## 4715 Reputation

10 years, 34 days

## Options...

You can try changing Options -> Precision

Or through Limit expression length

## Force variable of separation by product...

@farjad_etg There is a workaround for 2016.1 using boundary conditions (haven't been able to check with 2016.0).  That is to force maple to begin by trying to separate the variables by product.

pdsolve({equa1, u(0,y) = 0, D[1](u)(0,y) = 0},HINT=`*`);

u(x, y) = (1/6)*y*x^2*(3+x)

My guess is that it circumvents an issue that prevents it from evaluating at least in 2016.1.

## assignment...

It seems assigning change:=f2 is your problem.  Try f2:=change instead.

## lprint?...

Maybe lprint?

plot([cos(3*t), sin(2*t), t = 0 .. 2*Pi]);

lprint(%);
PLOT(CURVES(Matrix(209, 2, {(1, 1) = HFloat(1.), (2, 1) = HFloat(.995093264101945540), (2, 2) = HFloat(0.660209573197723110e-1), (3, 1) = HFloat(.982874948801488735), (3, 2) = HFloat(.123241184241304202), (4, 1) = HFloat(.960415331794754912), (4, 2) = HFloat(.187095559833458880), (5, 1) = HFloat(.928692888370737157), (5, 2) = HFloat(.250583123026205390), (6, 1) = HFloat(.888341049365922508), (6, 2) = HFloat(.312716031931642657), (7, 1) = HFloat(.843435582881161494), (7, 2) = HFloat(.369155248626400478), (8, 1) = HFloat(.789737481048331080), (8, 2) = HFloat(.426189998289056848), (9, 1) = HFloat(.726988273906466032), (9, 2) = HFloat(.483440255170793975), (10, 1) = HFloat(.657713718477610843), (10, 2) = HFloat(.538518445847828708), (11, 1) = HFloat(.580124538604127493), (11, 2) = HFloat(.592863355868342379), (12, 1) = HFloat(.507061588853425005), (12, 2) = HFloat(.638603964793882595), (13, 1) = HFloat(.420238020776815213), (13, 2) = HFloat(.687513346078893139), (14, 1) = HFloat(.328996184828279803), (14, 2) = HFloat(.733667728275790187), (15, 1) = HFloat(.238041581986947248), (15, 2) = HFloat(.775157844789451933), (16, 1) = HFloat(.153568372599895503), (16, 2) = HFloat(.810152318374346758), (17, 1) = HFloat(0.516903761583032209e-1), (17, 2) = HFloat(.848276396747285943), (18, 1) = HFloat(-0.350807193735846248e-1), (18, 2) = HFloat(.877483383648545501), (19, 1) = HFloat(-.135639118077677007), (19, 2) = HFloat(.907755898501108049), (20, 1) = HFloat(-.223529985692667771), (20, 2) = HFloat(.931125642447514057), (21, 1) = HFloat(-.317881575278769035), (21, 2) = HFloat(.952961215633009173), (22, 1) = HFloat(-.404900842257057803), (22, 2) = HFloat(.969970900850029349), (23, 1) = HFloat(-.491924216375459078), (23, 2) = HFloat(.983712180075785425), (24, 1) = HFloat(-.567748258469063294), (24, 2) = HFloat(.992677943036860744), (25, 1) = HFloat(-.644426299186268925), (25, 2) = HFloat(.998390136485883373), (26, 1) = HFloat(-.717714250173252410), (26, 2) = HFloat(.999949223787556019), (27, 1) = HFloat(-.775669174171986331), (27, 2) = HFloat(.997671804246988203), (28, 1) = HFloat(-.831619946383563624), (28, 2) = HFloat(.991421294045069290), (29, 1) = HFloat(-.881666027915066430), (29, 2) = HFloat(.980855601678915945), (30, 1) = HFloat(-.922547877554730666), (30, 2) = HFloat(.966521170869912294), (31, 1) = HFloat(-.954145429505132481), (31, 2) = HFloat(.948942736353007077), (32, 1) = HFloat(-.979732108253810963), (32, 2) = HFloat(.925232759205969923), (33, 1) = HFloat(-.987902672045105401), (33, 2) = HFloat(.913171937940988276), (34, 1) = HFloat(-.993985648764305951), (34, 2) = HFloat(.900253401738528192), (35, 1) = HFloat(-.998161690392944556), (35, 2) = HFloat(.885527019193549148), (36, 1) = HFloat(-.999933202852693825), (36, 2) = HFloat(.869852443315878299), (37, 