Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi, 

I was able to determine a cubic spline fit, F(v), to x1 and y1. Now I have vector x2 which I would like to use F(v) to calculate y2 as another Vector[row]. I am having trouble accomplishing this task. Any help is greatly appreciated. Thanks.
 

restart

 x1 := Vector[row]([0.8e-1, .28, .48, .68, .88, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2]);

 y1 := Vector[row]([-10.081, -10.054, -10.018, -9.982, -9.939, -9.911, -9.861, -9.8, -9.734, -9.659, -9.601, -9.509, -9.4, -9.293, -9.183, -9.057, -8.931, -8.806, -8.676, -8.542, -8.405, -8.265]);

 

m := ArrayTools[Dimensions](x1);

maxx := rhs(m[1]);

 

F := proc (v) options operator, arrow; CurveFitting:-Spline(x1, y1, v, degree = 3) end proc;

 

x2 := Vector[row]([seq(log10(2*10^x1[k]), k = 1 .. maxx)])

 

y2:=?

 

Pts1 := plot(x1, y1, style = point, symbol = diamond, gridlines = true, color = red);

plt_sp := plot(F(v), v = x1[1] .. x1[maxx], color = blue);

plots:-display(Pts1, plt_sp)``

"# How to calculate Vector y2 using spline fit F with x2"? "    x1:=Vector[row]([0.08,0.28,0.48,0.68,0.88,1,1.2,1.4,1.6,1.8,2,2.2,2.4,2.6,2.8,3,3.2,3.4,3.6,3.8,4,4.2]):    y1:=Vector[row]([-10.081,-10.054,-10.018,-9.982,-9.939,-9.911,-9.861,-9.8,-9.734,-9.659,-9.601,-9.509,-9.4,-9.293,-9.183,-9.057,-8.931,-8.806,-8.676,-8.542,-8.405,-8.265]):    m:=ArrayTools[Dimensions](x1):  maxx:=rhs(m[1]):      F:=v->CurveFitting:-Spline(x1,y1, v,degree=3):    x2:=Vector[row]([seq(log10(2*10^(x1[k])),k=1..maxx)]):                   #` PLOT RESULTS`   Pts1:=plot(x1,y1,style=point,symbol = diamond, gridlines=true, color = red):       plt_sp:=plot(F(v),v=x1[1]..x1[maxx],color = blue):     plots:-display(Pts1,plt_sp);     "

 

``

``


 

Download splfit.mw

I have a similar matrix.

Build through matrixplot, not exactly what I need to get. I need a way to plot without zero values on the graph.
 

how to compute example 1 of linear schrodinger equation?

[Edit: uploaded .pdf file of M.M. Mousa and S.F. Ragab, Z. Naturforsch. 63a, 140 – 144 (2008) removed for copyright reasons]

I am trying to get the function of the curve in this picture. But, I don't know how to start. How can I get function of the graph in this picture?
I guess f(x) = (x + 1) (x - 1) (x - 3), if -1 <= x <=3.5 and f(x) = -(x + 1) (x + 2.5), if -2.5 <=x <=-1.

In Maple 2018, I was playing around with some sums of infinite series, and I came across a result that made me wonder if Maple was perhaps using some other definition or understanding of the sum of a series in its calculation. Take a look at the screenshot linked below:

https://ibb.co/hMdkQHn

That first series is most certainly divergent since the limit as n approaches infinity of n^2/(n+1) is not equal to 0. And just to confirm my own sanity, I even checked some of the partial sums of the series, which sure enough are diverging. And yet for the infinite sum, Maple is giving this finite result.

I even checked a more familiar alternating series, the alternating harmonic series, which Maple does correctly calculate to be ln(2).

What am I missing here? Is Maple using a different definition for the sum of the series than the limit of the partial sums as n approaches infinity? Or is there a mistake with how I've written something that I'm not noticing?

Dear Users,

I am solving a large system of linear equation with the Hybrid solver. Up to 2400 equations, I get a solution, but if I change the number of equations to 3000, I don't get any solution in fact solution entry reads Float(undefined). All the entries in matrix and vector are floating point decimal with 32 digits of accuracy. Any idea how to overcome this?

 

thanks.

 

i attach my file

maple_pita_he.mw

Suppose I have

solution:=fsolve(f(x,y)=0,x,y)

this returns 

x=<result>, y=<result>

I want to continue the computation in my worksheet by assigning values to x and y without copying the numerical values by hand.

x:=<result>

y:=<result>

Then I want to make more computations with x and y.

