633 experts might be particularly surprised, that the brackets do not |
633 experts might be particularly surprised, that the brackets do not |
634 cause errors in typing (as lists).}: |
634 cause errors in typing (as lists).}: |
635 %\vbox{ |
635 %\vbox{ |
636 % \begin{example} |
636 % \begin{example} |
637 \label{eg:neuper1} |
637 \label{eg:neuper1} |
638 {\small\begin{tabbing} |
638 {\footnotesize\begin{tabbing} |
639 123\=123\=123\=123\=\kill |
639 123\=123\=123\=123\=\kill |
640 \hfill \\ |
640 |
641 \>axiomatization where \\ |
641 \>axiomatization where \\ |
642 \>\> rule1: ``${\cal Z}^{-1}\;1 = \delta [n]$'' and\\ |
642 \>\> rule1: ``${\cal Z}^{-1}\;1 = \delta [n]$'' and\\ |
643 \>\> rule2: ``$\vert\vert z \vert\vert > 1 \Rightarrow {\cal Z}^{-1}\;z / (z - 1) = u [n]$'' and\\ |
643 \>\> rule2: ``$\vert\vert z \vert\vert > 1 \Rightarrow {\cal Z}^{-1}\;z / (z - 1) = u [n]$'' and\\ |
644 \>\> rule3: ``$\vert\vert$ z $\vert\vert$ < 1 ==> z / (z - 1) = -u [-n - 1]'' and \\ |
644 \>\> rule3: ``$\vert\vert$ z $\vert\vert$ < 1 ==> z / (z - 1) = -u [-n - 1]'' and \\ |
645 %TODO |
645 %TODO |
646 \>\> rule4: ``$\vert\vert$ z $\vert\vert$ > $\vert\vert$ $\alpha$ $\vert\vert$ ==> z / (z - $\alpha$) = $\alpha^n$ $\cdot$ u [n]'' and\\ |
646 \>\> rule4: ``$\vert\vert$ z $\vert\vert$ > $\vert\vert$ $\alpha$ $\vert\vert$ ==> z / (z - $\alpha$) = $\alpha^n$ $\cdot$ u [n]'' and\\ |
647 %TODO |
647 %TODO |
648 \>\> rule5: ``$\vert\vert$ z $\vert\vert$ < $\vert\vert$ $\alpha$ $\vert\vert$ ==> z / (z - $\alpha$) = -($\alpha^n$) $\cdot$ u [-n - 1]'' and\\ |
648 \>\> rule5: ``$\vert\vert$ z $\vert\vert$ < $\vert\vert$ $\alpha$ $\vert\vert$ ==> z / (z - $\alpha$) = -($\alpha^n$) $\cdot$ u [-n - 1]'' and\\ |
649 %TODO |
649 %TODO |
650 \>\> rule6: ``$\vert\vert$ z $\vert\vert$ > 1 ==> z/(z - 1)$^2$ = n $\cdot$ u [n]''\\ |
650 \>\> rule6: ``$\vert\vert$ z $\vert\vert$ > 1 ==> z/(z - 1)$^2$ = n $\cdot$ u [n]'' |
651 %TODO |
651 %TODO |
652 \end{tabbing} |
652 \end{tabbing}} |
653 } |
|
654 % \end{example} |
653 % \end{example} |
655 %} |
654 %} |
656 These 6 rules can be used as conditional rewrite rules, depending on |
655 These 6 rules can be used as conditional rewrite rules, depending on |
657 the respective convergence radius. Satisfaction from accordance with traditional notation |
656 the respective convergence radius. Satisfaction from accordance with traditional notation |
658 contrasts with the above word {\em axiomatization}: As TP-based, the |
657 contrasts with the above word {\em axiomatization}: As TP-based, the |