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Pattern with powers
Posted:
Jul 30, 2013 6:39 AM


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
Example 2: this would be the form I would like most Cases[ls, (_.)*x^_?(#1 >= a & )*y^_?(#1 < a & )] gives {} 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, Wolfgang



