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Number of zeros finite or infinite?

• To: mathgroup at smc.vnet.net
• Subject: [mg115416] Number of zeros finite or infinite?
• From: "James" <icorone at hotmail.com>
• Date: Mon, 10 Jan 2011 02:40:20 -0500 (EST)

Hello everyone,

I'm working on a program that deals with zeros of functions and would 
like to know if the zeros are finite or not.  For example, in the finite 
case :

testcase1 = Reduce[2*x^2 + 3*x - 1 == 0, x]
x == (1/4)*(-3 - Sqrt[17]) || x == (1/4)*(-3 + Sqrt[17])

and in the infinite case for example, I would obtain something like:

thezeros = Reduce[1 - 4*Sin[z]^2 == 0, z]

Element[C[1], Integers] && (z == -(Pi/6) + 2*Pi*C[1] || z == (7*Pi)/6 + 2*Pi*C[1] || z == Pi/6 + 2*Pi*C[1] || z == (5*Pi)/6 + 2*Pi*C[1])

Can someone please help me distinguish the two cases so that I can then process them differently?  For example, in pseudo code:

If(finite) do onething, else doanotherthing

Thanks guys,