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November 8th, 2012, 05:44 AM  #1 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  direct image inverse image
Show that the subset X of polynominals in R2n[X] all of whose odd coefficients a2i+1 are zero forms a subspace of R2n[X]. Describe D>(X) and D<(X). I need some help with the bolded part. Thanks in advance! 
November 9th, 2012, 04:02 PM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: direct image inverse image
What is "D"?

November 10th, 2012, 08:04 AM  #3 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  Re: direct image inverse image
differentiation map D direct image: D>(x) inverse image: XD<(x) 
November 14th, 2012, 02:23 PM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: direct image inverse image
Okay, suppose p(x)= x^4 3x^2+ 2 (coefficients of all odd powers are 0), then Dp= 4x^3 6x. What can you say about the derivative of a polynomial with only even powers?

November 22nd, 2012, 07:35 AM  #5 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  Re: direct image inverse image
Thank you... That is a set of polynomials whose even coefficients are zero, but that is D<(X). What about the inverse image? 

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