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## Next step of problems....

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• Okay, previous error with matrix was, in my opinion, hardware failure - rerunning matsolve gets a result at 100.6% of estimated iterations count. The next
Message 1 of 1 , Nov 1, 2005
Okay, previous error with matrix was, in my opinion, hardware failure
- rerunning matsolve gets a result at 100.6% of estimated iterations
count.

The next problem: sqrt cannot find algebraic sqrt:
...
step 41638, sl=-1, logGam=617.87/-0.00, emb: 183.64 190.01 -17.72 130.
96 130.96 , diff=0.0000
Iterative portion of square root computation done.
step 41638, sl=-1, logGam=617.87/-0.00, emb: 183.64 190.01 -17.72 130.
96 130.96 , diff=0.0000
Final CRT residues:
6000000001 : 2807653308 + 5606679806X + 2646429913X^2 + 1386975034X^3
+ 3765699047X^4
6000000049 : 4380487222 + 5117678146X + 3698610860X^2 + 236688058X^3 +
4168475244X^4
6000000173 : 3986870200 + 146027350X + 5170236845X^2 + 5085923201X^3 +
548182475X^4
6000000289 : 3351912387 + 4520506299X + 4062644537X^2 + 3137400752X^3
+ 1903510342X^4
6000000323 : 3377879059 + 2777672915X + 5134881452X^2 + 5329094976X^3
+ 4781545720X^4
6000000341 : 3158994860 + 875068048X + 5305993070X^2 + 843191522X^3 +
5231229156X^4
Remaining ideals:
None.

Residues lifted to a remaining gamma = (1/480221453761920000) *
(17737301873473875626037914277256364756852588487498659189765 +
1142722952103440160046321686002680794511330368267915838069X-
1131248676132960452178858310274516486849141413196881876211X^2-
21262559013000708779934953815472958603277231324232491779766X^3-
1716063254329902745839521742386594830167987214723021243X^4

Attempting to compute a square root of:
a=85178328914936517541144271443043039831609111858188026720557294384107
48800000 +
5487600773062269116226502741001105520345880453667164712298983295985324
80000X-
5432498838188176808560935813652688599515096829079778152063807937056851
20000X^2-
1021073699992181522351572080036235807375979920734902940284900465683731
0720000X^3-
8240903907417173526947843360640306630247533873413050725050904244665600
00X^4
in Z[x]/<f, p>, where:
f=254893803644232981746579855159582830457936991247065600000 +
2791792269133534498014450163293313583002752000X-
23574256498940343041681950008398400X^2-274394485145667643021200X^3 +
387947509932X^4 + 1X^5

p=100000000003
p = 100000000003
Zalpha: SQRT mod p succeeded!
res = 11654818344-5786520030X + 41495299027X^2 + 33556347765X^3 +
2636477894X^4

Computed square root is invalid mod N.
*** Some serious error occurred computing remaining square root.
*** This run will most likely fail!
final beta =(1/k)*11654818344-5786520030X + 41495299027X^2 +
33556347765X^3 + 2636477894X^4
Beta evaluated at m =
5948967657355414261246160928385363674945671778547061515729262109138290
2028332844943298454379726212206185336339553713411226525880806395213534
81
ABexponentSum = -1412
Y1 corrected Beta =
4845481067859955458925354590451014661857209559074474873445292438318241
7732398292440355011960648417079035171674867893235491117770867489366669
2141032845139436834847315333660713908324363488131425716554042115488664
6169140559545467974695720887198548264782794660190812115960977766612255
1594
Beta^2 ==
9492153038329834913332087925059732265637599163478548422101471551398586
4787171381371392132447713425911188455718327721670138854281491515512355
81
Rational square root:
7860094804273322404686631291464796733327399705156363192703483048428544
6912598667957070953667455972394424288683764259014819855057635347667697
93
^2 ==
1036732040255582016444176921459301751367960409952958038481320214188977
7017698086131191842500081053048150235609646456009612713077875870415644
285
Square root computations result in N=(r1)(r2) where:
r1 = 1
r2 =
1107483931398966770187334001200459819074482576104981566201212874830646
8464983609193872721654904520657559536397894650047923109763933917313386
599
Elapsed time: 2353.6442 seconds.

and this result (or some similar) happens for each of 31 dependencies.
..
I think, it's also errors in relations, may be on procrels stage...

I have 2 ideas:
1) add CRC to matsolve, and after, for example, 1000 iterations
recalculate matrix CRC - in my task it occupies about 1.3Gb RAM, and
is very forgeable to hardware failures;
2) add a check-call to completePartialRelFact(...) function into
matbuild when it reads relations from .rels files...

I have captured (self-written filter on text relations) errors like
this:
Error (real part) with relation 87097309,298:193e0f1,514E7,E6333,
5C8CEB,17,1FD:d96b073,32CF,848AB,BDB1B,184D99,3,7,7,D,11,43,E3,209,2,
2,2,2,6B7DBB

f = 590180460624563540898390653053
ff = 590183523431982883186590653053

Error (alg part) with relation 87097309,298:193e0f1,514E7,E6333,
5C8CEB,17,1FD:d96b073,32CF,848AB,BDB1B,184D99,3,7,7,D,11,43,E3,209,2,
2,2,2,6B7DBB

g = 57804485617759498993411959351816928586233335293328
gg = 2609045589552731945194122292651660863735293328

where f,g are values of forms f(a,b) - rational, g(a,b) - algebraic
and ff,gg - products of factors from the relation.

I can understand diff betweeen g and gg - 1 factor is missed, but I
can't understand diff between f and ff - these numbers are too
similar, so this error, i think, can be only from hardware failures...
.

And, by the way: I use altogether 32-bit and 64-bit machines, shared
by NFS, so I have patched Makefile to build binaries into the
different dirs - bin and bin64... but also I need to put objs into it
and so on - I think, than dir must be chosen in root makefile - then
you choose architecture, you must be able to set binaries dir...
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