1) = HFloat(-.997006102055733034), (37, 2) = HFloat(.839084123645368218), (38, 1) = HFloat(-.984786488226064516), (38, 2) = HFloat(.802074455362625338), (39, 1) = HFloat(-.964786753172529044), (39, 2) = HFloat(.764170478498252037), (40, 1) = HFloat(-.935254589504708078), (40, 2) = HFloat(.721513059049358363), (41, 1) = HFloat(-.898112516187038801), (41, 2) = HFloat(.676970729790365766), (42, 1) = HFloat(-.850824619142301453), (42, 2) = HFloat(.627523533269496392), (43, 1) = HFloat(-.797570978035496481), (43, 2) = HFloat(.577371030739956326), (44, 1) = HFloat(-.735786610659668106), (44, 2) = HFloat(.523725493801580844), (45, 1) = HFloat(-.667760211506508328), (45, 2) = HFloat(.468386642662180275), (46, 1) = HFloat(-.599855216887644649), (46, 2) = HFloat(.415852585744740932), (47, 1) = HFloat(-.516368371666899195), (47, 2) = HFloat(.353898893434316020), (48, 1) = HFloat(-.437236627092241481), (48, 2) = HFloat(.297127125152112148), (49, 1) = HFloat(-.348976342827391262), (49, 2) = HFloat(.235421628643554953), (50, 1) = HFloat(-.261475977430020934), (50, 2) = HFloat(.175454466133063841), (51, 1) = HFloat(-.161763476824103719), (51, 2) = HFloat(.108106580473264227), (52, 1) = HFloat(-0.740213527132065063e-1), (52, 2) = HFloat(0.493726628305415013e-1), (53, 1) = HFloat(0.262293744673981893e-1), (53, 2) = HFloat(-0.174873638795113792e-1), (54, 1) = HFloat(.117393216169258907), (54, 2) = HFloat(-0.783626027905274108e-1), (55, 1) = HFloat(.215961974470104234), (55, 2) = HFloat(-.144609155232220787), (56, 1) = HFloat(.299311261051054600), (56, 2) = HFloat(-.201263025576119164), (57, 1) = HFloat(.391489098405798708), (57, 2) = HFloat(-.264963626440157696), (58, 1) = HFloat(.476950203554007413), (58, 2) = HFloat(-.325418569365158894), (59, 1) = HFloat(.558064738412816452), (59, 2) = HFloat(-.384532353352742717), (60, 1) = HFloat(.633890362602178681), (60, 2) = HFloat(-.441899748072451137), (61, 1) = HFloat(.701413171156469617), (61, 2) = HFloat(-.495362579944167714), (62, 1) = HFloat(.767890284790246458), (62, 2) = HFloat(-.551110184112867052), (63, 1) = HFloat(.824375231430874322), (63, 2) = HFloat(-.602049173252518388), (64, 1) = HFloat(.876026995964009569), (64, 2) = HFloat(-.653127725230104206), (65, 1) = HFloat(.915478127479820492), (65, 2) = HFloat(-.696945843641809448), (66, 1) = HFloat(.950612588090555821), (66, 2) = HFloat(-.742505055908345368), (67, 1) = HFloat(.975626490690282622), (67, 2) = HFloat(-.783143762911385988), (68, 1) = HFloat(.991931968635061834), (68, 2) = HFloat(-.820597266232610645), (69, 1) = HFloat(.999585319789284887), (69, 2) = HFloat(-.856266505733220828), (70, 1) = HFloat(.998094016522872329), (70, 2) = HFloat(-.885869493765740090), (71, 1) = HFloat(.994160830774133308), (71, 2) = HFloat(-.899785162623916501), (72, 1) = HFloat(.988090583676968670), (72, 2) = HFloat(-.912841105840068390), (73, 1) = HFloat(.978921728563026061), (73, 2) = HFloat(-.926242794912090828), (74, 1) = HFloat(.967187663656392194), (74, 2) = HFloat(-.938565611925027743), (75, 1) = HFloat(.939514541203616105), (75, 2) = HFloat(-.958088936782832024), (76, 1) = HFloat(.902870173151799960), (76, 2) = HFloat(-.974270660654016685), (77, 1) = HFloat(.857288501687358595), (77, 2) = HFloat(-.986736072040474421), (78, 1) = HFloat(.808354130363334034), (78, 2) = HFloat(-.994600140549084077), (79, 1) = HFloat(.749214705766426348), (79, 2) = HFloat(-.999160233538684439), (80, 1) = HFloat(.683917914786050796), (80, 2) = HFloat(-.999768472352535742), (81, 1) = HFloat(.607436507481678656), (81, 