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tomleslie

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Well...

tomleslie 13876
February 11 2019
0 0

@anton_dys

I agree that it is inconvenient that Maple uses different definitions for spherical polars in different places, but the AddCoordinates() command allows you to (mostly) workaround this issue

You are going to have to give me a better definition of the requirement for a "uniform distribution of arrows for a field defined in spherical coordinates", because I can't figure out what exactly you want - probably me being dumb

Another user problem...

tomleslie 13876
February 07 2019
0 0

@radaar 

Your code sets

h:=1

then computes

h=evalf( h-1/i)

with i=1, which is

h:=evalf(1-1/1)

in other words 0.

You then want to sample a normal distribution with zero variance and you are surprised that it fails?

Try thinking!

Not Useless...

tomleslie 13876
February 07 2019
0 0

@radaar 

Hardware floats ar used for efficiency purposes (depending on your current setting of Digits and UseHardwareFloats)

You can force software floats (and make your original error go away) in your original problem with the attached

> 

restart; UseHardwareFloats := false; with(Statistics); XG := RandomVariable(Normal(0, h)); SXG := Sample(XG, method = [envelope, range = -1 .. 1]); h := 1; randomize(); for i from 3 to 1000 do h := h-1/i; printf("%a\n%a\n", SXG(5), i) end do
> 

NULL
> 

NULL

Download softGaus.mw

Nonsense is a bit strong...

tomleslie 13876
February 05 2019
0 0

@acer 

Entries 1-16 in the variable 'SYSPDE' are a simple sum of (scalar) products

Entries 17-20 in the variable 'SYSPDE' are a nonsensical mixture where an attempt is made to add a matrix to (products of) scalars

You can see the distinction by adding the following to bottom of the worksheet

for k in SYSPDE do
     seq( whattype(op(j, k)), j=0..nops(k));
od;

OP has to ask one simple question - is the final system (ie SYSPDE) expected to contain matrices??

Can only think of two possibilities...

tomleslie 13876
February 04 2019
0 0

@mehran rajabi 

  1. Somehow you managed to install the DirectSearch package in the *wrong* place. Assuming that you are using Maple2018 on a 64-bit Windows system, then the default location for this package should be C:\Program Files\Maple 2018\lib\, so have a look at this directory. Amongst a few others, there should be three files here DirectSearch.hdb, DirectSearch.help and DirectSearch.mla. The first two of these are 'help' files and the third is the actual 'code' for the package
  2. Something wrong with (one of) your maple.ini file(s). Again assuming Maple2018 on a 64-bit Windows system, there may be two such initialisation files. The first of these applies to all users, and (by default, if it exists) it will be located at C:\Program Files\Maple 2018\lib\maple.ini. The second of these is specifici to individual users and (by default, if it exists) it will be located at  C:\Users\yourUsername\AppData\Roaming\Maple\2018\maple.ini. Use a simple text editor to find whether there are references to the DirectSearch in either of these files

 

Since you have tried...

tomleslie 13876
February 04 2019
0 0

@rana92 

pdsolve()

the only thing I can suggest is that you upload the worksheet here (using the big green up-arrow in the MaplePrimes toolbar) so that I can work out why it failed and whether it can be fixed.

So...

tomleslie 13876
February 03 2019
0 0

@rana92 

All you have to do now is enter your system in Maple then apply the command I gave previously and post the result. If you think someone here is going to do it for you -wrong! This site is not a typing service

No code = No answer...

tomleslie 13876
February 02 2019
0 0

@rana92 

With the information you provide the best I can suggest is to point out that the command

pdsolve( PDESys, numeric, tooManyOptionsToList)

*might* work. The entry PDESys in the above will evaulate to your partial differential equations and boundary/initial conditions: the entry 'numeric' specifies that a numeric solution is required; the entry 'tooManyOptionsToList' indicates that there are many options which may (should?) be used to facilitate solutions for specific problems

If you actually want to discover whether or not your specific problem can be solved, then you should create a worksheet containing the partial differential equations and any iniitial/boundary conditions, then upload it here using the big green up-arrow in the Mapleprimes toolbar

