       MonomialQ

• To: mathgroup at smc.vnet.net
• Subject: [mg33542] MonomialQ
• From: Detlef Mueller <dmueller at mathematik.uni-kassel.de>
• Date: Fri, 29 Mar 2002 06:13:46 -0500 (EST)
• Organization: University of Kassel - Germany
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I want to test, wether an expression is a Monomial
with respect to a List of Variables.
Here a Monomial is defined as some coefficient
multiplied by a product of powers of the
Variables: c*v1^p1*... vn^pn,
where c must not depend on any of v1,..vn.
(this is sometimes called "term").

Similar to the build in Function PolynomialQ.

Say

MonomialQ[(a b)^3/(b c),{a,b}] -> True
MonomialQ[(a b)^3/(b c),{a,c}] -> False
MonomialQ[(a b)^3/(b c)-c,{a,b}] -> False
MonomialQ[(a+b)(a+c),{a}] -> False
MonomialQ[(a+b)(a+c)-(a^2+bc),{a}]->True

My current Implementation is

MonomialQ[a_,L_List] :=
PolynomialQ[a, L] &&               (* must be Polynomial and *)
Head[Expand[a, x_ /; MemberQ[L, x]]] =!= Plus;

Maybe, there is no better way, but I wonder, if
the Expand with Pattern is a good Idea here.

Since in most Cases "a" _is_ in fact a Monomial
in simple power-product-form, and since this is
an often used Function, using "Expand" might be
nearly every time an Overkill.

Maybe there is a quick "pretest", checking
for the "simple power-product-form"
a = a1^k1*...an^kn, a1,..an Symbols or Constants,
k1..kn non negative integers?

Greetings,
Detlef

```

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