Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I create a lot of procs and functions and then find myself having to create sequences of their values. I use for loops, seq or create a new proc to do it.

 

e.g., suppose I have a proc like f := n->n^2 or whatever. I can do [seq(f(k),k=0..5)]. Is there a very simple notation that maple has to do the same? E.g., hypopthetically f($$0..5) and it handles the accumulation in to a sequence itself

e.g., I have an equation that is written like a/b*c and maple rewrites it as a*c/b.

c is a complicated expression and when it's written with b under it, it takes up far more vertical spaces than necessary giving less visual resolution even if b is just 2.

In latex notation it is the difference between \frac{a}{b} c and \frac{ac}{b}.

 

In general what is the process? I noticed I can sometimes use ` ` to block things in but this also interfers with mathamtical notation. e.g., `3^f` becomes just that rather than f writen as a superscript.

Clearly I could hack it using various things but I want something direct and simple that tells maple not to try to do it's magic tricks.

For example, sometimes I might have 2*(a + b) and maple displays it as 2a + 2b. If I write it as `2`*(a+b) then this is noted as 2*(a+b) but the 2 is different.. I guess it is treated as a string or something... For my cases it works since I'm not trying to calculate anything from the expression but just for visual purposes, other times though I might want to calculate(usually the visual doesn't matter in calculation but sometimes both are desired).

I really want to avoid having to litter the expressions with special syntax to get such simple behavior. Something to tell maple not to carry out whatever algebraic transform it is programmed to do.

 

BTW, what does ! do? !3 + 4 opens a new window with an exit code.

 

 

Hello,
the following command

collect(c4*dnub*kpbr*ksr*nur*nurdel + c4*dnur*kpbr*ksr*nub*nurdel, [nur, nub, dnur, dnub, nurdel, nubdel, dnurdel, dnubdel, c4], distributed)

returns

c4*dnub*kpbr*ksr*nur*nurdel + c4*dnur*kpbr*ksr*nub*nurdel

However, I am expecting it to return

c4*kpbr*ksr*(dnub*nur*nurdel+dnur*nub*nurdel)

Where is the error?
Thanks in advance

Hello,

Lets say I have an expression

f:=(a+b)*x1+(a^2+b^2)*(x1+x2^2)+c*(x2-x3)*a*b

and I have a list

p:=[a+b,a^2+b^2,c*b*a].

How can I get the coefficients of the element from p in f, ie,

cof=[x1,x1+x2^2, x2-x3].

such that cof[i] corresponds to p[i]?

Thanks in advance for your suggestions.


How do I remove these unwanted trailing zeros from my plot ? I have tried setting striptrailing=true from the Tyesetting package but no difference. Thanks

 

how can i extract solution for each GB to excel file


 

Eq1 := diff(f(x), `$`(x, 3))+2*GB*a*alpha*f(x) = 0; Eq2 := f(0) = 1, (D(f))(0) = 0, f(1) = 0

f(0) = 1, (D(f))(0) = 0, f(1) = 0

(1)

Eq3 := {Eq1, Eq2}

{diff(diff(diff(f(x), x), x), x)+2*GB*a*alpha*f(x) = 0, f(0) = 1, f(1) = 0, (D(f))(0) = 0}

(2)

Hlist := [0, 5, 6, 10]; params := {a = 7, alpha = 2}

{a = 7, alpha = 2}

(3)

for k to 4 do R := Hlist[k]; Sol_f[H] := dsolve(eval(Eq3, `union`(params, {GB = R})), numeric) end do