Post the worksheet...

tomleslie 13876
February 02 2019
0 0

using the big green up-arrow in the Mapleprimes toolbar

In light of mmcdara's comment...

tomleslie 13876
February 02 2019
0 0

No failure in Maple 2015.2, X86 64 WINDOWS, Dec 20 2015, Build ID 1097895

No failure in Maple 2016.2, X86 64 WINDOWS, Jan 13 2017, Build ID 1194701

Failures in Maple 2017.3, X86 64 WINDOWS, Sep 13 2017, Build ID 1262472

Failures in Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973

Not method=solve, but only sometimes!!...

tomleslie 13876
February 02 2019
0 0

@acer 

I had these four in different (consecutive) execution groups

X:=LinearAlgebra:-LinearSolve(A,B,method=LU):
LinearAlgebra:-Norm(A.X-B);
                               0

Xqr:=LinearAlgebra:-LinearSolve(A,B,method=QR):
LinearAlgebra:-Norm(A.Xqr-B);
                               0

Xqs:=LinearAlgebra:-LinearSolve(A,B,method=solve):
LinearAlgebra:-Norm(A.Xqs-B);
Error, (in LinearAlgebra:-Modular:-IntegerLinearSolve) invalid arguments to iratrecon
Error, (in LinearAlgebra:-Add) addition of a Vector[column] and a Matrix is not defined

kernelopts(version);
Xqsk:=LinearAlgebra:-LinearSolve(A,B,method=solve):
LinearAlgebra:-Norm(A.Xqsk-B);
  Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973
                               0

 and to make things worse, the kernelopts() command is "superfluous" because I can also generate

X:=LinearAlgebra:-LinearSolve(A,B,method=LU):
LinearAlgebra:-Norm(A.X-B);
                               0

Xqr:=LinearAlgebra:-LinearSolve(A,B,method=QR):
LinearAlgebra:-Norm(A.Xqr-B);
                               0

Xqs:=LinearAlgebra:-LinearSolve(A,B,method=solve):
LinearAlgebra:-Norm(A.Xqs-B);
Error, (in LinearAlgebra:-Modular:-IntegerLinearSolve) invalid arguments to iratrecon
Error, (in LinearAlgebra:-Add) addition of a Vector[column] and a Matrix is not defined

Xqs:=LinearAlgebra:-LinearSolve(A,B,method=solve):
LinearAlgebra:-Norm(A.Xqs-B);
                               0

What difference is there between the last two of these !!

NB re-executing the above four groups in the second code snip above leads to inconsistent outcomes. Sometimes the third group fails, sometimes the fourth group fails. Sometimes both third and fourth groups fail. I have never had both third and fourth groups succeed.

So even if it something to do with Maple's internal "state" - I can't generate the offending "state" consistently!

In case it matters, I am running Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973`

 

 

 

 

 

From the Error message...

tomleslie 13876
February 01 2019
0 0

@Joe Riel 

I have no doubt that the procedure iratrecon() is being called with incorrect arguments.

For me the "interesting" question is why this should be dependent on whether or not the worksheet contains a kernelopts(version) command in a prior execution group. This makes no sense (to me) at all.

Since I can't use trace() or the debugger for in-built functions, this is will remain a mystery to me - but I'm pretty sure it's a BUG

Convert it to an sfloat first!!...

tomleslie 13876
February 01 2019
0 0

@sand15 

Consider

restart;
numThrows:=10^5;
V := CodeTools:-Usage(convert~((SignalProcessing:-GenerateUniform(numThrows, 0, 2)), sfloat));
whattype(V[1]);
W := CodeTools:-Usage(round~(V));
whattype(W[1]);

For efficiency reasons I wouldn't recommend this as a way of generating random integers!

Definitely something fishy going on...

tomleslie 13876
January 31 2019
0 0

The attached produces a consistent ERROR, which is very, very weird

I tidied up your original code a little (not a reflection on your coding, just part of my debugging attempts) - but I still ended up with same error as you, which I could generate consistently.

