Re: PolynomialQ ?
- To: mathgroup at smc.vnet.net
- Subject: [mg34931] Re: PolynomialQ ?
- From: rainer gruber <rainer.gruber at gmx.at>
- Date: Thu, 13 Jun 2002 02:38:21 -0400 (EDT)
- Organization: Johannes Kepler Universitaet Linz
- References: <ae4en8$9bc$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Juan wrote:
> Hi,I tried to check is a polynomial have a variable, ussing the function
> PolynomialQ.
>
> In[1]:=p = x^3 - 2*x^2 + x - 1;
> In[2]:=PolynomialQ[p, x]
> Out[2]=True
> In[3]:=PolynomialQ[p, y]
> Out[3]=True
> In[4]:=PolynomialQ[p, z^2]
> Out[4]=True
> In[5]:=PolynomialQ[p, {u, v}]
> Out[5]=True
>
> What is the thing I am doing wrong?
>
> Regards.Juan
You're assuming that a polynomial in a certain variable has to contain
the variable. Thats not true! The variable can also appear with exponent
zero. So, as long as all exponents of a variable in a polynomial are
- nonnegativ
- finite
- integers
it is a polynomial in this variable:
negativ,
In[1]:=
PolynomialQ[1/x, x]
Out[1]=
False
infinite,
In[2]:=
PolynomialQ[Sin[x], x]
Out[2]=
False
and non integer exponents
In[3]:=
PolynomialQ[Sqrt[x], x]
Out[3]=
False
are not allowed in the polynomial.
Next Time if you have a problem like this I recommend to take a look in
the HELP BROWSER!
--
Rainer Gruber