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(78, {(1) = .0, (2) = 0.7422014940098305e-2, (3) = 0.15247037874053848e-1, (4) = 0.23520755103823496e-1, (5) = 0.3229677454019059e-1, (6) = 0.4163972613012182e-1, (7) = 0.5163047433585985e-1, (8) = 0.6236471548371652e-1, (9) = 0.7395995268651741e-1, (10) = 0.865635409488798e-1, (11) = .10037386494155838, (12) = .11564679222653715, (13) = .13272336112005387, (14) = .1520729596986236, (15) = .1744030835655522, (16) = .20081719187277686, (17) = .23287978474503113, (18) = .2696382833116828, (19) = .30942370514871853, (20) = .35052688440207136, (21) = .39189960663752765, (22) = .43045939689378565, (23) = .46406520016444347, (24) = .4926053926873776, (25) = .5167851003350923, (26) = .5376216024209438, (27) = .5559231840204688, (28) = .5722936854718627, (29) = .5871581085615549, (30) = .6008206508251621, (31) = .613507361562576, (32) = .6253918899303244, (33) = .6366076943924017, (34) = .6472594108447342, (35) = .6574286185464324, (36) = .667182426192274, (37) = .6765759166669013, (38) = .6856560419917522, (39) = .694464489935754, (40) = .7030331909945008, (41) = .7113893933075516, (42) = .7195587800827726, (43) = .7275642453721933, (44) = .7354262387990891, (45) = .7431631740698084, (46) = .7507921727962193, (47) = .7583272647542358, (48) = .7657828547984458, (49) = .7731719918385156, (50) = .7805069149512255, (51) = .787800042336253, (52) = .7950633754902232, (53) = .802308883829374, (54) = .8095471292208104, (55) = .816788620070316, (56) = .8240445807266021, (57) = .8313260771552303, (58) = .8386433234849713, (59) = .8460074049212739, (60) = .8534299380344416, (61) = .8609213167489855, (62) = .8684912825541682, (63) = .8761497779391109, (64) = .8839064180293265, (65) = .8917702742321805, (66) = .8997477423309259, (67) = .9078436543374889, (68) = .9160613937315915, (69) = .9244024655177719, (70) = .9328635823555885, (71) = .9414402432317543, (72) = .9501252904326655, (73) = .9589057176767743, (74) = .9677706161338872, (75) = .9764838806404585, (76) = .9847529627091501, (77) = .9925779854438055, (78) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(78, 3, {(1, 1) = 1.0, (1, 2) = .0, (1, 3) = 38.386176015354714, (2, 1) = 1.0010381945843554, (2, 2) = .2771893448193658, (2, 3) = 36.30728934760168, (3, 1) = 1.0042963757113128, (3, 2) = .55270571236988, (3, 3) = 34.110832525099134, (4, 1) = 1.0100102471873285, (4, 2) = .8252878570049964, (4, 3) = 31.778055437429416, (5, 1) = 1.0184448193935531, (5, 2) = 1.093253963708355, (5, 3) = 29.28629045181688, (6, 1) = 1.0298983861788318, (6, 2) = 1.3543840804437328, (6, 3) = 26.60756232968718, (7, 1) = 1.044709521932798, (7, 2) = 1.605755570899463, (7, 3) = 23.706383861466097, (8, 1) = 1.0632513045490988, (8, 2) = 1.8432767789658882, (8, 3) = 20.53919210009709, (9, 1) = 1.0859275260569894, (9, 2) = 2.061281786793718, (9, 3) = 17.05104269389171, (10, 1) = 1.1131592778616584, (10, 2) = 2.2518387196230063, (10, 3) = 13.171455221803619, (11, 1) = 1.1453761649071785, (11, 2) = 2.4037357375480184, (11, 3) = 8.805376459470997, (12, 1) = 1.1829232618447163, (12, 2) = 2.5004107831489004, (12, 3) = 3.8275101658570896, (13, 1) = 1.2259023831041698, (13, 2) = 2.5168946136272687, (13, 3) = -1.9312040672586204, (14, 1) = 1.273823202340899, (14, 2) = 2.41442292263844, (14, 3) = -8.703714673093767, (15, 1) = 1.32489881040714, (15, 2) = 2.1299191347716695, (15, 3) = -16.831193254948268, (16, 1) = 1.3741361227552364, (16, 2) = 1.55419875396813, (16, 3) = -26.82152738780503, (17, 1) = 1.4080508419131426, (17, 2) = .49443414154220483, (17, 3) = -39.33552182611952, (18, 1) = 1.3963830671356963, (18, 2) = -1.2180825786825746, (18, 3) = -53.82166494495346, (19, 1) = 1.3012694763249404, (19, 2) = -3.663599829854037, (19, 3) = -68.9378273523391, (20, 1) = 1.0883742078812664, (20, 2) = -6.790682032244631, (20, 3) = -82.81223942735504, (21, 1) = .7332094872654484, (21, 2) = -10.452310970196194, (21, 3) = -93.50953969605982, (22, 1) = .25897959052489655, (22, 2) = -14.180229882914377, (22, 3) = -98.99519214944469, (23, 1) = -.2736962891670773, (23, 2) = -17.521396851088035, (23, 3) = -99.01407158290625, (24, 1) = -.8136490124950762, (24, 2) = -20.296295881657187, (24, 3) = -94.7222241169801, (25, 1) = -1.3314780494820997, (25, 2) = -22.506289855361793, (25, 3) = -87.49079585871775, (26, 1) = -1.8188105138896593, (26, 2) = -24.238671480113556, (26, 3) = -78.31861638361846, (27, 1) = -2.274980464806825, (27, 2) = -25.579703152510636, (27, 3) = -67.83990377359022, (28, 1) = -2.7023359694535296, (28, 2) = -26.59962914680849, (28, 3) = -56.43892166690841, (29, 