It is too time consuming to copy the numbers by hand each time I run the worksheet

Larry

 

 

And y

the principle is so easy as the method for demonstration of area of a disk by dissecting it to tiny sectors ...

and i just reversed the topic and i formed a shape by rearranging the tiny triangles that made the area of point and straight line as you can see in graph or interactively download the maple 18 worksheet that i attached ...

 

BUT my problem is that i can't yet underastand what is the formula or equation of this curve ?

the only obvious prperties of the curve is its ARC LENGTH that must be the half of straight line !
SO I NEED THE HELP OF PROFESSIONALs ?

also the programming and impelmenting of this subject in maple language was so hard for me !!!

I hope mapleprimes employee or developers offer more efficent and intelgent algorithm for using Maple in such cases ...

unknown_curve_by_shekofte.mw
 

ALGORITHM

hlf := proc (x, y, z, i) options operator, arrow; geometry[point](ds1, [x[1], x[2]]), geometry[point](ds2, [y[1], y[2]]), geometry[point](ds3, [z[1], z[2]]), geometry[dsegment](tt1, [ds2, ds3]), geometry[translation](dss, ds3, tt1), geometry[PerpenBisector](pb, ds3, ds1), geometry[reflection](ds4, dss, pb), assign(('crv[i, 1]', 'crv[i, 2]') = (geometry[HorizontalCoord](ds4), geometry[VerticalCoord](ds4))) end proc

proc (x, y, z, i) options operator, arrow; geometry[point](ds1, [x[1], x[2]]), geometry[point](ds2, [y[1], y[2]]), geometry[point](ds3, [z[1], z[2]]), geometry[dsegment](tt1, [ds2, ds3]), geometry[translation](dss, ds3, tt1), geometry[PerpenBisector](pb, ds3, ds1), geometry[reflection](ds4, dss, pb), assign(('crv[i, 1]', 'crv[i, 2]') = (geometry[HorizontalCoord](ds4), geometry[VerticalCoord](ds4))) end proc

(1)

MATRIX WITH DESIRE SIZE AND THREE INITIAL VALUES

crv := Matrix(400, 2, {(2, 1) = HFloat(1.0), (2, 2) = HFloat(0.0), (3, 1) = HFloat(1.0), (3, 2) = HFloat(0.1)}, datatype = float[8], storage = rectangular, order = Fortran_order, shape = [])