2) = HFloat(-.996097108568060996), (82, 1) = HFloat(.534848109093290169), (82, 2) = HFloat(-.989159193130524250), (83, 1) = HFloat(.445932284292002323), (83, 2) = HFloat(-.976879206933512156), (84, 1) = HFloat(.361677898743807680), (84, 2) = HFloat(-.961910954801300955), (85, 1) = HFloat(.275289484206780899), (85, 2) = HFloat(-.943528610575696702), (86, 1) = HFloat(.179862932911773604), (86, 2) = HFloat(-.919875247348552305), (87, 1) = HFloat(0.823135670878773901e-1), (87, 2) = HFloat(-.892173946003792184), (88, 1) = HFloat(-0.715923643143954493e-2), (88, 2) = HFloat(-.863629116200008040), (89, 1) = HFloat(-.102096312896319180), (89, 2) = HFloat(-.829948042850447654), (90, 1) = HFloat(-.193862362832848245), (90, 2) = HFloat(-.793861120317075342), (91, 1) = HFloat(-.291427682463165472), (91, 2) = HFloat(-.751314442328326781), (92, 1) = HFloat(-.373504758209699750), (92, 2) = HFloat(-.711765148609128318), (93, 1) = HFloat(-.464245107585174510), (93, 2) = HFloat(-.663391994916401329), (94, 1) = HFloat(-.545332107735446603), (94, 2) = HFloat(-.615227126771057287), (95, 1) = HFloat(-.620892281187063522), (95, 2) = HFloat(-.565146302134166501), (96, 1) = HFloat(-.691128770153389027), (96, 2) = HFloat(-.512846920317007848), (97, 1) = HFloat(-.756586153184119259), (97, 2) = HFloat(-.457468810033391238), (98, 1) = HFloat(-.818504578353094425), (98, 2) = HFloat(-.396770099996740677), (99, 1) = HFloat(-.867999692433419900), (99, 2) = HFloat(-.339536796759702386), (100, 1) = HFloat(-.909602992964738011), (100, 2) = HFloat(-.281777211418164752), (101, 1) = HFloat(-.945713944592248001), (101, 2) = HFloat(-.218887944828852737), (102, 1) = HFloat(-.972800641317989490), (102, 2) = HFloat(-.155214744000589155), (103, 1) = HFloat(-.989290339391220019), (103, 2) = HFloat(-0.975010830516318955e-1), (104, 1) = HFloat(-.999071706820651273), (104, 2) = HFloat(-0.287236868334883391e-1), (105, 1) = HFloat(-.999057373303013807), (105, 2) = HFloat(0.289445676979894866e-1), (106, 1) = HFloat(-.989562010713673668), (106, 2) = HFloat(0.962581899740645730e-1), (107, 1) = HFloat(-.971055471764343259), (107, 2) = HFloat(.160098461874967096), (108, 1) = HFloat(-.946876818902685380), (108, 2) = HFloat(.216547531764909762), (109, 1) = HFloat(-.911290461770500437), (109, 2) = HFloat(.279166555016422957), (110, 1) = HFloat(-.866820740398964507), (110, 2) = HFloat(.341022077787115963), (111, 1) = HFloat(-.814366945698000944), (111, 2) = HFloat(.401150529926342814), (112, 1) = HFloat(-.758862301943241335), (112, 2) = HFloat(.455399853250309461), (113, 1) = HFloat(-.694912962690416136), (113, 2) = HFloat(.509839588760538698), (114, 1) = HFloat(-.622429912169550459), (114, 2) = HFloat(.564066152125074827), (115, 1) = HFloat(-.544419988611536954), (115, 2) = HFloat(.615798664311906552), (116, 1) = HFloat(-.458937986297073330), (116, 2) = HFloat(.666371127580410727), (117, 1) = HFloat(-.379901758909653553), (117, 2) = HFloat(.708523809513541214), (118, 1) = HFloat(-.287509500615067526), (118, 2) = HFloat(.753112602378217311), (119, 1) = HFloat(-.191959418220285449), (119, 2) = HFloat(.794646677475388197), (120, 1) = HFloat(-0.981088171354586591e-1), (120, 2) = HFloat(.831435491015080852), (121, 1) = HFloat(-0.120961004499473106e-1), (121, 2) = HFloat(.861965155992681642), (122, 1) = HFloat(0.902457096602296283e-1), (122, 2) = HFloat(.894558903914745351), (123, 1) = HFloat(.176244582389329302), (123, 2) = HFloat(.918911015468448444), (124, 1) = HFloat(.274568180373232940), (124, 2) = HFloat(.943362799860770540), (125, 1) = HFloat(.359299052333536428), (125, 