1) = -3.1035298077817575, (29, 2) = -27.350861692718976, (29, 3) = -44.360678454090205, (30, 1) = -3.480971874211851, (30, 2) = -27.872564247073623, (30, 3) = -31.768407619168595, (31, 1) = -3.8367994850784832, (31, 2) = -28.194497966345814, (31, 3) = -18.772234877979404, (32, 1) = -4.1728963854105405, (32, 2) = -28.339516338097162, (32, 3) = -5.445909446947036, (33, 1) = -4.490809409335731, (33, 2) = -28.32524046551249, (33, 3) = 8.15799212324777, (34, 1) = -4.79180151570542, (34, 2) = -28.165414760706334, (34, 3) = 22.00101835188759, (35, 1) = -5.07684520530807, (35, 2) = -27.87092798584902, (35, 3) = 36.05161315989217, (36, 1) = -5.346755175391735, (36, 2) = -27.45046541461933, (36, 3) = 50.2863172936417, (37, 1) = -5.602182989617742, (37, 2) = -26.91099448460295, (37, 3) = 64.68625227277516, (38, 1) = -5.843673697667125, (38, 2) = -26.258035422800074, (38, 3) = 79.23768210215435, (39, 1) = -6.071704048752482, (39, 2) = -25.495766256210366, (39, 3) = 93.93289981377228, (40, 1) = -6.2865413908219105, (40, 2) = -24.62772878811068, (40, 3) = 108.75956231452248, (41, 1) = -6.488365978798334, (41, 2) = -23.65679257680415, (41, 3) = 123.70610360203507, (42, 1) = -6.677333159112298, (42, 2) = -22.58497056483621, (42, 3) = 138.7655689743947, (43, 1) = -6.853528847273043, (43, 2) = -21.41364299686328, (43, 3) = 153.9322389267795, (44, 1) = -7.016969051653059, (44, 2) = -20.143642894855606, (44, 3) = 169.20103738641026, (45, 1) = -7.167602423383424, (45, 2) = -18.77531208673614, (45, 3) = 184.56726411455978, (46, 1) = -7.305318948190193, (46, 2) = -17.308463785577665, (46, 3) = 200.02720191881534, (47, 1) = -7.429914789924158, (47, 2) = -15.742833500440952, (47, 3) = 215.57366381270867, (48, 1) = -7.5411512337736974, (48, 2) = -14.07748834798679, (48, 3) = 231.2023620438113, (49, 1) = -7.6387175183803055, (49, 2) = -12.311201649894752, (49, 3) = 246.90787049883542, (50, 1) = -7.722236201337924, (50, 2) = -10.442397132353205, (50, 3) = 262.6842145190337, (51, 1) = -7.791267758846605, (51, 2) = -8.468923343360544, (51, 3) = 278.52653824235927, (52, 1) = -7.8452938116098725, (52, 2) = -6.388204943712167, (52, 3) = 294.42939738489036, (53, 1) = -7.883711765855054, (53, 2) = -4.197150420318326, (53, 3) = 310.38713103269964, (54, 1) = -7.905821198580051, (54, 2) = -1.892601667252537, (54, 3) = 326.3903402911911, (55, 1) = -7.910828488449073, (55, 2) = .5290144403384773, (55, 3) = 342.4283606903575, (56, 1) = -7.897834733740855, (56, 2) = 3.071950114910132, (56, 3) = 358.4904700009592, (57, 1) = -7.865820550715685, (57, 2) = 5.740854241512291, (57, 3) = 374.5633917646863, (58, 1) = -7.8136422508457315, (58, 2) = 8.540470599699889, (58, 3) = 390.62915821433086, (59, 1) = -7.740012374279895, (59, 2) = 11.476245256966607, (59, 3) = 406.6682461492493, (60, 1) = -7.643479793744403, (60, 2) = 14.554220207210015, (60, 3) = 422.65803020173627, (61, 1) = -7.522439269923206, (61, 2) = 17.780264481034628, (61, 3) = 438.5681647539286, (62, 1) = -7.375125762150111, (62, 2) = 21.160183253505476, (62, 3) = 454.3610522058657, (63, 1) = -7.1995921572266015, (63, 2) = 24.70000314066167, (63, 3) = 469.9927541150128, (64, 1) = -6.993708734091879, (64, 2) = 28.405653224338753, (64, 3) = 485.41088215213205, (65, 1) = -6.75516438589842, (65, 2) = 32.282737127940095, (65, 3) = 500.55315920962886, (66, 1) = -6.48154379932051, (66, 2) = 36.33528116108361, (66, 3) = 515.3425355069513, (67, 1) = -6.170329168881457, (67, 2) = 40.565998727887454, (67, 3) = 529.6889889597641, (68, 1) = -5.818925492294148, (68, 2) = 44.97610249233706, (68, 3) = 543.4893781093477, (69, 1) = -5.42471537565811, (69, 2) = 49.564815551335016, (69, 3) = 556.626589733943, (70, 1) = -4.9852667690195, (70, 2) = 54.327433776793995, (70, 3) = 568.9657561995768, (71, 1) = -4.498249202540579, (71, 2) = 59.25696421609918, (71, 3) = 580.3613834866482, (72, 1) = -3.9615778090146163, (72, 2) = 64.34308239636641, (72, 3) = 590.6566951289624, (73, 1) = -3.3737288363633975, (73, 2) = 69.56998582501373, (73, 3) = 599.6830958927808, (74, 1) = -2.7333299078047895, (74, 2) = 74.9209285737396, (74, 3) = 607.2722920468946, (75, 1) = -2.0573924158706256, (75, 2) = 80.23895127261001, (75, 3) = 613.1257096022034, (76, 1) = -1.372878019405228, (76, 2) = 85.32648255190304, (76, 3) = 617.1049532901717, (77, 1) = -.6862764603683912, (77, 2) = 90.16517673340196, (77, 3) = 619.3676770101681, (78, 1) = .0, (78, 2) = 94.76568300546467, (78, 3) = 620.0866880268571}, datatype = float[8], order = C_order); YP := Matrix(78, 3, {(1, 1) = .0, (1, 2) = 38.386176015354714, (1, 3) = -280.0, (2, 