crv := Matrix(400, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = 1.0, (2, 2) = .0, (3, 1) = 1.0, (3, 2) = .1, (4, 1) = -0.1980198019801982e-1, (4, 2) = 0.9801980198019805e-1, (5, 1) = 1.0194211728865195, (5, 2) = .19809596344249814, (6, 1) = -0.57585751517988726e-1, (6, 2) = .19060698589266134, (7, 1) = 1.0559137411806545, (7, 2) = .2911996285652951, (8, 1) = -.1101731426397452, (8, 2) = .2756632396016475, (9, 1) = 1.1062163692195215, (9, 2) = .37762674012401487, (10, 1) = -.17416214658765472, (10, 2) = .3525098880240373, (11, 1) = 1.1671423424235312, (11, 2) = .4569238131415244, (12, 1) = -.2466255700808896, (12, 2) = .4214232557812443, (13, 1) = 1.2360557101807381, (13, 2) = .5293872366347594, (14, 1) = -.3253094338429394, (14, 2) = .48313913366915184, (15, 1) = 1.3109487458308529, (15, 2) = .595652108256989, (16, 1) = -.408567746414083, (16, 2) = .5385291452940439, (17, 1) = 1.3903473987423378, (17, 2) = .656445643405403, (18, 1) = -.495222799209344, (18, 2) = .5884380806167939, (19, 1) = 1.4731818019427334, (19, 2) = .7124676180799383, (20, 1) = -.5844340423821378, (20, 2) = .6336194273382524, (21, 1) = 1.558673790835259, (21, 2) = .7643436225058795, (22, 1) = -.6755973629522178, (22, 2) = .6747199015768401, (23, 1) = 1.6462521625681776, (23, 2) = .8126139944187906, (24, 1) = -.768273483034192, (24, 2) = .7122850019567344, (25, 1) = 1.7354923582507662, (25, 2) = .8577381284773329, (26, 1) = -.8621385794010603, (26, 2) = .7467718644414333, (27, 1) = 1.8260744290544424, (27, 2) = .9001042523136931, (28, 1) = -.9569505091805229, (28, 2) = .7785633408383272, (29, 1) = 1.9177538611154679, (29, 2) = .9400402227785242, (30, 1) = -1.0525256440627835, (30, 2) = .8079809136858231, (31, 1) = 2.0103412288236853, (31, 2) = .97782354371334, (32, 1) = -1.1487228445027227, (32, 2) = .8352957196986452, (33, 1) = 2.103687872783331, (33, 2) = 1.0136900191670435, (34, 1) = -1.2454322462280305, (34, 2) = .860737646078795, (35, 1) = 2.197675702033759, (35, 2) = 1.0478409774668087, (36, 1) = -1.3425673140215706, (36, 2) = .8845027171862903, (37, 1) = 2.2922098421158257, (37, 2) = 1.0804492027933132, (38, 1) = -1.4400591369052527, (38, 2) = .906759052707141, (39, 1) = 2.387213267433803, (39, 2) = 1.1116637695506997, (40, 1) = -1.5378522792667093, (40, 2) = .9276516664036538, (41, 1) = 2.4826228333296245, (41, 2) = 1.1416139738166264, (42, 1) = -1.635901725574782, (42, 2) = .9473063370618, (43, 1) = 2.578386307440582, (43, 2) = 1.1704125332632354, (44, 1) = -1.734170603348866, (44, 2) = .9658327414895891, (45, 1) = 2.6744601230711718, (45, 2) = 1.198158198693699, (46, 1) = -1.8326284667701598, (46, 2) = .9833270014200253, (47, 1) = 2.770807660389581, (47, 2) = 1.2249378934768282, (48, 1) = -1.9312499889549857, (48, 2) = .9998737643042781, (49, 1) = 2.867397917870683, (49, 2) = 1.2508284739982083, (50, 1) = -2.030013955484974, (50, 2) = 1.0155479122958924, (51, 1) = 2.9642044754014845, (51, 2) = 1.2758981851859215, (52, 1) = -2.1289024824111373, (52, 2) = 1.0304159734463314, (53, 1) = 3.061204677621959, (53, 2) = 1.3002078698648063, (54, 1) = -2.227900403227824, (54, 2) = 1.0445372932845332, (55, 1) = 3.158378985196276, (55, 2) = 1.3238119785633315, (56, 1) = -2.3269947842657284, (56, 2) = 1.0579650126260454, (57, 1) = 3.2557104553194773, (57, 2) = 1.3467594168442423, (58, 1) = -2.4261745385759257, (58, 2) = 1.0707468878784756, (59, 1) = 3.3531843225532487, (59, 2) = 1.3690942597246591, (60, 1) = -2.525430116002866, (60, 2) = 1.0829259826578275, (61, 1) = 