2) = HFloat(.961444789047370185), (126, 1) = HFloat(.448937935648393349), (126, 2) = HFloat(.977355768217095355), (127, 1) = HFloat(.530298376559004248), (127, 2) = HFloat(.988626590324497179), (128, 1) = HFloat(.610253528329505301), (128, 2) = HFloat(.996303271681065028), (129, 1) = HFloat(.678596392773996193), (129, 2) = HFloat(.999652451922633301), (130, 1) = HFloat(.746212838049202798), (130, 2) = HFloat(.999279183113629066), (131, 1) = HFloat(.809086638780554424), (131, 2) = HFloat(.994513634808954938), (132, 1) = HFloat(.857225232338885368), (132, 2) = HFloat(.986749366985044563), (133, 1) = HFloat(.901879357489389188), (133, 2) = HFloat(.974614971110934758), (134, 1) = HFloat(.939601235770873733), (134, 2) = HFloat(.958040566059456977), (135, 1) = HFloat(.967894375197106083), (135, 2) = HFloat(.937920591653075397), (136, 1) = HFloat(.978445394198942275), (136, 2) = HFloat(.926824514348714934), (137, 1) = HFloat(.986919187167190626), (137, 2) = HFloat(.914853846350839106), (138, 1) = HFloat(.993872549167743147), (138, 2) = HFloat(.900551555303991780), (139, 1) = HFloat(.998224771172738001), (139, 2) = HFloat(.885201625085295207), (140, 1) = HFloat(.999907229218049975), (140, 2) = HFloat(.870530123433630010), (141, 1) = HFloat(.999476732754708164), (141, 2) = HFloat(.855040959018391833), (142, 1) = HFloat(.991493866143389857), (142, 2) = HFloat(.819295786251743263), (143, 1) = HFloat(.976010307005786060), (143, 2) = HFloat(.783871171306493308), (144, 1) = HFloat(.950256661933032709), (144, 2) = HFloat(.741993645657856304), (145, 1) = HFloat(.917818190727948457), (145, 2) = HFloat(.699739586695532489), (146, 1) = HFloat(.875705748307880838), (146, 2) = HFloat(.652791582113811497), (147, 1) = HFloat(.826789697628834475), (147, 2) = HFloat(.604324382047172204), (148, 1) = HFloat(.767845059519881801), (148, 2) = HFloat(.551070911013765485), (149, 1) = HFloat(.704114699808206401), (149, 2) = HFloat(.497560137692068472), (150, 1) = HFloat(.632475830420674567), (150, 2) = HFloat(.440806462822373124), (151, 1) = HFloat(.555624328424223934), (151, 2) = HFloat(.382723504604894627), (152, 1) = HFloat(.480511671748108882), (152, 2) = HFloat(.327974528230208562), (153, 1) = HFloat(.389899709807566441), (153, 2) = HFloat(.263853512652095279), (154, 1) = HFloat(.305479198730463530), (154, 2) = HFloat(.205486799561757499), (155, 1) = HFloat(.212757754732972842), (155, 2) = HFloat(.142444814262494696), (156, 1) = HFloat(.122163067946142886), (156, 2) = HFloat(0.815553095377624937e-1), (157, 1) = HFloat(0.203939098100098110e-1), (157, 2) = HFloat(0.135964635506402240e-1), (158, 1) = HFloat(-0.679405883589561527e-1), (158, 2) = HFloat(-0.453131224544987693e-1), (159, 1) = HFloat(-.167520870928223709), (159, 2) = HFloat(-.111974318859801747), (160, 1) = HFloat(-.256835678931248201), (160, 2) = HFloat(-.172300293829411311), (161, 1) = HFloat(-.352048697882217765), (161, 2) = HFloat(-.237546579692993948), (162, 1) = HFloat(-.431407930252718452), (162, 2) = HFloat(-.293005264509637653), (163, 1) = HFloat(-.517846220784493050), (163, 2) = HFloat(-.354975245017543406), (164, 1) = HFloat(-.596604630548027814), (164, 2) = HFloat(-.413391645989387824), (165, 1) = HFloat(-.669944358066613010), (165, 2) = HFloat(-.470116313883948200), (166, 1) = HFloat(-.737023027338493231), (166, 2) = HFloat(-.524763019572474398), (167, 1) = HFloat(-.795274565623967478), (167, 2) = HFloat(-.575302194904628972), (168, 1) = HFloat(-.850861712390843072), (168, 2) = HFloat(-.627560177199392166), (169, 