However I could make this 'Error' appear or disappear by the simple inclusion/exclusion of a kernelopts(version) command in an unrelated execution group!!!!

The attached worksheet shows the error when solving 33 equations in 32 unknowns, but also shows that if you pick any 32 of the 33 equations, then a solution can be obtained, and that all of these solutions are the same.

The mindblowing part is that if you uncomment the kernelopts(version) command in the second execution group, then the error disappears, and the attached will run with no errors - I have no idea why the inclusion of this totally unrelated command should make the slightest difference!!

If no one else picks this up, I will have another look tomorrow (past my bedtime!), but I suspect this problem is too subtle for me

> 

restart;
> 

#
# Uncomment the kerneelopts() command below if
# you want to make everything work
#

# kernelopts(version);
  lisvar1 := [seq(cat(x__,j), j=0..31)];

[x__0, x__1, x__2, x__3, x__4, x__5, x__6, x__7, x__8, x__9, x__10, x__11, x__12, x__13, x__14, x__15, x__16, x__17, x__18, x__19, x__20, x__21, x__22, x__23, x__24, x__25, x__26, x__27, x__28, x__29, x__30, x__31]

 (1)
> 

liseq1 := [32/4554576811212553125 = 34359738368*x__7+1099511627776*x__8+35184372088832*x__9+1125899906842624*x__10+36028797018963968*x__11+1152921504606846976*x__12+36893488147419103232*x__13+1180591620717411303424*x__14+37778931862957161709568*x__15+1208925819614629174706176*x__16+38685626227668133590597632*x__17+1237940039285380274899124224*x__18+39614081257132168796771975168*x__19+1267650600228229401496703205376*x__20+40564819207303340847894502572032*x__21+1298074214633706907132624082305024*x__22+41538374868278621028243970633760768*x__23+1329227995784915872903807060280344576*x__24+42535295865117307932921825928971026432*x__25+1361129467683753853853498429727072845824*x__26+43556142965880123323311949751266331066368*x__27+1393796574908163946345982392040522594123776*x__28+44601490397061246283071436545296723011960832*x__29+1427247692705959881058285969449495136382746624*x__30+45671926166590716193865151022383844364247891968*x__31+x__0+32*x__1+1024*x__2+32768*x__3+1048576*x__4+33554432*x__5+1073741824*x__6, 9704/1219384428092815359375 = 42618442977*x__7+1406408618241*x__8+46411484401953*x__9+1531578985264449*x__10+50542106513726817*x__11+1667889514952984961*x__12+55040353993448503713*x__13+1816331681783800622529*x__14+59938945498865420543457*x__15+1977985201462558877934081*x__16+65273511648264442971824673*x__17+2154025884392726618070214209*x__18+71082854184959978396317068897*x__19+2345734188103679287078463273601*x__20+77409228207421416473589288028833*x__21+2554504530844906743628446504951489*x__22+84298649517881922539738734663399137*x__23+2781855434090103443811378243892171521*x__24+91801229324973413645775482048441660193*x__25+3029440567724122650310590907598574786369*x__26+99971538734896047460249499950752967950177*x__27+3299060778251569566188233498374847942355841*x__28+108869005682301795684211705446369982097742753*x__29+3592677187515959257578986279730209409225510849*x__30+118558347188026655500106547231096910504441858017*x__31+x__0+33*x__1+1089*x__2+35937*x__3+1185921*x__4+39135393*x__5+1291467969*x__6, 120304/13413228709020968953125 = 52523350144*x__7+1785793904896*x__8+60716992766464*x__9+2064377754059776*x__10+70188843638032384*x__11+2386420683693101056*x__12+81138303245565435904*x__13+2758702310349224820736*x__14+93795878551873643905024*x__15+3189059870763703892770816*x__16+108428035605965932354207744*x__17+3686553210602841700043063296*x__18+125342809160496617801464152064*x__19+4261655511456885005249781170176*x__20+144896287389534090178492559785984*x__21+4926473771244159066068747032723456*x__22+167500108222301408246337399112597504*x__23+5695003679558247880375471569828315136*x__24+193630125104980427932766033374162714624*x__25+6583424253569334549714045134721532297216*x__26+223836424621357374690277534580532098105344*x__27+7610438437126150739469436175738091335581696*x__28+258754906862289125141960829975095105409777664*x__29+8797666833317830254826668219153233583932440576*x__30+299120672332806228664106719451209941853702979584*x__31+x__0+34*x__1+1156*x__2+39304*x__3+1336336*x__4+45435424*x__5+1544804416*x__6, 