1) = .2771893448193658, (2, 2) = 36.30728934760168, (2, 3) = -280.2906944836195, (3, 1) = .55270571236988, (3, 2) = 34.110832525099134, (3, 3) = -281.2029851991676, (4, 1) = .8252878570049964, (4, 2) = 31.778055437429416, (4, 3) = -282.802869212452, (5, 1) = 1.093253963708355, (5, 2) = 29.28629045181688, (5, 3) = -285.1645494301949, (6, 1) = 1.3543840804437328, (6, 2) = 26.60756232968718, (6, 3) = -288.3715481300729, (7, 1) = 1.605755570899463, (7, 2) = 23.706383861466097, (7, 3) = -292.5186661411834, (8, 1) = 1.8432767789658882, (8, 2) = 20.53919210009709, (8, 3) = -297.71036527374764, (9, 1) = 2.061281786793718, (9, 2) = 17.05104269389171, (9, 3) = -304.059707295957, (10, 1) = 2.2518387196230063, (10, 2) = 13.171455221803619, (10, 3) = -311.6845978012643, (11, 1) = 2.4037357375480184, (11, 2) = 8.805376459470997, (11, 3) = -320.70532617401, (12, 1) = 2.5004107831489004, (12, 2) = 3.8275101658570896, (12, 3) = -331.21851331652056, (13, 1) = 2.5168946136272687, (13, 2) = -1.9312040672586204, (13, 3) = -343.25266726916755, (14, 1) = 2.41442292263844, (14, 2) = -8.703714673093767, (14, 3) = -356.67049665545176, (15, 1) = 2.1299191347716695, (15, 2) = -16.831193254948268, (15, 3) = -370.9716669139992, (16, 1) = 1.55419875396813, (16, 2) = -26.82152738780503, (16, 3) = -384.7581143714662, (17, 1) = .49443414154220483, (17, 2) = -39.33552182611952, (17, 3) = -394.2542357356799, (18, 1) = -1.2180825786825746, (18, 2) = -53.82166494495346, (18, 3) = -390.98725879799497, (19, 1) = -3.663599829854037, (19, 2) = -68.9378273523391, (19, 3) = -364.3554533709833, (20, 1) = -6.790682032244631, (20, 2) = -82.81223942735504, (20, 3) = -304.7447782067546, (21, 1) = -10.452310970196194, (21, 2) = -93.50953969605982, (21, 3) = -205.29865643432555, (22, 1) = -14.180229882914377, (22, 2) = -98.99519214944469, (22, 3) = -72.51428534697104, (23, 1) = -17.521396851088035, (23, 2) = -99.01407158290625, (23, 3) = 76.63496096678163, (24, 1) = -20.296295881657187, (24, 2) = -94.7222241169801, (24, 3) = 227.8217234986213, (25, 1) = -22.506289855361793, (25, 2) = -87.49079585871775, (25, 3) = 372.81385385498794, (26, 1) = -24.238671480113556, (26, 2) = -78.31861638361846, (26, 3) = 509.2669438891046, (27, 1) = -25.579703152510636, (27, 2) = -67.83990377359022, (27, 3) = 636.994530145911, (28, 1) = -26.59962914680849, (28, 2) = -56.43892166690841, (28, 3) = 756.6540714469883, (29, 1) = -27.350861692718976, (29, 2) = -44.360678454090205, (29, 3) = 868.9883461788921, (30, 1) = -27.872564247073623, (30, 2) = -31.768407619168595, (30, 3) = 974.6721247793183, (31, 1) = -28.194497966345814, (31, 2) = -18.772234877979404, (31, 3) = 1074.3038558219753, (32, 1) = -28.339516338097162, (32, 2) = -5.445909446947036, (32, 3) = 1168.4109879149514, (33, 1) = -28.32524046551249, (33, 2) = 8.15799212324777, (33, 3) = 1257.4266346140048, (34, 1) = -28.165414760706334, (34, 2) = 22.00101835188759, (34, 3) = 1341.7044243975176, (35, 1) = -27.87092798584902, (35, 2) = 36.05161315989217, (35, 3) = 1421.5166574862594, (36, 1) = -27.45046541461933, (36, 2) = 50.2863172936417, (36, 3) = 1497.0914491096858, (37, 1) = -26.91099448460295, (37, 2) = 64.68625227277516, (37, 3) = 1568.611237092968, (38, 1) = -26.258035422800074, (38, 2) = 79.23768210215435, (38, 3) = 1636.228635346795, (39, 1) = -25.495766256210366, (39, 2) = 93.93289981377228, (39, 3) = 1700.0771336506948, (40, 1) = -24.62772878811068, (40, 2) = 108.75956231452248, (40, 3) = 1760.231589430135, (41, 1) = -23.65679257680415, (41, 2) = 123.70610360203507, (41, 3) = 1816.7424740635336, (42, 1) = -22.58497056483621, (42, 2) = 138.7655689743947, (42, 3) = 1869.6532845514434, (43, 1) = -21.41364299686328, (43, 2) = 153.9322389267795, (43, 3) = 1918.988077236452, (44, 1) = -20.143642894855606, (44, 2) = 169.20103738641026, (44, 3) = 1964.7513344628567, (45, 1) = -18.77531208673614, (45, 2) = 184.56726411455978, (45, 3) = 2006.9286785473587, (46, 1) = -17.308463785577665, (46, 2) = 200.02720191881534, (46, 3) = 2045.489305493254, (47, 1) = -15.742833500440952, (47, 2) = 215.57366381270867, (47, 3) = 2080.376141178764, (48, 1) = -14.07748834798679, (48, 2) = 231.2023620438113, (48, 3) = 2111.5223454566353, (49, 1) = -12.311201649894752, (49, 2) = 246.90787049883542, (49, 3) = 2138.8409051464855, (50, 1) = -10.442397132353205, (50, 2) = 262.6842145190337, (50, 3) = 2162.226136374619, (51, 1) = -8.468923343360544, (51, 2) = 278.52653824235927, (51, 3) = 2181.5549724770494, (52, 1) = -6.388204943712167, (52, 2) = 294.42939738489036, (52, 3) = 2196.682267250764, (53, 1) = -4.197150420318326, (53, 2) = 