1) = HFloat(-.896222605548881779), (169, 2) = HFloat(-.674868457399333321), (170, 1) = HFloat(-.935490032503407898), (170, 2) = HFloat(-.721820286664437982), (171, 1) = HFloat(-.963230229146209815), (171, 2) = HFloat(-.761647060563439449), (172, 1) = HFloat(-.984984762427186689), (172, 2) = HFloat(-.802529998039201664), (173, 1) = HFloat(-.996868790332053556), (173, 2) = HFloat(-.838446724351124772), (174, 1) = HFloat(-.999887970842842200), (174, 2) = HFloat(-.870971772918978981), (175, 1) = HFloat(-.997944658660394945), (175, 2) = HFloat(-.886602839079551064), (176, 1) = HFloat(-.993590400180439204), (176, 2) = HFloat(-.901281819053078692), (177, 1) = HFloat(-.987456034194965637), (177, 2) = HFloat(-.913945815351264401), (178, 1) = HFloat(-.979297876550140778), (178, 2) = HFloat(-.925777229337745866), (179, 1) = HFloat(-.956344743548646292), (179, 2) = HFloat(-.947367448869784856), (180, 1) = HFloat(-.921465139823633539), (180, 2) = HFloat(-.966997859176745633), (181, 1) = HFloat(-.881546519240037130), (181, 2) = HFloat(-.980888459750203889), (182, 1) = HFloat(-.832894562745947198), (182, 2) = HFloat(-.991219790139763246), (183, 1) = HFloat(-.775746722506624686), (183, 2) = HFloat(-.997666214135419449), (184, 1) = HFloat(-.716846506997171340), (184, 2) = HFloat(-.999957245606440503), (185, 1) = HFloat(-.647876575260122656), (185, 2) = HFloat(-.998556546300095382), (186, 1) = HFloat(-.573717438221209797), (186, 2) = HFloat(-.993251674169345455), (187, 1) = HFloat(-.488829425272471141), (187, 2) = HFloat(-.983283885524348533), (188, 1) = HFloat(-.409810122357457784), (188, 2) = HFloat(-.970836294914462661), (189, 1) = HFloat(-.314693271869310065), (189, 2) = HFloat(-.952279727923407204), (190, 1) = HFloat(-.226015047027563559), (190, 2) = HFloat(-.931744362076591504), (191, 1) = HFloat(-.136382360249396956), (191, 2) = HFloat(-.907965594101156181), (192, 1) = HFloat(-0.387553207809959721e-1), (192, 2) = HFloat(-.878656457849667616), (193, 1) = HFloat(0.596398641464917154e-1), (193, 2) = HFloat(-.845453640685242203), (194, 1) = HFloat(.148687986694261615), (194, 2) = HFloat(-.812077408376920884), (195, 1) = HFloat(.241932088878842516), (195, 2) = HFloat(-.773467153639162852), (196, 1) = HFloat(.330826976067736533), (196, 2) = HFloat(-.732788568211495961), (197, 1) = HFloat(.423948929915850481), (197, 2) = HFloat(-.685529097059929815), (198, 1) = HFloat(.501097422188309660), (198, 2) = HFloat(-.642139991866428783), (199, 1) = HFloat(.584987135988432216), (199, 2) = HFloat(-.589646768721602377), (200, 1) = HFloat(.658532716923785788), (200, 2) = HFloat(-.537907253647431860), (201, 1) = HFloat(.725638944707979405), (201, 2) = HFloat(-.484585448285424714), (202, 1) = HFloat(.786506547213669638), (202, 2) = HFloat(-.429353091420042354), (203, 1) = HFloat(.841556618713768190), (203, 2) = HFloat(-.371315313141940495), (204, 1) = HFloat(.891608559235583020), (204, 2) = HFloat(-.308174981261063963), (205, 1) = HFloat(.929568939609444200), (205, 2) = HFloat(-.249053664812155823), (206, 1) = HFloat(.959270841354030623), (206, 2) = HFloat(-.189766662182448170), (207, 1) = HFloat(.982205776992280066), (207, 2) = HFloat(-.125620483500565344), (208, 1) = HFloat(.995799859113089436), (208, 2) = HFloat(-0.610853875403885929e-1), (209, 1) = HFloat(1.), (209, 2) = HFloat(0.164082742812264922e-8)}, datatype = float[8], storage = rectangular, order = Fortran_order, shape = []), COLOUR(RGB, .47058824, 0., 0.54901961e-1, _ATTRIBUTE("source" = "mathdefault"))), AXESLABELS("", ""), VIEW(DEFAULT, DEFAULT))

