By Hadley, A.; Sandia National Labs., Arms Control Dept., Albuquerque, NM (United States); United States. Dept. of Energy.; Sandia National Laboratories.; United States. Dept. of Energy. Office of Scientific and Technical Information

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The distance x from the origin to the X-axis intercept is called the x coordinate number. The y coordinate number is deﬁned analogously. The location of a point P , whose coordinate numbers are (x, y), in a contravariant cartesian coordinate system, and whose axes are (X, Y ), is obtained by the intersection of two lines. 2. 2 Contravariant cartesian coordinate system representation of a point P which is deﬁned by the intersection of lines parallel to each coordinate axis. 3 The line AB represents the constraint equation in a contravariant system of coordinates.

The value of the dual sublevel of order i = 0 of the constrained number w = (w0 , w1 , w2 , w3 ) = (1, 2, 0, 1) is given by λ0 (w) = |w0 | + |w1 | + |w2 | + |w3 | = 1 + 2 + 0 + 1 = 4 and its dimension is evaluated from δ − i = 3 − 0 = 3. Recalling that the level of the number (1, 2, 0, 1) is obtained from λ0 (w) = |w0 | + |w1 | + |w2 | + |w3 | = 4, it can be seen that the value of the sublevel λ0 (w) equals to the value of the level sublevel λ0 (w) that is λ0 (w) = λ0 (w) = . 2. Dual sublevel λ1 (w).

Given > 0 and λ0 = , the coordinate number w0 takes the sequence of values w0 = λ0 , (λ0 − 1), . . , 1, 0, −1, . . 12) where λ0 is the value of the level. 2. 15) 3. 19) which are nested unions. The value of λ1 must be evaluated just after the computation of w0 to be used in the next union. 4. 22) wk−1 λk−1 5. 25) A=a where A = wδ−1 , a = λδ−1 , and b = −λδ−1 . 6. 28) wδ−1 =λδ−1 which are nested unions. The value of λk must be evaluated just after the computation of wk to be used in the next union.