PolynomialQ
- To: mathgroup at smc.vnet.net
- Subject: [mg34115] PolynomialQ
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Sat, 4 May 2002 04:28:41 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
The following strange behaviour of PolynomialQ has been recently observed on the Japan Mathematica Users mailing list: In[1]:= PolynomialQ[1/x,1/x] Out[1]= False To see that this is odd compare: In[2]:= PolynomialQ[x,Sqrt[x]] Out[2]= True with In[2]:= PolynomialQ[1/x,Sqrt[1/x]] Out[2]= False or, more generally In[4]:= PolynomialQ[x^a,x^a] Out[4]= True while In[5]:= PolynomialQ[x^-a,x^-a] Out[5]= False It certainly makes no mathematical sense and looks like a bug. A possibly related curiosity is that PolynomialQ returns an answer when no variables are specified, though it is rather unclear if this is intended or a "side-effect" of something (this behaviour does not seem to be documented). Again we see things like: In[6]:= PolynomialQ[2^-x] Out[6]= True In[7]:= PolynomialQ[x^-2] Out[7]= False In[9]:= PolynomialQ[x^y] Out[9]= True In[10]:= PolynomialQ[x^-y] Out[10]= False Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/