310.38713103269964, (53, 3) = 2207.439294439415, (54, 1) = -1.892601667252537, (54, 2) = 326.3903402911911, (54, 3) = 2213.629935602414, (55, 1) = .5290144403384773, (55, 2) = 342.4283606903575, (55, 3) = 2215.03197676574, (56, 1) = 3.071950114910132, (56, 2) = 358.4904700009592, (56, 3) = 2211.3937254474395, (57, 1) = 5.740854241512291, (57, 2) = 374.5633917646863, (57, 3) = 2202.429754200392, (58, 1) = 8.540470599699889, (58, 2) = 390.62915821433086, (58, 3) = 2187.8198302368046, (59, 1) = 11.476245256966607, (59, 2) = 406.6682461492493, (59, 3) = 2167.2034647983705, (60, 1) = 14.554220207210015, (60, 2) = 422.65803020173627, (60, 3) = 2140.174342248433, (61, 1) = 17.780264481034628, (61, 2) = 438.5681647539286, (61, 3) = 2106.282995578498, (62, 1) = 21.160183253505476, (62, 2) = 454.3610522058657, (62, 3) = 2065.035213402031, (63, 1) = 24.70000314066167, (63, 2) = 469.9927541150128, (63, 3) = 2015.8858040234484, (64, 1) = 28.405653224338753, (64, 2) = 485.41088215213205, (64, 3) = 1958.238445545726, (65, 1) = 32.282737127940095, (65, 2) = 500.55315920962886, (65, 3) = 1891.4460280515575, (66, 1) = 36.33528116108361, (66, 2) = 515.3425355069513, (66, 3) = 1814.8322638097427, (67, 1) = 40.565998727887454, (67, 2) = 529.6889889597641, (67, 3) = 1727.692167286808, (68, 1) = 44.97610249233706, (68, 2) = 543.4893781093477, (68, 3) = 1629.2991378423615, (69, 1) = 49.564815551335016, (69, 2) = 556.626589733943, (69, 3) = 1518.9203051842708, (70, 1) = 54.327433776793995, (70, 2) = 568.9657561995768, (70, 3) = 1395.87469532546, (71, 1) = 59.25696421609918, (71, 2) = 580.3613834866482, (71, 3) = 1259.5097767113623, (72, 1) = 64.34308239636641, (72, 2) = 590.6566951289624, (72, 3) = 1109.2417865240925, (73, 1) = 69.56998582501373, (73, 2) = 599.6830958927808, (73, 3) = 944.6440741817513, (74, 1) = 74.9209285737396, (74, 2) = 607.2722920468946, (74, 3) = 765.332374185341, (75, 1) = 80.23895127261001, (75, 2) = 613.1257096022034, (75, 3) = 576.0698764437751, (76, 1) = 85.32648255190304, (76, 2) = 617.1049532901717, (76, 3) = 384.4058454334638, (77, 1) = 90.16517673340196, (77, 2) = 619.3676770101681, (77, 3) = 192.15740890314953, (78, 1) = 94.76568300546467, (78, 2) = 620.0866880268571, (78, 3) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(78, {(1) = .0, (2) = 0.7422014940098305e-2, (3) = 0.15247037874053848e-1, (4) = 0.23520755103823496e-1, (5) = 0.3229677454019059e-1, (6) = 0.4163972613012182e-1, (7) = 0.5163047433585985e-1, (8) = 0.6236471548371652e-1, (9) = 0.7395995268651741e-1, (10) = 0.865635409488798e-1, (11) = .10037386494155838, (12) = .11564679222653715, (13) = .13272336112005387, (14) = .1520729596986236, (15) = .1744030835655522, (16) = .20081719187277686, (17) = .23287978474503113, (18) = .2696382833116828, (19) = .30942370514871853, (20) = .35052688440207136, (21) = .39189960663752765, (22) = .43045939689378565, (23) = .46406520016444347, (24) = .4926053926873776, (25) = .5167851003350923, (26) = .5376216024209438, (27) = .5559231840204688, (28) = .5722936854718627, (29) = .5871581085615549, (30) = .6008206508251621, (31) = .613507361562576, (32) = .6253918899303244, (33) = .6366076943924017, (34) = .6472594108447342, (35) = .6574286185464324, (36) = .667182426192274, (37) = .6765759166669013, (38) = .6856560419917522, (39) = .694464489935754, (40) = .7030331909945008, (41) = .7113893933075516, (42) = .7195587800827726, (43) = .7275642453721933, (44) = .7354262387990891, (45) = .7431631740698084, (46) = .7507921727962193, (47) = .7583272647542358, (48) = .7657828547984458, (49) = .7731719918385156, (50) = .7805069149512255, (51) = .787800042336253, (52) = .7950633754902232, (53) = .802308883829374, (54) = .8095471292208104, (55) = .816788620070316, (56) = .8240445807266021, (57) = .8313260771552303, (58) = .8386433234849713, (59) = .8460074049212739, (60) = .8534299380344416, (61) = .8609213167489855, (62) = .8684912825541682, (63) = .8761497779391109, (64) = .8839064180293265, (65) = .8917702742321805, (66) = .8997477423309259, (67) = .9078436543374889, (68) = .9160613937315915, (69) = .9244024655177719, (70) = .9328635823555885, (71) = .9414402432317543, (72) = .9501252904326655, (73) = .9589057176767743, (74) = .9677706161338872, (75) = .9764838806404585, (76) = .9847529627091501, (77) = .9925779854438055, (78) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(78, 3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.21374101479472934e-9, (2, 1) = 0.6617043163614648e-14, (2, 2) = 0.15815604852839844e-11, (2, 3) = 0.21311837323331495e-9, (3, 1) = 0.25343727453304818e-13, (3, 2) = 