3.450787658195739, (61, 2) = 1.390856356853824, (62, 1) = -2.624753252674097, (62, 2) = 1.0945412537174226, (63, 1) = 3.548509091606773, (63, 2) = 1.4120818474745995, (64, 1) = -2.7241367671830483, (64, 2) = 1.1056280496409003, (65, 1) = 3.64633858077174, (65, 2) = 1.43280360053078, (66, 1) = -2.823574393732581, (66, 2) = 1.1162185371743174, (67, 1) = 3.7442672222719096, (67, 2) = 1.4530515923801233, (68, 1) = -2.923060644736592, (68, 2) = 1.1263420672486881, (69, 1) = 3.8422870930015427, (69, 2) = 1.4728532322653893, (70, 1) = -3.0225906970527, (70, 2) = 1.136025490504571, (71, 1) = 3.9403911176217967, (71, 2) = 1.4922336438530825, (72, 1) = -3.1221602972884583, (72, 2) = 1.145293430345279, (73, 1) = 4.038572957003524, (73, 2) = 1.5112159096720095, (74, 1) = -3.2217656825924834, (74, 2) = 1.1541685201158893, (75, 1) = 4.1368269138837945, (75, 2) = 1.5298212840936567, (76, 1) = -3.3214035140867813, (76, 2) = 1.1626716098551355, (77, 1) = 4.235147852715831, (77, 2) = 1.548069379533639, (78, 1) = -3.421070820673153, (78, 2) = 1.1708219471376027, (79, 1) = 4.333531131281794, (79, 2) = 1.5659783297712109, (80, 1) = -3.520764951395804, (80, 2) = 1.1786373357686766, (81, 1) = 4.431972542101462, (81, 2) = 1.5835649336455564, (82, 1) = -3.620483534894472, (82, 2) = 1.186134275478924, (83, 1) = 4.530468262036541, (83, 2) = 1.600844781864521, (84, 1) = -3.720224444760148, (84, 2) = 1.1933280852600467, (85, 1) = 4.629014808782039, (85, 2) = 1.617832369231097, (86, 1) = -3.8199857698257804, (86, 2) = 1.2002330125695062, (87, 1) = 4.7276090031694675, (87, 2) = 1.6345411942374746, (88, 1) = -3.919765788600015, (88, 2) = 1.206862330288027, (89, 1) = 4.826247936394211, (89, 2) = 1.6509838476816228, (90, 1) = -4.0195629471928465, (90, 2) = 1.213228423029804, (91, 1) = 4.924928941431071, (91, 2) = 1.6671720917159443, (92, 1) = -4.119375840195512, (92, 2) = 1.2193428641684605, (93, 1) = 5.0236495680250846, (93, 2) = 1.6831169305324716, (94, 1) = -4.219203194068761, (94, 2) = 1.2252164847439373, (95, 1) = 5.122407560745161, (95, 2) = 1.698828673717137, (96, 1) = -4.3190438526683055, (96, 2) = 1.230859435249552, (97, 1) = 5.221200839670427, (97, 2) = 1.714316993160968, (98, 1) = -4.418896764597212, (98, 2) = 1.2362812411587893, (99, 1) = 5.320027483346861, (99, 2) = 1.7295909742939517, (100, 1) = -4.518760972125019, (100, 2) = 1.2414908529334576, (101, 1) = 5.418885713707807, (101, 2) = 1.7446591623038485, (102, 1) = -4.6186356014544945, (102, 2) = 1.2464966911549156, (103, 1) = 5.517773882698374, (103, 2) = 1.7595296039143944, (104, 1) = -4.7185198541510305, (104, 2) = 1.251306687335172, (105, 1) = 5.616690460382383, (105, 2) = 1.7742098852224268, (106, 1) = -4.818412999577848, (106, 2) = 1.2559283208922685, (107, 1) = 5.715634024342858, (107, 2) = 1.7887071660294933, (108, 1) = -4.918314368203739, (108, 2) = 1.2603686527124744, (109, 1) = 5.814603250214132, (109, 2) = 1.8030282110486413, (110, 1) = -5.018223345669672, (110, 2) = 1.2646343556687651, (111, 1) = 5.913596903206451, (111, 2) = 1.8171794183199657, (112, 1) = -5.118139367517097, (112, 2) = 1.2687317424194353, (113, 1) = 6.012613830503219, (113, 2) = 1.831166845127858, (114, 1) = -5.21806191449458, (114, 2) = 1.2726667907713844, (115, 1) = 6.111652954427307, (115, 2) = 1.8449962316778337, (116, 1) = -5.317990508371122, (116, 2) = 1.2764451668586307, (117, 1) = 6.2107132662867155, (117, 2) = 1.8586730227604047, (118, 1) = -5.41792470819436, (118, 2) = 1.2800722463571568, (119, 1) = 6.309793820821663, (119, 2) = 