       Re: Pattern with powers

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• Subject: [mg131472] Re: Pattern with powers
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Wed, 31 Jul 2013 04:53:09 -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]
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

Hi, Wolfgang,

Your explanation is not quite clear. Have a look:

Clear[a, u, v, b];

a = 2;
Cases[ls, (Times[_, x, Power[y, v_]] /;
v <= a) | (Times[_, Power[x, u_]] /; u >= a)]

{5 x^3, 15 x^2 y, 15 x y^2}

Is it, what you are after? Or this:

Clear[a, u, v, b];
a = 2;
Cases[ls, (Times[_, x, Power[y, v_]] /;
v < a) | (Times[_, Power[x, u_]] /; u >= a)]

{5 x^3, 15 x^2 y}

??

Have fun, Alexei

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu

```

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