0.3236859819203722e-11, (3, 3) = 0.21227882088379557e-9, (4, 1) = 0.608178113423069e-13, (4, 2) = 0.4970351848975599e-11, (4, 3) = 0.21125160962194817e-9, (5, 1) = 0.11336987512724689e-12, (5, 2) = 0.6786995734632931e-11, (5, 3) = 0.20993325149852807e-9, (6, 1) = 0.1850029120583241e-12, (6, 2) = 0.8693080167652104e-11, (6, 3) = 0.20819378569749641e-9, (7, 1) = 0.28253966655178614e-12, (7, 2) = 0.10684057021809762e-10, (7, 3) = 0.2058724893755894e-9, (8, 1) = 0.4083861282846956e-12, (8, 2) = 0.12759826289631252e-10, (8, 3) = 0.20278447790781166e-9, (9, 1) = 0.5665515205281028e-12, (9, 2) = 0.14908481409452215e-10, (9, 3) = 0.19858389734160558e-9, (10, 1) = 0.765632284881089e-12, (10, 2) = 0.1710637073672902e-10, (10, 3) = 0.19283723931777497e-9, (11, 1) = 0.10095317904433423e-11, (11, 2) = 0.19293637254403415e-10, (11, 3) = 0.18490648517398407e-9, (12, 1) = 0.13018676569087828e-11, (12, 2) = 0.21365714310981305e-10, (12, 3) = 0.17382791885584998e-9, (13, 1) = 0.16425961487017066e-11, (13, 2) = 0.23112487818588823e-10, (13, 3) = 0.15809028547142478e-9, (14, 1) = 0.20174042817671427e-11, (14, 2) = 0.24066937733876484e-10, (14, 3) = 0.13530521149880537e-9, (15, 1) = 0.23588523733158e-11, (15, 2) = 0.23231216316050875e-10, (15, 3) = 0.10156224121561319e-9, (16, 1) = 0.2393011093467379e-11, (16, 2) = 0.18149054144044492e-10, (16, 3) = 0.51706195251559185e-10, (17, 1) = 0.9084877415827434e-12, (17, 2) = 0.314096305880786e-11, (17, 3) = -0.32841258405195813e-11, (18, 1) = -0.45491514609546456e-11, (18, 2) = -0.20025596832171e-10, (18, 3) = 0.51921619668659705e-10, (19, 1) = -0.146658137108361e-10, (19, 2) = -0.2416251850244477e-10, (19, 3) = 0.43252805140703903e-9, (20, 1) = -0.24237492293530955e-10, (20, 2) = 0.3599372556048811e-10, (20, 3) = 0.1223259174809578e-8, (21, 1) = -0.24535443635530228e-10, (21, 2) = 0.1903555252463994e-9, (21, 3) = 0.2245871545259929e-8, (22, 1) = -0.11739792007986929e-10, (22, 2) = 0.37030660671350455e-9, (22, 3) = 0.28847498354569104e-8, (23, 1) = 0.6161988712155101e-11, (23, 2) = 0.5116509035009505e-9, (23, 3) = 0.30511215548502548e-8, (24, 1) = 0.24143172302904838e-10, (24, 2) = 0.6156361580552844e-9, (24, 3) = 0.2967037607906237e-8, (25, 1) = 0.4099280962473993e-10, (25, 2) = 0.6934931258243783e-9, (25, 3) = 0.27586166265908647e-8, (26, 1) = 0.5667287481842802e-10, (26, 2) = 0.7529934557834415e-9, (26, 3) = 0.24793432501917947e-8, (27, 1) = 0.7128596741818145e-10, (27, 2) = 0.7986347832025048e-9, (27, 3) = 0.21545638229423175e-8, (28, 1) = 0.8495334319877626e-10, (28, 2) = 0.8332910094275046e-9, (28, 3) = 0.17982758736276522e-8, (29, 1) = 0.9776913816729528e-10, (29, 2) = 0.8589525126881634e-9, (29, 3) = 0.14187573949711434e-8, (30, 1) = 0.10982483919576233e-9, (30, 2) = 0.876990864247837e-9, (30, 3) = 0.10219138652783984e-8, (31, 1) = 0.12119861873621406e-9, (31, 2) = 0.8884384414068472e-9, (31, 3) = 0.6113196945671567e-9, (32, 1) = 0.13194536181092119e-9, (32, 2) = 0.8940935343871139e-9, (32, 3) = 0.18958612224147546e-9, (33, 1) = 0.1421034511267267e-9, (33, 2) = 0.8946023759386806e-9, (33, 3) = -0.24151798358672923e-9, (34, 1) = 0.15173459103634197e-9, (34, 2) = 0.890292600785599e-9, (34, 3) = -0.680621711939455e-9, (35, 1) = 0.16085584900871135e-9, (35, 2) = 0.8816923848879957e-9, (35, 3) = -0.112675278788525e-8, (36, 1) = 0.1694927906902929e-9, (36, 2) = 0.8689606740007918e-9, (36, 3) = -0.15790797703029465e-8, (37, 1) = 0.17766688271008688e-9, (37, 2) = 0.8524194555746267e-9, (37, 3) = -0.2037000474455717e-8, (38, 1) = 0.1854153557046071e-9, (38, 2) = 0.8321878405243527e-9, (38, 3) = -0.24999561526619108e-8, (39, 1) = 0.19271741055197827e-9, (39, 2) = 0.8084450298695515e-9, (39, 3) = -0.2967596855008954e-8, (40, 1) = 0.19960793855467597e-9, (40, 2) = 0.7812801551816712e-9, (40, 3) = -0.3439694098295936e-8, (41, 1) = 0.20608273385672261e-9, (41, 2) = 0.7508009529277227e-9, (41, 3) = -0.3915938494413602e-8, (42, 1) = 0.21214411615546314e-9, (42, 2) = 0.7170679029918045e-9, (42, 3) = -0.4395917295441028e-8, (43, 1) = 0.2178162740801877e-9, (43, 2) = 0.6801782610494025e-9, (43, 3) = -0.4879454958084554e-8, (44, 1) = 0.22307505792290622e-9, (44, 2) = 0.6400707246037973e-9, (44, 3) = -0.5366363171426886e-8, (45, 1) = 0.22792663267245126e-9, (45, 2) = 0.596788468093401e-9, (45, 3) = -0.5856735844943015e-8, (46, 1) = 0.23235772030479177e-9, (46, 2) = 0.5503712224233628e-9, (46, 3) = -0.6350243465827074e-8, (47, 1) = 0.23638476869867436e-9, (47, 2) = 0.5007838964884985e-9, (47, 3) = -0.6846352628530876e-8, (48, 1) = 0.2399826547596872e-9, (48, 2) = 0.44797493712876514e-9, (48, 