## Multiply by a scalar with explicit decim...

Try this and see what you get.  I tried and haven't been able to get a different value which is good.

evalf(add(sin(k*1.), k = 1 .. 10000))

evalf(add(sin(1.*k), k = 1 .. 10000), 25);
1.633891021792462265108364

This seems to fix the randomness of the answer.

## Preview...

I think Preview is the command from tha audiotools package you need.  The y axes represents the amplitude.

## file error...

First try a different .wav file.  If that works then there is a problem with your 440.wav file you are trying to Read.

It's probable that your 440.wav wasn't written correctly or it's corrupt.

You could load your 440.wav with one of a multitude of free audio editing softwares (ie. Audacity) and resave.

## apparent fuzzy 2d plot lines...

The reason the lines are fuzzy is because you have multiple lines overlaying one another in the 2d.

change your range to 0..15 and you will see what I mean.

## Windows...

It's a windows setting.  Windows -> control panel -> display and change the icon sizes.

## ImageTools...

For example

```with(ImageTools):
plot(x^2,axis=[gridlines=[10,color=black]],background=a) #x^2 is plotted over yourimage.jpg with gridlines```

## substitute...

So you're saying given 3 equations with 3 unknowns and only have 2 of the solutions can we get the third?

Certainly, substitute the 2 solutions into any one of the equations to find the removed solution.

In terms of Maple, an example

```a := 7*x+5*y-3*z = 16;
b := 3*x-5*y+2*z = -8;
c := 5*x+3*y-7*z = 0;
d:=solve({a,b,c})
{x = 1, y = 3, z = 2}

So if the z solution was pulled away finding it just involves substituting into any one of the others, we'll use equation c here

solve(subs({d[1],d[2]},c),{z})
{z = 2}
```

## elif or else...

I think the problem is the use of double if statements, try using elif or else.  Look here on the if help http://www.maplesoft.com/support/help/Maple/view.aspx?path=if

## One way...

After 4 rides there is really no best possible time, that much variablity in the data you're almost at the limit.  Meaning the spread of times after 4 rides is almost 30 minutes saying it doesn't really matter when you show up after 2 hours, you're just as likely to arrive for a ride as any other time.  Nevertheless, here's one way using random selections from the given data.

monte-carlo_2_test.mw

## functions...

So here's a start, for example x is some function of t

x := t -> t^2+t-3

x(5)
27

and y is some other function of t

y:=t->3*t^3-4*t

y(2)
16

t going from -n to n could be something like

for i from -5 to 5 do
x(t):
end do;

or

seq(x(i),i=-5..5)
17, 9, 3, -1, -3, -3, -1, 3, 9, 17, 27

## writedata...

writedata is another command you could use.

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