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Strange Series BUg
*To*: mathgroup at yoda.physics.unc.edu (Mathematica User's Group)
*Subject*: Strange Series BUg
*From*: Keith Clay <clay at galileo.phys.washington.edu>
*Date*: Thu, 23 Sep 93 15:06:17 MDT
Here is a bug that calls into question not only the way in which Mma
deals with series, but the way in which Mma deals with constants
whether they are constants I invent like "z" or one that it is supposed
to know about like "Pi".
Here is is:
------------------------------------------------------------------------
DEFINE A SIMPLE FUNCTION AND ASK FOR THE SERIES. KEEP YOUR EYES ON "d".
In[1]:= expr1 = E^( (a - b x) (c - d) )
(c - d) (a - b x)
Out[1]= E
In[2]:= Series[expr1,{x,0,1}]
a (c - d) a (c - d) 2
Out[2]= E - b (c - d) E x + O[x]
NO PROBLEM. IT SHOULDN'T MATTER IF WE LET d BE SOMETHING LIKE Log[z], RIGHT?
In[3]:= expr2 = expr1/.(d->Log[z])
(a - b x) (c - Log[z])
Out[3]= E
In[4]:= Series[expr2,{x,0,1}]
Series::esss: Essential singularity encountered in
2
Exp[a (c - Log[z]) - b (c + <<1>>) x + O[x] ].
(a - b x) (c - Log[z])
Out[4]= Series[E , {x, 0, 1}]
SOMEHOW THE PRESENCE OF "z" BOTHERED IT.
NOW WE MAKE IT EASIER BY PUTTING A NUMBER LIKE "E" IN THE LOG TERM
In[5]:= expr3 = expr2/.z->E
(-1 + c) (a - b x)
Out[5]= E
In[6]:= Series[expr3,{x,0,1}]
a (-1 + c) a (-1 + c) 2
Out[6]= E - b (-1 + c) E x + O[x]
IT IS EASY TO THINK ABOUT THE LOG OF "E" OR A REAL NUMBER. NO PROBLEM, RIGHT?
In[7]:= expr4 = expr2/.z->1.1
(-0.0953102 + c) (a - b x)
Out[7]= E
In[8]:= Series[expr4,{x,0,1}]
a (-0.0953102 + c) a (-0.0953102 + c) 2
Out[8]= E - b (-0.0953102 + c) E x + O[x]
FOR SOME REASON HAVING A VARIABLE IN THE LOG FUNCTION THREW MMA OFF, BUT
AS LONG AS IT IS JUST A NUMBER, THERE IS NO PROBLEM RIGHT? WRONG!!!
In[9]:= expr5 = expr2/.z->Pi
(a - b x) (c - Log[Pi])
Out[9]= E
In[10]:= Series[expr5,{x,0,1}]
Series::esss: Essential singularity encountered in
2
Exp[a (c - Log[Pi]) - b (c + <<1>>) x + O[x] ].
(a - b x) (c - Log[Pi])
Out[10]= Series[E , {x, 0, 1}]
This is scary.
------------------------------------------------------------------------
Keith Clay Department of Physics, FM-15
(clay at galileo.phys.washington.edu) University of Washington
( -or- clay at phys.washington.edu ) Seattle, WA 98195
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