3) = -0.7345909288023861e-8, (49, 1) = 0.24314767746970955e-9, (49, 2) = 0.3919441530467946e-9, (49, 3) = -0.7847826952926815e-8, (50, 1) = 0.2458633553763264e-9, (50, 2) = 0.3325930338144637e-9, (50, 3) = -0.8351962221384333e-8, (51, 1) = 0.2481176496667275e-9, (51, 2) = 0.2698850071047016e-9, (51, 3) = -0.8858604164736875e-8, (52, 1) = 0.24989864164578096e-9, (52, 2) = 0.2037421854623591e-9, (52, 3) = -0.9367169852109535e-8, (53, 1) = 0.2511868319065834e-9, (53, 2) = 0.13403592712019737e-9, (53, 3) = -0.9877961190186058e-8, (54, 1) = 0.25194722806050053e-9, (54, 2) = 0.6068854794188144e-10, (54, 3) = -0.10389999059726765e-7, (55, 1) = 0.25216103000641414e-9, (55, 2) = -0.16426412087914983e-10, (55, 3) = -0.10904142671968567e-7, (56, 1) = 0.25181047788846003e-9, (56, 2) = -0.9744592357883526e-10, (56, 3) = -0.11418952784898342e-7, (57, 1) = 0.25084708208867255e-9, (57, 2) = -0.18252768360712056e-9, (57, 3) = -0.1193350480225618e-7, (58, 1) = 0.24924216152550573e-9, (58, 2) = -0.2718278165342341e-9, (58, 3) = -0.12449299125456e-7, (59, 1) = 0.2469647322823809e-9, (59, 2) = -0.3654926237200361e-9, (59, 3) = -0.12964216944950137e-7, (60, 1) = 0.2439385432872567e-9, (60, 2) = -0.46374566629486124e-9, (60, 3) = -0.13477191099854094e-7, (61, 1) = 0.2401392779850783e-9, (61, 2) = -0.5667827937551021e-9, (61, 3) = -0.13989002634087752e-7, (62, 1) = 0.2354974830501514e-9, (62, 2) = -0.6748203135319071e-9, (62, 3) = -0.144966926321542e-7, (63, 1) = 0.2299556698858384e-9, (63, 2) = -0.7879969316169068e-9, (63, 3) = -0.1499985558975845e-7, (64, 1) = 0.22344335042145828e-9, (64, 2) = -0.906569122267802e-9, (64, 3) = -0.15496633446164436e-7, (65, 1) = 0.21588699161848774e-9, (65, 2) = -0.1030706052504292e-8, (65, 3) = -0.1598507069938262e-7, (66, 1) = 0.2072001570759953e-9, (66, 2) = -0.11604415138593787e-8, (66, 3) = -0.16462981859028595e-7, (67, 1) = 0.1973239834078538e-9, (67, 2) = -0.12960869498348117e-8, (67, 3) = -0.16926252731900467e-7, (68, 1) = 0.1861481274670076e-9, (68, 2) = -0.14375072189369759e-8, (68, 3) = -0.17373690408853017e-7, (69, 1) = 0.17360182955573136e-9, (69, 2) = -0.15847891575527738e-8, (69, 3) = -0.17799737782051196e-7, (70, 1) = 0.1595911628943475e-9, (70, 2) = -0.17377594077856065e-8, (70, 3) = -0.18200148769816036e-7, (71, 1) = 0.14405378999774726e-9, (71, 2) = -0.1896185117484409e-8, (71, 3) = -0.1857211954096187e-7, (72, 1) = 0.12690950590380987e-9, (72, 2) = -0.20597762848508742e-8, (72, 3) = -0.1890888800221457e-7, (73, 1) = 0.10811586884916081e-9, (73, 2) = -0.2228107102170434e-8, (73, 3) = -0.1920524894652217e-7, (74, 1) = 0.8762389472881187e-10, (74, 2) = -0.2400509994779305e-8, (74, 3) = -0.19456175522202756e-7, (75, 1) = 0.6597647839692229e-10, (75, 2) = -0.2571949957407786e-8, (75, 3) = -0.19650196577522936e-7, (76, 1) = 0.4403563168815861e-10, (76, 2) = -0.27358008655389504e-8, (76, 3) = -0.19784033238859742e-7, (77, 1) = 0.2201801640944132e-10, (77, 2) = -0.28918571075789674e-8, (77, 3) = -0.1986208486392248e-7, (78, 1) = .0, (78, 2) = -0.3040105066991136e-8, (78, 3) = -0.19890096842081592e-7}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[78] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.9890096842081592e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [3, 78, [f(x), diff(f(x), x), diff(diff(f(x), x), x)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[78] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[78] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(3, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(78, 3, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(3, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(78, 3, X, Y, outpoint, yout, L, V) end if; [x = outpoint, seq('[f(x), diff(f(x), x), diff(diff(f(x), x), x)]'[i] = yout[i], i = 1 .. 3)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[78] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.9890096842081592e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [3, 78, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[78] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[78] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(78, 3, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(3, {(1) = 0., (2) = 0., (3) = 0.}); `dsolve/numeric/hermite`(78, 3, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 3)] end proc, (2) = Array(0..0, {}), (3) = [x, f(x), diff(f(x), x), diff(diff(f(x), x), x)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [x = res[1], seq('[f(x), diff(f(x), x), diff(diff(f(x), x), x)]'[i] = res[i+1], i = 1 .. 3)] catch: error  end try end proc