36808/3658153284278446078125 = 64339296875*x__7+2251875390625*x__8+78815638671875*x__9+2758547353515625*x__10+96549157373046875*x__11+3379220508056640625*x__12+118272717781982421875*x__13+4139545122369384765625*x__14+144884079282928466796875*x__15+5070942774902496337890625*x__16+177482997121587371826171875*x__17+6211904899255558013916015625*x__18+217416671473944530487060546875*x__19+7609583501588058567047119140625*x__20+266335422555582049846649169921875*x__21+9321739789445371744632720947265625*x__22+326260892630588011062145233154296875*x__23+11419131242070580387175083160400390625*x__24+399669593472470313551127910614013671875*x__25+13988435771536460974289476871490478515625*x__26+489595252003776134100131690502166748046875*x__27+17135833820132164693504609167575836181640625*x__28+599754183704625764272661320865154266357421875*x__29+20991396429661901749543146230280399322509765625*x__30+734698875038166561234010118059813976287841796875*x__31+x__0+35*x__1+1225*x__2+42875*x__3+1500625*x__4+52521875*x__5+1838265625*x__6, 452288/40239686127062906859375 = 78364164096*x__7+2821109907456*x__8+101559956668416*x__9+3656158440062976*x__10+131621703842267136*x__11+4738381338321616896*x__12+170581728179578208256*x__13+6140942214464815497216*x__14+221073919720733357899776*x__15+7958661109946400884391936*x__16+286511799958070431838109696*x__17+10314424798490535546171949056*x__18+371319292745659279662190166016*x__19+13367494538843734067838845976576*x__20+481229803398374426442198455156736*x__21+17324272922341479351919144385642496*x__22+623673825204293256669089197883129856*x__23+22452257707354557240087211123792674816*x__24+808281277464764060643139600456536293376*x__25+29098125988731506183153025616435306561536*x__26+1047532535594334222593508922191671036215296*x__27+37711171281396032013366321198900157303750656*x__28+1357602166130257152481187563160405662935023616*x__29+48873677980689257489322752273774603865660850176*x__30+1759452407304813269615619081855885739163790606336*x__31+x__0+36*x__1+1296*x__2+46656*x__3+1679616*x__4+60466176*x__5+2176782336*x__6, 4376/349910314148373103125 = 94931877133*x__7+3512479453921*x__8+129961739795077*x__9+4808584372417849*x__10+177917621779460413*x__11+6582952005840035281*x__12+243569224216081305397*x__13+9012061295995008299689*x__14+333446267951815307088493*x__15+12337511914217166362274241*x__16+456487940826035155404146917*x__17+16890053810563300749953435929*x__18+624931990990842127748277129373*x__19+23122483666661158726686253786801*x__20+855531895666462872887391390111637*x__21+31654680139659126296833481434130569*x__22+1171223165167387672982838813062831053*x__23+43335257111193343900365036083324748961*x__24+1603404513114153724313506335083015711557*x__25+59325966985223687799599734398071581327609*x__26+2195060778453276448585190172728648509121533*x__27+81217248802771228597652036390959994837496721*x__28+3005038205702535458113125346465519808987378677*x__29+111186413610993811950185637819224232932533011049*x__30+4113897303606771042156868599311296618503721408813*x__31+x__0+37*x__1+1369*x__2+50653*x__3+1874161*x__4+69343957*x__5+2565726409*x__6, 4688/338148622916495015625 = 114415582592*x__7+4347792138496*x__8+165216101262848*x__9+6278211847988224*x__10+238572050223552512*x__11+9065737908494995456*x__12+344498040522809827328*x__13+13090925539866773438464*x__14+497455170514937390661632*x__15+18903296479567620845142016*x__16+718325266223569592115396608*x__17+27296360116495644500385071104*x__18+1037261684426834491014632701952*x__19+39415944008219710658556042674176*x__20+1497805872312349005025129621618688*x__21+56916623147869262190954925621510144*x__22+2162831679619031963256287173617385472*x__23+82187603825523214603738912597460647936*x__24+3123128945369882154942078678703504621568*x__25+118678899924055521887798989790733175619584*x__26+4509798197114109831736361612047860673544192*x__27+171372331490336173605981741257818705594679296*x__28+6512148596632774597027306167797110812597813248*x__29+247461646672045434687037634376290210878716903424*x__30+9403542573537726518107430106299028013391242330112*x__31+x__0+38*x__1+1444*x__2+54872*x__3+2085136*x__4+79235168*x__5+3010936384*x__6, 