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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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