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 :: I agree that Sturm was inspired by Fourier, but this does not mean that Sturm's sequence is a ""modification"" of Fourier sequence, nor that it is ""based on"" Fourier's sequence. These wordings would be correct only if Sturm's theorem did not contain a completely new idea, namely the use of remainder sequences. This for this reason that I have replaced ""based on"" by ""inspired by"".    

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