Re: Pattern with powers

*To*: mathgroup at smc.vnet.net*Subject*: [mg131471] Re: Pattern with powers*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 31 Jul 2013 04:52:49 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

On 7/30/13 at 6:40 AM, weh at snafu.de (Dr. Wolfgang Hintze) wrote: >I must admit that I am an absolute beginner in patterns, as I cannot >cope with a little problem with patterns consisting of powers of >variables x and y. >Specifically, I would like to select from a list all terms of the >form >c x^u y^v (numerical coefficient c times x to the power u times y to >the power v) >where u and v are allowed to take the values 0 and 1. >How can I do this using Cases? >I have already accomplished the first non trivial step using _. >(blank followed by a dot) in order to get first powers of the >variables: >ls = List@@Expand[5 (x + y)^3] {5*x^3, 15*x^2*y, 15*x*y^2, 5*y^3} >Example 1 a = 2; Cases[ls, (_.)*x^(u_.)*y^(v_.) /; u >= a && v < a] >gives {15*x^2*y} but misses the term 5*x^3 It is not necessary to convert the polynomial to a List since Cases can be applied directly to the polynomial. That is: In[1]:= ls = Expand[5 (x + y)^3]; a = 2; Cases[ls, (_.)*x^(u_.)*y^(v_.) /; u >= a && v < a] Out[2]= {15*x^2*y} yields the same result as you get below after making ls a List Why use Cases? It appears you want an output with with all terms of the form a x^u y^v with v either 1 or 0. Although this isn't what you state initially, it does seem to accurately describe what you indicate is your desired result. If this is what you want then how about In[3]:= CoefficientList[ls, y][[;; 2]] {1, y} Out[3]= {5*x^3, 15*x^2*y}