616312/40239686127062906859375 = 137231006679*x__7+5352009260481*x__8+208728361158759*x__9+8140406085191601*x__10+317475837322472439*x__11+12381557655576425121*x__12+482880748567480579719*x__13+18832349194131742609041*x__14+734461618571137961752599*x__15+28644003124274380508351361*x__16+1117116121846700839825703079*x__17+43567528752021332753202420081*x__18+1699133621328831977374894383159*x__19+66266211231824447117620880943201*x__20+2584382238041153437587214356784839*x__21+100790907283604984065901359914608721*x__22+3930845384060594378570153036669740119*x__23+153302969978363180764235968430119864641*x__24+5978815829156164049805202768774674720999*x__25+233173817337090397942402907982212314118961*x__26+9093778876146525519753713411306280250639479*x__27+354657376169714495270394823040944929774939681*x__28+13831637670618865315545398098596852261222647559*x__29+539433869154135747306270525845277238187683254801*x__30+21037920897011294144944550507965812289319646937239*x__31+x__0+39*x__1+1521*x__2+59319*x__3+2313441*x__4+90224199*x__5+3518743761*x__6, 678688/40239686127062906859375 = 163840000000*x__7+6553600000000*x__8+262144000000000*x__9+10485760000000000*x__10+419430400000000000*x__11+16777216000000000000*x__12+671088640000000000000*x__13+26843545600000000000000*x__14+1073741824000000000000000*x__15+42949672960000000000000000*x__16+1717986918400000000000000000*x__17+68719476736000000000000000000*x__18+2748779069440000000000000000000*x__19+109951162777600000000000000000000*x__20+4398046511104000000000000000000000*x__21+175921860444160000000000000000000000*x__22+7036874417766400000000000000000000000*x__23+281474976710656000000000000000000000000*x__24+11258999068426240000000000000000000000000*x__25+450359962737049600000000000000000000000000*x__26+18014398509481984000000000000000000000000000*x__27+720575940379279360000000000000000000000000000*x__28+28823037615171174400000000000000000000000000000*x__29+1152921504606846976000000000000000000000000000000*x__30+46116860184273879040000000000000000000000000000000*x__31+x__0+40*x__1+1600*x__2+64000*x__3+2560000*x__4+102400000*x__5+4096000000*x__6, 82792/4471076236340322984375 = 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1727094849536*x__7+96717311574016*x__8+5416169448144896*x__9+303305489096114176*x__10+16985107389382393856*x__11+951166013805414055936*x__12+53265296773103187132416*x__13+2982856619293778479415296*x__14+167039970680451594847256576*x__15+9354238358105289311446368256*x__16+523837348053896201440996622336*x__17+29334891491018187280695810850816*x__18+1642753923497018487718965407645696*x__19+91994219715833035312262062828158976*x__20+5151676304086649977486675518376902656*x__21+288493873028852398739253829029106548736*x__22+16155656889615734329398214425629966729216*x__23+904716785818481122446300007835278136836096*x__24+50664140005834942856992800438775575662821376*x__25+2837191840326756799991596824571432237117997056*x__26+158882743058298380799529422176000205278607835136*x__27+8897433611264709324773647641856011495602038767616*x__28+498256282230823722187324267943936643753714170986496*x__29+27902351804926128442490159004860452050207993575243776*x__30+1562531701075863192779448904272185314811647640213651456*x__31+x__0+56*x__1+3136*x__2+175616*x__3+9834496*x__4+550731776*x__5+30840979456*x__6, 3448/56279281296591478125 = 1954897493193*x__7+111429157112001*x__8+6351461955384057*x__9+362033331456891249*x__10+20635899893042801193*x__11+1176246293903439668001*x__12+67046038752496061076057*x__13+3821624208892275481335249*x__14+217832579906859702436109193*x__15+12416457054691003038858224001*x__16+707738052117387173214918768057*x__17+40341068970691068873250369779249*x__18+2299440931329390925775271077417193*x__19+131068133085775282769190451412780001*x__20+7470883585889191117843855730528460057*x__21+425840364395683893717099776640122223249*x__22+24272900770553981941874687268486966725193*x__23+1383555343921576970686857174303757103336001*x__24+78862654603529887329150858935314154890152057*x__25+4495171312401203577761598959312906828738667249*x__26+256224764806868603932411140680835689238104033193*x__27+14604811593991510424147435018807634286571929892001*x__28+832474260857516094176403796072035154334600003844057*x__29+47451032868878417368055016376106003797072200219111249*x__30+2704708873526069789979135933438042216433115412489341193*x__31+x__0+57*x__1+3249*x__2+185193*x__3+10556001*x__4+601692057*x__5+34296447249*x__6, 