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Re: Pattern with powers
Posted:
Jul 31, 2013 4:48 AM


On 7/30/13 at 6:40 AM, weh@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}



