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MathGroup Archive 2006

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Re: Re: Extracting terms from an equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69822] Re: [mg69786] Re: Extracting terms from an equation
  • From: "Carl K. Woll" <carlw at wolfram.com>
  • Date: Sat, 23 Sep 2006 23:45:30 -0400 (EDT)
  • References: <eevubf$hqu$1@smc.vnet.net> <200609230844.EAA22454@smc.vnet.net>

dimmechan at yahoo.com wrote:
> Can someone explain the difference in the following?
> 
> Cases[a + b*x^2 + c*y^2 + d*x*y + e*x^3, _?( !FreeQ[#1, x] & )]
> {b*x^2, e*x^3, d*x*y}
> 
> Cases[a + b*x^2 + c*y^2 + d*x*y + e*x^3, _?(MemberQ[#1, x] & )]
> {d*x*y}
> 

MemberQ has a default level specification of {1}, while FreeQ has a 
default level specification of {0,Infinity}. If one uses the same level 
specifications, then !FreeQ and MemberQ are equivalent:

expr = a + b*x^2 + c*y^2 + d*x*y + e*x^3;

Give FreeQ the level spec (1):

In[27]:= Cases[expr, _?(! FreeQ[#1, x, {1}] &)] ==
  Cases[expr, _?(MemberQ[#1, x] &)]

Out[27]= True

Give MemberQ the level spec {0,Infinity}:

In[28]:= Cases[expr, _?(! FreeQ[#1, x] &)] ==
  Cases[expr, _?(MemberQ[#1, x, {0, Infinity}] &)]

Out[28]= True

Carl Woll
Wolfram Research

> Thanks
> 
> Î?/Î? Coleman, Mark έγÏ?αÏ?ε:
>> Greetings,
>>
>> I'd like to find a general way to extract all of the terms from an
>> equation that involve a given variable. For instance, consider the
>> equation
>>
>> myEquation == Exp[a + b x^2 + c y^2 + d x y + e x^3]]
>>
>> I'd like to define a function such that
>>
>>    myFunction[myEquation,x] returns the result {b x^2, d x y, e x^3}
>>
>> Thanks,
>>
>> -Mark


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