2620432/40239686127062906859375 = 2207984167552*x__7+128063081718016*x__8+7427658739644928*x__9+430804206899405824*x__10+24986644000165537792*x__11+1449225352009601191936*x__12+84055070416556869132288*x__13+4875194084160298409672704*x__14+282761256881297307761016832*x__15+16400152899115243850138976256*x__16+951208868148684143308060622848*x__17+55170114352623680311867516125184*x__18+3199866632452173458088315935260672*x__19+185592264682226060569122324245118976*x__20+10764351351569111513009094806216900608*x__21+624332378391008467754527498760580235264*x__22+36211277946678491129762594928113653645312*x__23+2100254120907352485526230505830591911428096*x__24+121814739012626444160521369338174330862829568*x__25+7065254862732333761310239421614111190044114944*x__26+409784782038475358155993886453618449022558666752*x__27+23767517358231570773047645414309870043308402671616*x__28+1378516006777431104836763434029972462511887354953728*x__29+79953928393091004080532279173738402825689466587316224*x__30+4637327846799278236670872192076827363889989062064340992*x__31+x__0+58*x__1+3364*x__2+195112*x__3+11316496*x__4+656356768*x__5+38068692544*x__6, 132472/1916175529860138421875 = 2488651484819*x__7+146830437604321*x__8+8662995818654939*x__9+511116753300641401*x__10+30155888444737842659*x__11+1779197418239532716881*x__12+104972647676132430295979*x__13+6193386212891813387462761*x__14+365409786560616989860302899*x__15+21559177407076402401757871041*x__16+1271991467017507741703714391419*x__17+75047496554032956760519149093721*x__18+4427802296687944448870629796529539*x__19+261240335504588722483367157995242801*x__20+15413179794770734626518662321719325259*x__21+909377607891473342964601076981440190281*x__22+53653278865596927234911463541904971226579*x__23+3165543453070218706859776348972393302368161*x__24+186767063731142903704726804589371204839721499*x__25+11019256760137431318578881470772901085543568441*x__26+650136148848108447796154006775601164047070538019*x__27+38358032782038398419973086399760468678777161743121*x__28+2263123934140265506778412097585867652047852542844139*x__29+133524312114275664899926313757566191470823300027804201*x__30+7877934414742264229095652511696405296778574701640447859*x__31+x__0+59*x__1+3481*x__2+205379*x__3+12117361*x__4+714924299*x__5+42180533641*x__6, 42752/583183856913955171875 = 2799360000000*x__7+167961600000000*x__8+10077696000000000*x__9+604661760000000000*x__10+36279705600000000000*x__11+2176782336000000000000*x__12+130606940160000000000000*x__13+7836416409600000000000000*x__14+470184984576000000000000000*x__15+28211099074560000000000000000*x__16+1692665944473600000000000000000*x__17+101559956668416000000000000000000*x__18+6093597400104960000000000000000000*x__19+365615844006297600000000000000000000*x__20+21936950640377856000000000000000000000*x__21+1316217038422671360000000000000000000000*x__22+78973022305360281600000000000000000000000*x__23+4738381338321616896000000000000000000000000*x__24+284302880299297013760000000000000000000000000*x__25+17058172817957820825600000000000000000000000000*x__26+1023490369077469249536000000000000000000000000000*x__27+61409422144648154972160000000000000000000000000000*x__28+3684565328678889298329600000000000000000000000000000*x__29+221073919720733357899776000000000000000000000000000000*x__30+13264435183244001473986560000000000000000000000000000000*x__31+x__0+60*x__1+3600*x__2+216000*x__3+12960000*x__4+777600000*x__5+46656000000*x__6, 1041496/13413228709020968953125 = 