### Table 2. Even jXEj, no rational 2-torsion, all N 5500

"... In PAGE 16: ... Here a similar pattern is found. In Table2 , the congruences listed between curves with the same conductor are in most cases true modular 2-congruences proved using our rst computational strategy. In a few such cases, and in all cases where the conductors are not equal, the rst strategy failed and so we only claim that the curves \seem to quot; satisfy a congruence modulo 2, in the sense de ned earlier.... ..."

Cited by 6

### Table 2. results for compact time-tables For both tables and both solvers we see that, as is expected, there is a deterio- ration in performance with the introduction of supplementary levels of preferred constraints. The deterioration in computation time for the relational optimiza- tion approach is less sensitive to the number of levels of preferred constraints to be treated and the number of constraints relaxed than the IHCS solver. These timings show that our current RO implementation competes well with the HCLP implementation of [14].

1994

Cited by 20

### Table 8.4 Efficiency of the floating point filter: The top part contains the results for random points on the unit circle and the lower part contains the results for random points in the unit square. The first column shows the precision (= number of binary places) used for the Cartesian coordinates of the points. The other columns show the running time with the floating point filter, with the rational kernel with the floating point filter, and with the rational kernel without its floating point filter. A star in the second column indicates that the computation with the floating point kernel produced an incorrect result. geometry kernels!running time

in Contents

### Table 1: Rendering times for the six images in Figure 6, for a 512x512 size image, on a 150MHz R4400 system. The coverage as computed in [9] is hierarchical. Parameter values of isoparametric curves introduced at level l +1 are of the rational form of ti l+1 = ti l+ti+1 l 2

1997

"... In PAGE 11: ... Figure 6 shows an example of this multi-resolution approach. Table1 shows the time that was necessary to compute the di erent images, at di erent resolutions.Freeform trimmed surfaces [22, 28, 30, 31] can also be scan converted using the ruled... ..."

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### Table 1: Rational Operations

1994

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### Table 2. The rational operations

2007

"... In PAGE 6: ... We briefly describe some of them below. Table2 shows the library operations for the sum, product, and Kleene closure of weighted transducers. Both destructive implementations, using the Thompson construction, and lazy implementations are provided.... ..."

Cited by 1

### Table 1. Cost properties of common auctions. Key: ICB Buyer incentive compatible, BRC Bounded-rational compatible, COMML Low communication cost.

"... In PAGE 6: ...optimization problem. We summarize the cost and trust properties over six di erent auction mech- anisms in Table1 and Table 2.3 We will introduce two new auction properties: bounded-rational compatible and untrusted-auctioneer compatible.... In PAGE 6: ... The premise of our work is that the cost of the rst cognitive process, that of determining a reservation price for a new, previously unvalued, good is nontrivial, and will often dominate any other costs to participation in an agent mediated on-line auction. In an auction that is buyer incentive compatible (IC B, Table1 ) the dominant strategy for a buyer is to bid her true value for a good [9]. It is not necessary for a buyer to incur the cognitive cost of strategic counterspeculation that can be useful in some auction mechanisms.... In PAGE 7: ... Di erent auction structures require vastly di erent expected e ort by buyers to determine a value for a good that is being auctioned. We introduce a new auc- tion property, bounded-rational compatible ( BRC, Table1 ). A bounded-rational compatible auction, such as the English auction, will often allow a bidding agent to follow an optimal bidding strategy with only approximate information on the value of a good.... In PAGE 8: ...price that is below the buyer apos;s true value. Finally, we also consider whether an auction mechanism has low communica- tion costs (COMM L, Table1 ). The communication cost of an auction mechanism depends on the size of a single bid, and the expected number of auction rounds.... In PAGE 10: ... This allows buyers to defray, and if possible avoid, the cogni- tive cost of placing an accurate valuation on a good. The auction mechanisms that we have considered that are both buyer incen- tive compatible and bounded-rational compatible are the rst price ascending auction and the second price descending auction (see Table1 ). We rule out the second price sealed bid (Vickrey) auction because it is not bounded-rational com- patible and we want to avoid the high cognitive cost of computing the reservation price for every auction.... In PAGE 11: ... Both progressive auctions are however susceptible to indirect price manipulation (ICS, Table 2). It is interesting to note that it is impossible for an auction mechanism to be both buyer and seller in- centive compatible (compare Table1 and Table 2) [22], and that we must accept indirect price manipulation in return for simple optimal bidding strategies. We conclude that the most suitable auction for agent mediated on-line auc- tions, when the space of possible goods is large and diverse, and users do not know their reservation prices for all goods, is the rst price ascending auction.... ..."

### Table 2: Error Analysis for Lines 1-6 ( = 2?29 + 2?31 + (9=512)2?31) the particulars of Table 1 are involved in the proof is when the predicate is executed. This example illustrates the value of computation in a general-purpose logic. 8.2 Digit Separation Lemma 8.2.1 (Digit Separation) Suppose that p and d are rationals and d 6 = 0. Let

1998

"... In PAGE 26: ... Observe that if 0 x lt; 2, then trunc(x; 32) = x(1 ? x), for some 0 x lt; 2?31, and away(x; 32) = x(1 + x), for some 0 x lt; 2?31. These two observations, along with the de nition of comp and appropriate de nitions of quot;sdd0, quot;sd1, quot;sdd1, and quot;sd2 (as functions of d analogous to quot;sd0 above) allow us to derive the equations and inequalities of Table2 . From these inequalities it readily follows that 0 quot;sd2(d) lt; 2?28 and hence Lemma 8.... ..."

Cited by 27