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Pattern with powers

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  • Subject: [mg131469] Pattern with powers
  • From: "Dr. Wolfgang Hintze" <weh at>
  • Date: Tue, 30 Jul 2013 06:40:55 -0400 (EDT)
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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]
but misses the term

Example 2: this would be the form I would like most
Cases[ls, (_.)*x^_?(#1 >= a & )*y^_?(#1 < a & )]
Here even I didn't get the dot behind the blank before the test, so it misses first powers.

Thanks in advance for any help.

Best regards,

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