1.8722023876030995, (120, 1) = -5.517864106940267, (120, 2) = 1.2835531339316275, (121, 1) = 6.408893731185266, (121, 2) = 1.885589238088756, (122, 1) = -5.617808328508073, (122, 2) = 1.2868926810872656, (123, 1) = 6.508012164398588, (123, 2) = 1.898838245498212, (124, 1) = -5.717757025020236, (124, 2) = 1.290095502580743, (125, 1) = 6.607148337228266, (125, 2) = 1.9119538559180023, (126, 1) = -5.817709874392481, (126, 2) = 1.293165991526965, (127, 1) = 6.706301512441308, (127, 2) = 1.9249403044383377, (128, 1) = -5.917666578143407, (128, 2) = 1.2961083333237493, (129, 1) = 6.8054709953971475, (129, 2) = 1.9378016282532036, (130, 1) = -6.0176268594169855, (130, 2) = 1.2989265185033287, (131, 1) = 6.904656130941838, (131, 2) = 1.9505416787625545, (132, 1) = -6.117590461194588, (132, 2) = 1.3016243546081112, (133, 1) = 7.003856300573377, (133, 2) = 1.9631641327661697, (134, 1) = -6.21755714467603, (134, 2) = 1.3042054771780078, (135, 1) = 7.103070919850769, (135, 2) = 1.9756725028295183, (136, 1) = -6.317526687811594, (136, 2) = 1.306673359927663, (137, 1) = 7.202299436022552, (137, 2) = 1.9880701468938442, (138, 1) = -6.417498883969152, (138, 2) = 1.3090313241840286, (139, 1) = 7.301541325853255, (139, 2) = 2.0003602771954387, (140, 1) = -6.5174735407223325, (140, 2) = 1.3112825476476813, (141, 1) = 7.400796093628638, (141, 2) = 2.012545968552697, (142, 1) = -6.617450478747347, (142, 2) = 1.313430072535057, (143, 1) = 7.50006326932267, (143, 2) = 2.024630166073826, (144, 1) = -6.717429530817475, (144, 2) = 1.3154768131532322, (145, 1) = 7.5993424069110365, (145, 2) = 2.0366156923330117, (146, 1) = -6.817410540885456, (146, 2) = 1.3174255629539324, (147, 1) = 7.698633082817586, (147, 2) = 2.0485052540583215, (148, 1) = -6.917393363245122, (148, 2) = 1.3192790011090527, (149, 1) = 7.797934894481557, (149, 2) = 2.0603014483705757, (150, 1) = -7.0173778617645555, (150, 2) = 1.321039698646012, (151, 1) = 7.8972474590346895, (151, 2) = 2.0720067686087926, (152, 1) = -7.117363909183894, (152, 2) = 1.3227101241777621, (153, 1) = 7.996570412078425, (153, 2) = 2.0836236097745826, (154, 1) = -7.217351386471633, (154, 2) = 1.3242926492590916, (155, 1) = 8.095903406552413, (155, 2) = 2.095154273624947, (156, 1) = -7.31734018223395, (156, 2) = 1.3257895533980282, (157, 1) = 8.19524611168639, (157, 2) = 2.106600973440315, (158, 1) = -7.417330192172108, (158, 2) = 1.3272030287486039, (159, 1) = 8.294598212028305, (159, 2) = 2.1179658384923075, (160, 1) = -7.517321318583555, (160, 2) = 1.3285351845089273, (161, 1) = 8.393959406542223, (161, 2) = 2.1292509182335895, (162, 1) = -7.61731346990274, (162, 2) = 1.3297880510464566, (163, 1) = 8.493329407770212, (163, 2) = 2.140458186230258, (164, 1) = -7.7173065602780975, (164, 2) = 1.330963583770492, (165, 1) = 8.592707941052902, (165, 2) = 2.151589543855484, (166, 1) = -7.817300509181985, (166, 2) = 1.3320636667702082, (167, 1) = 8.692094743803963, (167, 2) = 2.1626468237615546, (168, 1) = -7.917295241050697, (168, 2) = 1.3330901162350286, (169, 1) = 8.79148956483414, (169, 2) = 2.17363179314606, (170, 1) = -8.017290684951938, (170, 2) = 1.3340446836727593, (171, 1) = 8.890892163720926, (171, 2) = 2.1845461568266593, (172, 1) = -8.117286774277405, (172, 2) = 1.3349290589396254, (173, 1) = 8.990302310220263, (173, 2) = 2.1953915601377187, (174, 1) = -8.217283446458348, (174, 2) = 1.3357448730952464, (175, 1) = 9.089719783717038, (175, 2) = 2.2061695916610335, (176, 1) = -8.317280642702178, (176, 2) = 1.3364937010945086, (177, 1) = 