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Re: How to define the coefficients of a polynomial to be real?

• To: mathgroup at smc.vnet.net
• Subject: [mg100955] Re: [mg100925] How to define the coefficients of a polynomial to be real?
• From: "David Park" <djmpark at comcast.net>
• Date: Thu, 18 Jun 2009 20:46:33 -0400 (EDT)
• References: <18883255.1245315881604.JavaMail.root@n11>

The command you want is ComplexExpand, which is often overlooked by new
users. ComplexExpand assumes all symbols are real, except those you specify
to be complex.

poly[z_] = a0 + a1 z + a2 z^2 + a3 z^3;

poly[1 + I]
ComplexExpand[Re[%]]
a0 + (1 + I) a1 + 2 I a2 - (2 - 2 I) a3
a0 + a1 - 2 a3


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: BHUPALA [mailto:bhupala at gmail.com] 

I have a 10th order polynomial (a0+a1 z+a2 z^2 + ... + an z^10). I
want to define all the coefficients to be real. I want to substitute z
= 1+i and extract only real part of it.

I have done this by defining

Element[a0,Reals];
Element[a1,Reals];