3142742836021*x__7+191707312997281*x__8+11694146092834141*x__9+713342911662882601*x__10+43513917611435838661*x__11+2654348974297586158321*x__12+161915287432152755657581*x__13+9876832533361318095112441*x__14+602486784535040403801858901*x__15+36751693856637464631913392961*x__16+2241853325254885342546716970621*x__17+136753052840548005895349735207881*x__18+8341936223273428359616333847680741*x__19+508858109619679129936596364708525201*x__20+31040344686800426926132378247220037261*x__21+1893461025894826042494075073080422272921*x__22+115501122579584388592138579457905758648181*x__23+7045568477354647704120453346932251277539041*x__24+429779677118633509951347654162867327929881501*x__25+26216560304236644107032206903934907003722771561*x__26+1599210178558435290528964621140029327227089065221*x__27+97551820892064552722266841889541788960852432978481*x__28+5950661074415937716058277355262049126611998411687341*x__29+362990325539372200679554918670984996723331903112927801*x__30+22142409857901704241452850038930084800123246089888595861*x__31+x__0+61*x__1+3721*x__2+226981*x__3+13845841*x__4+844596301*x__5+51520374361*x__6, 21328/259610878239115528125 = 3521614606208*x__7+218340105584896*x__8+13537086546263552*x__9+839299365868340224*x__10+52036560683837093888*x__11+3226266762397899821056*x__12+200028539268669788905472*x__13+12401769434657526912139264*x__14+768909704948766668552634368*x__15+47672401706823533450263330816*x__16+2955688905823059073916326510592*x__17+183252712161029662582812243656704*x__18+11361668153983839080134359106715648*x__19+704423425546998022968330264616370176*x__20+43674252383913877424036476406214950912*x__21+2707803647802660400290261537185326956544*x__22+167883826163764944817996215305490271305728*x__23+10408797222153426578715765348940396820955136*x__24+645345427773512447880377451634304602899218432*x__25+40011416521957771768583402001326885379751542784*x__26+2480707824361381849652170924082266893544595652608*x__27+153803885110405674678434597293100547399764930461696*x__28+9535840876845151830062945032172233938785425688625152*x__29+591222134364399413463902591994678504204696392694759424*x__30+36655772330592763634761960703670067260691176347075084288*x__31+x__0+62*x__1+3844*x__2+238328*x__3+14776336*x__4+916132832*x__5+56800235584*x__6, 112712/1298054391195577640625 = 3938980639167*x__7+248155780267521*x__8+15633814156853823*x__9+984930291881790849*x__10+62050608388552823487*x__11+3909188328478827879681*x__12+246278864694166156419903*x__13+15515568475732467854453889*x__14+977480813971145474830595007*x__15+61581291280182164914327485441*x__16+3879621350651476389602631582783*x__17+244416145091043012544965789715329*x__18+15398217140735709790332844752065727*x__19+970087679866349716790969219380140801*x__20+61115523831580032157831060820948870463*x__21+3850278001389542025943356831719778839169*x__22+242567514087541147634431480398346066867647*x__23+15281753387515092300969183265095802212661761*x__24+962750463413450814961058545701035539397690943*x__25+60653279195047401342546688379165238982054529409*x__26+3821156589287986284580441367887410055869435352767*x__27+240732865125143135928567806176906833519774427224321*x__28+15166170502884017563499771789145130511745788915132223*x__29+955468741681693106500485622716143222239984701653330049*x__30+60194530725946665709530594231117023001119036204159793087*x__31+x__0+63*x__1+3969*x__2+250047*x__3+15752961*x__4+992436543*x__5+62523502209*x__6, 335392/3658153284278446078125 = 4398046511104*x__7+281474976710656*x__8+18014398509481984*x__9+1152921504606846976*x__10+73786976294838206464*x__11+4722366482869645213696*x__12+302231454903657293676544*x__13+19342813113834066795298816*x__14+1237940039285380274899124224*x__15+79228162514264337593543950336*x__16+5070602400912917605986812821504*x__17+324518553658426726783156020576256*x__18+20769187434139310514121985316880384*x__19+1329227995784915872903807060280344576*x__20+85070591730234615865843651857942052864*x__21+5444517870735015415413993718908291383296*x__22+348449143727040986586495598010130648530944*x__23+22300745198530623141535718272648361505980416*x__24+1427247692705959881058285969449495136382746624*x__25+91343852333181432387730302044767688728495783936*x__26+5846006549323611672814739330865132078623730171904*x__27+374144419156711147060143317175368453031918731001856*x__28+23945242826029513411849172299223580994042798784118784*x__29+1532495540865888858358347027150309183618739122183602176*x__30+98079714615416886934934209737619787751599303819750539264*x__31+x__0+64*x__1+4096*x__2+262144*x__3+16777216*x__4+1073741824*x__5+68719476736*x__6 ]:
> 