9.189144372711352, (177, 2) = 2.2168817858018923, (178, 1) = -8.417278307748376, (178, 2) = 1.3371770643273901, (179, 1) = 9.288575874337885, (179, 2) = 2.2275296252208676, (180, 1) = -8.51727638964211, (180, 2) = 1.3377964330169019, (181, 1) = 9.38801409391586, (181, 2) = 2.238114543130887, (182, 1) = -8.617274839524129, (182, 2) = 1.3383532284845332, (183, 1) = 9.487458844527328, (183, 2) = 2.248637925468447, (184, 1) = -8.717273611435608, (184, 2) = 1.338848825291885, (185, 1) = 9.586909946621702, (185, 2) = 2.259101112947129, (186, 1) = -8.81727266213676, (186, 2) = 1.3392845532665083, (187, 1) = 9.686367227644634, (187, 2) = 2.2695054030009856, (188, 1) = -8.917271950938124, (188, 2) = 1.3396616994193669, (189, 1) = 9.785830521689496, (189, 2) = 2.279852051624801, (190, 1) = -9.01727143954354, (190, 2) = 1.3399815097608, (191, 1) = 9.885299669169834, (191, 2) = 2.290142275117709, (192, 1) = -9.117271091903897, (192, 2) = 1.3402451910213613, (193, 1) = 9.984774516511353, (193, 2) = 2.3003772517361876, (194, 1) = -9.21727087408083, (194, 2) = 1.3404539122834236, (195, 1) = 10.084254915862049, (195, 2) = 2.3105581232620165, (196, 1) = -9.317270754119619, (196, 2) = 1.340608806529065, (197, 1) = 10.183740724819254, (197, 2) = 2.3206859964903903, (198, 1) = -9.417270701930574, (198, 2) = 1.3407109721093091, (199, 1) = 10.283231806172436, (199, 2) = 2.330761944643004, (200, 1) = -9.517270689178297, (200, 2) = 1.3407614741394762, (201, 1) = 10.382728027660692, (201, 2) = 2.340787008710608, (202, 1) = -9.617270689178213, (202, 2) = 1.3407613458250416, (203, 1) = 10.482229261743957, (203, 2) = 2.3507621987291967, (204, 1) = -9.717270676799862, (204, 2) = 1.3407115897221153, (205, 1) = 10.581735385387018, (205, 2) = 2.360688494993737, (206, 1) = -9.817270628376434, (206, 2) = 1.340613178936369, (207, 1) = 10.6812462798555, (207, 2) = 2.3705668492130583, (208, 1) = -9.917270521620122, (208, 2) = 1.3404670582639766, (209, 1) = 10.78076183052304, (209, 2) = 2.3803981856092897, (210, 1) = -10.017270335542845, (210, 2) = 1.340274145277895, (211, 1) = 10.880281926688948, (211, 2) = 2.3901834019650092, (212, 1) = -10.117270050382006, (212, 2) = 1.3400353313626012, (213, 1) = 10.979806461405664, (213, 2) = 2.39992337062105, (214, 1) = -10.217269647530875, (214, 2) = 1.3397514827001804, (215, 1) = 11.079335331315425, (215, 2) = 2.4096189394277356, (216, 1) = -10.31726910947333, (216, 2) = 1.339423441210489, (217, 1) = 11.17886843649554, (217, 2) = 2.4192709326521147, (218, 1) = -10.417268419722603, (218, 2) = 1.3390520254479306, (219, 1) = 11.278405680311755, (219, 2) = 2.4288801518436194, (220, 1) = -10.517267562763804, (220, 2) = 1.3386380314572164, (221, 1) = 11.377946969279217, (221, 2) = 2.4384473766604065, (222, 1) = -10.617266523999925, (222, 2) = 1.3381822335903517, (223, 1) = 11.477492212930567, (223, 2) = 2.4479733656585063, (224, 1) = -10.717265289701118, (224, 2) = 1.3376853852869233, (225, 1) = 11.577041323690738, (225, 2) = 2.4574588570457663, (226, 1) = -10.817263846957006, (226, 2) = 1.3371482198196523, (227, 1) = 11.676594216758058, (227, 2) = 2.466904569402453, (228, 1) = -10.91726218363185, (228, 2) = 1.3365714510070488, (229, 1) = 11.776150809991291, (229, 2) = 2.4763112023702676, (230, 1) = -11.01726028832235, (230, 2) = 1.3359557738948915, (231, 1) = 11.87571102380226, (231, 2) = 2.485679437311423, (232, 1) = -11.11725815031794, (232, 2) = 1.3353018654081579, (233, 1) = 11.975274781053738, (233, 2) = 2.495009937939321, (234, 1) = -11.217255759563406, (234, 