(4)

``


 

Download Untitled.mw

Hi

I would like to use  the Liebniz notation that someone from the technical support posted here
Writing Derivatives at a Point Using Leibniz Notation
to display a formula that is not just a partial derivative but a more complex expression invoking partial derivatives. 
Typically an expression like this one:

2*(Diff(f(mu__1, mu__2), mu__1))^2*lambda__1^2-(Diff(f(mu__1, mu__2), mu__1))^2*mu__1^2+2*(Diff(f(mu__1, mu__2), mu__2))^2*lambda__2^2-(Diff(f(mu__1, mu__2), mu__2))^2*mu__2^2+2*(Diff(f(mu__1, mu__2), mu__1))*(Diff(f(mu__1, mu__2), mu__2))*lambda__1*lambda__2-2*(Diff(f(mu__1, mu__2), mu__1))*mu__1*(Diff(f(mu__1, mu__2), mu__2))*mu__2

Could anyone help me to do this?
Thanks in advance

(PS: I'm still using Maple 2015.2)

Can I get to know how to interface maple with gnu plot. Thank you.

Bonjour,

Comment écrire les composantes d'un vecteur contravariant avec des indices numériques ? Ce vecteur n'est pas un spacetimevector.

Par exemple : <x^1, x^2,x^3> avec cette écriture maple interprète ces indices comme des nombres et non comme des symboles

Merci pour vore retour

I do a calculation o a simple integral

 

      int(cosh(cos(2*t)), t = 0 .. 2*Pi)

 

and get the answer 0 (zero), which I know is incorrect. The cosh function of a real argument is always positive.

 

If I represent the cosh function as a sum of two exponentials

(1/2)*(int(cosh(cos(2*t)), t = 0 .. 2*Pi) + int(cosh(-cos(2*t)), t = 0 .. 2*Pi))

 

I get    

2*Pi*BesselI(0, 1)

which looks much better.

 

What's the matter? Why Maple yields two different results? Victor.

 

 

 

I'm trying to create an iterator function

Iter := proc(ff, n)    
    local i,f;
    if n = 0 then return (x->x); end;
    f := x->ff:
    f := apply(unapply(ff))(x);
    for i from 1 to n-1 do
        f := ff(f);
    end;    
    return unapply(f,x);
end:

 

This seems to work except that it converts the independent variable to x, which can cause problems.

 

That is, if I pass something like n->sin(n) then it will output something like x->sin(sin(x))...

 

Of course, I do explicitly use x but it is because I don't know how to get the input's independent variable.

 

Ideally I'd like to be able to work on multiple arguments and iterate over the first, by default.

 

e.g., f#2(x,y,z) = f(f(x,y,z),y,z)

 

Ultimately the proc above doesn't work well as I want to be able to use it in all contexts(I could pass the value to Iter but I'd rather use function notation.

 

This must be so complicated process to describe the exact mechanism in human or animals ... and there are many reserchs on web for this subject ! Not expected Large answer !

By this way i am just curious to know by support of signal processing methods available in maple we can model a very basic vibrator as larynx and variable duct (what kind of filter we can call ?) or cavity that play the role of tongue or lips for changing of main stream to made various phonemes or frequencies

Here is a movie that show the section of human vocal system :

Anatomy

is it possible to get all the iteration values for a minimization problem

Hey,

I want to animate action of linear transformation on multiple polygons, in the end, it should be a grid of multiple parallel lines that will get morphed. The transformation is defined by a matrix A.

So far I got this code to work:

with(plots):
with(plottools):
setoptions(style=patch,view=[-5..5,-5..5], scaling=constrained):
basis_i:=polygon([[0,0],[1,0]],color=red):

N:=20:
F:=(x,y) -> (1-k/N)*<x,y> + k/N*(A.<x,y>):
L := transform((x,y)->convert(F(x,y),list)):
A:=<<2,1>|<-1,1>>;
                          

frames:=seq(L(basis_i),k=0..N):

display(frames, insequence=true);
 

It animates the basis vector nicely, but I can't seem to figure out, how to animate multiple lines, multiple polygons.

Anyone knows how to do this?

Any help will be much appreciated.

 

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