#
# Solve the 33 equations in 32 unknowns. This fails with
# a very odd Error message!!!
#
  solve(liseq1,lisvar1);

Error, (in LinearAlgebra:-Modular:-IntegerLinearSolve) invalid arguments to iratrecon

  
> 

#
# Select any 32 of the 33 equations and compute
# the solution
#
  answers:=[seq( solve(j, lisvar1)[], j in combinat:-choose( liseq1, 32))]:
#
# Check the number of answers (hould be 33!)
#
  numelems(answers);
#
# Verify that all of these answers are the same
#
  seq( evalb(answers[1]=answers[j]), j=1..32);

33

  

true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true

 (2)
> 

 

> 

 


 

Download solProb.mw

 

The distinction...

tomleslie 13876
January 30 2019
0 0

Recommend that you read the Maple help at

?HFloat

and

?SFloat

Excerpts from the Maple help

A hardware floating-point number (an object of type hfloat) is represented internally in Maple as a 64-bit IEEE binary floating-point value.

An arbitrary-precision software floating-point number (an object of type sfloat) is represented internally in Maple by a pair of integers (the mantissa M and the exponent E).

The first of these is (more-or-less) equivalent to the term "double precision" in other programming languages, so is restricted to 15-16 digits of precision, with mantissa in the range -308..308 (more or less).

The second (ie software floats) has range/prcision which are only really restricted by the size of the integers which Maple can handle. By default, Maple will use 10 digits in the mantissa (can be changed by setting 'Digits'). The maximum/minimum exponent on my system (may be  machine-dependent?) is always 9223372036854775806

 

 

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