2) = 1.334610384974921, (235, 1) = 12.074842006962298, (235, 2) = 2.5043033509222887, (236, 1) = -11.31725310662365, (236, 2) = 1.3338819751236488, (237, 1) = 12.174412629005845, (237, 2) = 2.513560306461744, (238, 1) = -11.417250182650509, (238, 2) = 1.3331172620552616, (239, 1) = 12.273986576835556, (239, 2) = 2.5227814188460744, (240, 1) = -11.51724697935146, (240, 2) = 1.3323168561911984, (241, 1) = 12.373563782191994, (241, 2) = 2.531967286981442, (242, 1) = -11.61724348896011, (242, 2) = 1.3314813526987077, (243, 1) = 12.473144178825155, (243, 2) = 2.5411184949006618, (244, 1) = -11.717239704208351, (244, 2) = 1.3306113319944717, (245, 1) = 12.57272770241824, (245, 2) = 2.550235612251222, (246, 1) = -11.817235618300094, (246, 2) = 1.329707360227638, (247, 1) = 12.672314290514938, (247, 2) = 2.559319194763473, (248, 1) = -11.91723122488645, (248, 2) = 1.328769989743256, (249, 1) = 12.77190388245004, (249, 2) = 2.5683697846999345, (250, 1) = -12.017226518042307, (250, 2) = 1.3277997595270632, (251, 1) = 12.8714964192832, (251, 2) = 2.577387911286639, (252, 1) = -12.117221492244191, (252, 2) = 1.326797195632515, (253, 1) = 12.971091843735675, (253, 2) = 2.5863740911273467, (254, 1) = -12.217216142349347, (254, 2) = 1.3257628115909013, (255, 1) = 13.07069010012989, (255, 2) = 2.5953288286014606, (256, 1) = -12.31721046357596, (256, 2) = 1.3246971088053434, (257, 1) = 13.170291134331679, (257, 2) = 2.6042526162463906, (258, 1) = -12.417204451484448, (258, 2) = 1.3236005769294308, (259, 1) = 13.269894893695065, (259, 2) = 2.6131459351250985, (260, 1) = -12.517198101959776, (260, 2) = 1.322473694231205, (261, 1) = 13.36950132700944, (261, 2) = 2.622009255179501, (262, 1) = -12.617191411194707, (262, 2) = 1.321316927943172, (263, 1) = 13.469110384449028, (263, 2) = 2.6308430355703867, (264, 1) = -12.717184375673952, (264, 2) = 1.32013073459897, (265, 1) = 13.568722017524523, (265, 2) = 2.639647725004448, (266, 1) = -12.817176992159169, (266, 2) = 1.3189155603573148, (267, 1) = 13.668336179036778, (267, 2) = 2.648423762049022, (268, 1) = -12.917169257674749, (268, 2) = 1.3176718413137758, (269, 1) = 13.767952823032449, (269, 2) = 2.6571715754350738, (270, 1) = -13.017161169494347, (270, 2) = 1.3164000038009407, (271, 1) = 13.867571904761498, (271, 2) = 2.6658915843489646, (272, 1) = -13.11715272512813, (272, 2) = 1.3151004646774762, (273, 1) = 13.967193380636468, (273, 2) = 2.674584198713481, (274, 1) = -13.217143922310681, (274, 2) = 1.313773631606583, (275, 1) = 14.06681720819343, (275, 2) = 2.683249819458609, (276, 1) = -13.317134758989527, (276, 2) = 1.3124199033242943, (277, 1) = 14.166443346054534, (277, 2) = 2.6918888387824906, (278, 1) = -13.41712523331427, (278, 2) = 1.3110396698980673, (279, 1) = 14.266071753892078, (279, 2) = 2.7005016404029916, (280, 1) = -13.517115343626271, (280, 2) = 1.309633312976095, (281, 1) = 14.365702392394034, (281, 2) = 2.709088599800275, (282, 1) = -13.61710508844886, (282, 2) = 1.3082012060277095, (283, 1) = 14.465335223230948, (283, 2) = 2.7176500844507765, (284, 1) = -13.717094466478049, (284, 2) = 1.3067437145752803, (285, 1) = 14.56497020902416, (285, 2) = 2.726186454052925, (286, 1) = -13.817083476573716, (286, 2) = 1.305261196417956, (287, 1) = 14.664607313315273, (287, 2) = 2.734698060744982, (288, 1) = -13.917072117751228, (288, 2) = 1.3037540018475924, (289, 1) = 14.764246500536817, (289, 2) = 2.743185249315299, (290, 1) = -14.017060389173494, (290, 2) = 1.3022224738571855, (291, 1) = 