### Table 2: Genus of 0 in terms of genus of . genus ( ) genus ( 0)

1998

"... In PAGE 17: ... It follows that the form at level 2 must be Type II. We thus obtain the list of transforms shown in Table2 (using the notation of [15, Chap. 15]).... In PAGE 18: ... The 2-adic genus of must be [1n=2 2n=2]o. From Table2 , the genera of 0 and 0 are respectively 1(n?4)=2 [2(n+4)=2]o and [1(n+4)=2]o 2(n?4)=2, and so 0 is integral. Then ( 0)0 has 2-adic genus 1n=2 : 2n=2 if o = 0 and 1?n=2 : 2?n=2 if o = 4.... ..."

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### Table 1: Results of genus-reducing and genus-preserving simplifications

1998

"... In PAGE 13: ... We first simplified the given objects using the genus-preserving approach with a tolerance of #0F. Then on this simplified object we compared the results of the following two simplification strategies: (a) genus-reducing simplifications with a tolerance of #0B followed by genus-preserving simplifications with a tolerance of #0F (b) genus-preserving simplifications with a tolerance of #0B + #0F The results of our comparisons are given in Table1 . As can be seen, performing genus-reducing simpli- fication with genus-preserving simplifications vastly improves the overall simplification ratio.... In PAGE 15: ... 12. (a) 612 triangles (b) (c) (d) (e) (f) 12 triangles Figure 14: Alternating geometry and protuberance simplifications As can be seen from Table1 and the accompanying figures, our approach indicates promising results for genus reduction, protuberance simplification, and crack repair. Using our approach for genus-reductions and protuberance simplifications with traditional geometry simplification techniques we have been able to achieve significant simplification factors over what genus-preserving geometry simplifications alone could accomplish.... ..."

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### Table 3: Results for polysemous genus.

1997

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### Table 5. Genus 2 Examples

"... In PAGE 16: ... We computed the order of a 186-bit Jacobian, finding a 372-bit trace zero variety of near-prime order for the curve y2 = x5 + 2x3 + 3x2 + 5x + 1050. See Table5 for the zeta functions of all the curves mentioned above. 7.... ..."

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### Table 1: Conformal invariants of genus one surfaces.

"... In PAGE 6: ... This shows the algorithm is intrinsic to the geometry and inde- pendent of the surface representation. Table1 shows the conformal invariants of the genus one surfaces illustrated in figure 9. By examining their shape Figure 6: Canonical homology bases.... ..."

### Table 1: Geodesic Spectrum of Genus One Surfaces.

2007

"... In PAGE 6: ... Figure 7(a) shows six genus one closed surfaces. Table1 lists part of their geodesic spectra, lengths of the first 8 shortest geodesic. And figure 8(a) depicts the spectra for easier com- parison purpose.... ..."

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### Table 4. Parallel arithmetic of HECADD for genus three

"... In PAGE 6: ... 4 Parallel Genus Three Hyperelliptic Curve Arithmetic with SIMD Operations We reschedule manually long procedures of the Harley algorithm for genus three [30] into parallel sequences to apply the proposed nite eld multiplication PMUL. Table4 and 5 in the Appendices show the two-processor version of a ne coordinate HECADD and HECDBL for genus three curves [30]. We assume that these parallel sequences have SIMD-style operations in order to be applicable not only the hardware implementation but also software implementation.... In PAGE 11: ...Table4 . Parallel arithmetic of HECADD for genus three { continued R03 R03 R12 R04 R04 + R03 R00 v12 R01 v11 R03 v10 R02 R02 + R10 R05 R02 R04 R12 R02 R15 R05 R05 + R11 R12 R12 + R07 R12 R12 + R04 R05 R06 R05 R12 R06 R12 R05 R05 + h0 R12 R12 + h1 R05 R05 + R03 R12 R12 + R01 R01 R02 R13 R03 R02 R10 R01 R01 + R15 R03 R03 + R13 R01 R01 + R08 R03 R03 + R09 R01 R06 R01 R03 R06 R03 R01 R01 + h2 R03 R03 + 1 R01 R01 + R00 R00 R03 R03 R02 R03 h1 R06 R00 + f6 R07 R15 + R02 R00 h2 R03 R02 h2 R01 R08 R13 + R00 R07 R07 + R02 R06 R06 + R10 R08 R08 + f5 R06 R06 + R03 R08 R08 + R01 R00 R06 R10 R02 R06 R13 R08 R08 + R00 R07 R07 + R02 R00 R01 R01 R00 R00 + f4 R07 R07 + R12 R07 R07 + R00 R03 R03 + 1 R00 R08 R10 R02 R08 R03 R07 R07 + R00 R12 R12 + R02 R00 R03 R06 R02 R03 R07 R01 R01 + R00 R05 R05 + R02 R01 R01 + h2 R12 R12 + h1 R05 R05 + h0 u32 R06 u31 R08 u30 R07 v32 R01 v31 R12... ..."

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### Table 5. Parallel arithmetic of HECDBL for genus three

"... In PAGE 13: ...Table5 . Parallel arithmetic of HECDBL for genus three { continued R12 R12 + R03 R03 v12 R04 v11 R05 v10 R09 R09 + R01 R08 R08 + R10 R00 R02 R01 R13 R02 R10 R14 R02 R12 R12 R12 + R07 R14 R14 + R11 R00 R00 + R08 R13 R13 + R12 R00 R06 R00 R13 R06 R13 R14 R06 R14 R15 R06 R09 R15 R15 + 1 R00 R00 + h2 R13 R13 + h1 R14 R14 + h0 R00 R00 + R03 R13 R13 + R04 R14 R14 + R05 R04 R15 + f6 R02 R15 R15 R03 R15 h1 R03 R03 + R10 R02 R02 + R04 R04 R00 R00 R05 R00 h2 R03 R03 + R04 R06 R01 + f5 R03 R03 + f4 R05 R05 + R13 R07 R15 h2 R06 R06 + R07 R03 R03 + R05 R15 R15 + 1 R06 R06 + R00 R01 R02 R01 R04 R02 R15 R03 R03 + R01 R04 R04 + R00 R05 R15 R06 R07 R15 R03 R05 R05 + R13 R07 R07 + R14 R04 R04 + h2 R05 R05 + h1 R07 R07 + h0 u32 R02 u31 R06 u30 R03 v32 R04 v31 R05... ..."

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