Peter Alfeld Department of Mathematics College of Science University of Utah
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Residual Arithmetic, r=3, d=10

The following table illustrates the performance of residual arithmetic. The dimension of the spline space on the generic double Clough-Tocher split, for r=3 and d=10 is 184. It was computed using three consecutive prime numbers. The table gives the top one of those prime numbers, and the color indicates the result, as follows:

57111317192329313741434753596167717379
838997101103107109113127131137139149151157163167173179181
191193197199211223227229233239241251257263269271277281283293
307311313317331337347349353359367373379383389397401409419421
431433439443449457461463467479487491499503509521523541547557
563569571577587593599601607613617619631641643647653659661673
677683691701709719727733739743751757761769773787797809811821
823827829839853857859863877881883887907911919929937941947953
96797197798399199710091013101910211031103310391049105110611063106910871091
10931097110311091117112311291151115311631171118111871193120112131217122312291231
12371249125912771279128312891291129713011303130713191321132713611367137313811399
14091423142714291433143914471451145314591471148114831487148914931499151115231531
15431549155315591567157115791583159716011607160916131619162116271637165716631667
16691693169716991709172117231733174117471753175917771783178717891801181118231831
18471861186718711873187718791889190119071913193119331949195119731979198719931997
19992003201120172027202920392053206320692081208320872089209921112113212921312137
21412143215321612179220322072213222122372239224322512267226922732281228722932297
23092311233323392341234723512357237123772381238323892393239924112417242324372441
24472459246724732477250325212531253925432549255125572579259125932609261726212633
26472657265926632671267726832687268926932699270727112713271927292731274127492753
27672777278927912797280128032819283328372843285128572861287928872897290329092917
29272939295329572963296929712999300130113019302330373041304930613067307930833089
31093119312131373163316731693181318731913203320932173221322932513253325732593271
32993301330733133319332333293331334333473359336133713373338933913407341334333449
50035009501150215023503950515059507750815087509951015107511351195147515351675171
1000710009100371003910061100671006910079100911009310099101031011110133101391014110151101591016310169
2001120021200232002920047200512006320071200892010120107201132011720123201292014320147201492016120173
4000940013400314003740039400634008740093400994011140123401274012940151401534016340169401774018940193
8002180039800518007180077801078011180141801478014980153801678017380177801918020780209802218023180233
160001160009160019160031160033160049160073160079160081160087160091160093160117160141160159160163160169160183160201160207
320009320011320027320039320041320053320057320063320081320083320101320107320113320119320141320143320149320153320179320209
640007640009640019640027640039640043640049640061640069640099640109640121640127640139640151640153640163640193640219640223
1000003100003310000371000039100008110000991000117100012110001331000151
1000159100017110001831000187100019310001991000211100021310002311000249

Notes


[15-Mar-1999]