[x],{x,0,5}]] /. x->#)&

Out[10]= Normal[Series[Sin[x], {x, 0, 5}]] /. x -> #1 & 

In[11]:= f[x]

              3    5
             x    x
Out[11]= x - -- + ---
             6    120

In[12]:= f[r]

              3    5
             r    r
Out[12]= r - -- + ---
             6    120


==========================================================================
The transforming of general expressions into functions is something
that I regularly accomplish with the following inelegant but quick
solution.  Say I have an exression called bob:


In[1]:= bob = Normal[ Series[ Sin[x], {x,0,5} ] ]

             3    5
            x    x
Out[1]= x - -- + ---
            6    120




Now turn that into a function:

In[2]:= fun[z_]:=bob/.{x->z}



It now has all of the properties of ordinary functions of arbitrary arguments:

In[3]:= fun[alpha]

                     3        5
                alpha    alpha
Out[3]= alpha - ------ + ------
                  6       120

In[4]:= D[fun[alpha],alpha]

                 2        4
            alpha    alpha
Out[4]= 1 - ------ + ------
              2        24

==========================================================================


In[1]:=
 a=Normal[Series[Sin[x],{x,0,5}]]

Out[1]=
     3    5
    x    x
x - -- + ---
    6    120
In[5]:=
f[x_]:=a

The definition of the function f is not exactly what you want.

In[6]:=
??f
Global`f

f[x_] := a

The reason is that ":=", or in FullForm SetDelayed[],  has the attribute HoldAll
, which means it does not evaluate it's arguments.  In this example it means tha
t "a" does not evaluate to the series with "x" in it.

In[7]:=
Attributes[SetDelayed]

Out[7]=
{HoldAll, Protected}
You can force evaluation of the right hand side by the following definition:

In[9]:=
f1[x_] := Evaluate[ a ]
Note that you now get the desired result.

In[10]:=

??f1
Global`f1

f1[x_] := x - x^3/6 + x^5/120

Wanting to assign a function to c computed result occurs often.


==========================================================================

  You asked about a=Normal[Series[Sin[x],{x,0,5}]] and f[x_]:=a ...
What you want instead of f[x_]:=a is f[x_]:=Release[a]. That should do it.

==========================================================================

        Suppose I create a series, using   
                                                                                
        a=Normal[Series[Sin[x],{x,0,5}]]                                        
                                                                                
        giving a = x - x^3/3! + x^5/5!.                                         
                                                                                
        I now want to use a to create a function of x, which, functionally,     
        is                                                                      
                                                                                
        f[x_]:=a.    

Define   a=Normal[Series[Sin[x],{x,0,5}]] // InputForm

and then F[x_] := Evaluate[a] // N.

==========================================================================

You need to understand the distinction between Set[ ] ("=") and SetDelayed[ ]
(":=").  With SetDelayed[ ] you form a rule with the *unevaluated* right
hand side.  So if you type f[x_] := a you get exactly what you typed in
and since there is no "x" in "a" there is nothing for the pattern matcher
to match.  It doesn't work.  If you type f[x_] = a the "a" first gets
evaluated to x - x^3/3! + x^5/5! and the rule that you get is then
f[x_] = x - x^3/6 + x^5/120.  This rule will then work.

==========================================================================

You need to do an immediate assignment:

f[x_] = a    (* NOT f[x_] := a *)






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