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We consider real  polynomials in one variable without vanishing coefficients and with  all roots real and of distinct moduli.  We show that the signs of the coefficients define the order of  the moduli of the roots on the real positive half-line exactly when no four  consecutive signs of coefficients equal $(+,+,-,-)$, $(-,-,+,+)$,  $(+,-,-,+)$ or $(-,+,+,-)$.

Descartes' rule of signs, canonical sign patterns and rigid orders of moduli