first of all thank you for cleaning up my messages i am new to this and have already learnt a lot from you and about you second i reverted to vas is based on budan's theorem but i still disagree with you here are the reasons why a sturm himself said m'appuyant sur by relying upon and not having been inspired by b in greek to rely upon is and there you can see the word which means base i also leave it up to you to decide the wording for sturm's method and fourier's theorem i simply cannot accept the word inspiration reminds me of religion