14.863887735984068, (291, 2) = 2.751648357405329, (292, 1) = -14.117048290143412, (292, 2) = 1.300666948342132, (293, 1) = 14.963530985787939, (293, 2) = 2.760087715705675, (294, 1) = -14.217035820096694, (294, 2) = 1.299087754294598, (295, 1) = 15.063176216888916, (295, 2) = 2.7685036481454657, (296, 1) = -14.317022978595046, (296, 2) = 1.2974852139912891, (297, 1) = 15.16282339701199, (297, 2) = 2.776896472075339, (298, 1) = -14.417009765319689, (298, 2) = 1.2958596431748846, (299, 1) = 15.262472494642534, (299, 2) = 2.785266498444272, (300, 1) = -14.516996180065195, (300, 2) = 1.2942113512293756, (301, 1) = 15.362123479003083, (301, 2) = 2.7936140319705083, (302, 1) = -14.616982222733638, (302, 2) = 1.2925406413495817, (303, 1) = 15.461776320030989, (303, 2) = 2.8019393713068355, (304, 1) = -14.716967893329013, (304, 2) = 1.290847810705046, (305, 1) = 15.561430988356891, (305, 2) = 2.810242809200408, (306, 1) = -14.816953191951946, (306, 2) = 1.2891331505985515, (307, 1) = 15.661087455283988, (307, 2) = 2.818524632647351, (308, 1) = -14.91693811879465, (308, 2) = 1.2873969466194581, (309, 1) = 15.760745692768063, (309, 2) = 2.8267851230423413, (310, 1) = -15.016922674136131, (310, 2) = 1.2856394787920657, (311, 1) = 15.860405673398233, (311, 2) = 2.8350245563233485, (312, 1) = -15.116906858337623, (312, 2) = 1.2838610217191921, (313, 1) = 15.960067370378395, (313, 2) = 2.8432432031117494, (314, 1) = -15.216890671838248, (314, 2) = 1.2820618447211607, (315, 1) = 16.05973075750933, (315, 2) = 2.851441328847962, (316, 1) = -15.316874115150878, (316, 2) = 1.2802422119703567, (317, 1) = 16.159395809171464, (317, 2) = 2.859619193922795, (318, 1) = -15.416857188858206, (318, 2) = 1.2784023826215303, (319, 1) = 16.2590625003082, (319, 2) = 2.867777053804653, (320, 1) = -15.516839893608992, (320, 2) = 1.2765426109380082, (321, 1) = 16.35873080640988, (321, 2) = 2.8759151591627723, (322, 1) = -15.616822230114503, (322, 2) = 1.2746631464139617, (323, 1) = 16.45840070349827, (323, 2) = 2.884033755986621, (324, 1) = -15.716804199145102, (324, 2) = 1.2727642338928775, (325, 1) = 16.5580721681116, (325, 2) = 2.8921330857016065, (326, 1) = -15.816785801527022, (326, 2) = 1.2708461136823792, (327, 1) = 16.65774517729012, (327, 2) = 2.9002133852812437, (328, 1) = -15.91676703813928, (328, 2) = 1.268909021665523, (329, 1) = 16.75741970856215, (329, 2) = 2.9082748873558875, (330, 1) = -16.01674790991074, (330, 2) = 1.2669531894087096, (331, 1) = 16.85709573993059, (331, 2) = 2.9163178203181714, (332, 1) = -16.116728417817317, (332, 2) = 1.2649788442663215, (333, 1) = 16.956773249859907, (333, 2) = 2.924342408425271, (334, 1) = -16.2167085628793, (334, 2) = 1.2629862094822095, (335, 1) = 17.05645221726355, (335, 2) = 2.932348871898094, (336, 1) = -16.316688346158827, (336, 2) = 1.2609755042881479, (337, 1) = 17.156132621491775, (337, 2) = 2.9403374270175253, (338, 1) = -16.416667768757446, (338, 2) = 1.2589469439993572, (339, 1) = 17.255814442319885, (339, 2) = 2.948308286217816, (340, 1) = -16.516646831813816, (340, 2) = 1.2569007401072017, (341, 1) = 17.35549765993686, (341, 2) = 2.9562616581772185, (342, 1) = -16.61662553650151, (342, 2) = 1.2548371003691625, (343, 1) = 17.455182254934353, (343, 2) = 2.964197747905985, (344, 1) = -16.716603884026913, (344, 2) = 1.2527562288961858, (345, 1) = 17.55486820829605, (345, 2) = 2.9721167568317868, (346, 1) = -16.816581875627225, (346, 2) = 1.2506583262374833, (347, 1) = 17.654555501387364, (347, 2) = 2.9800188828826726, (348, 1) = -16.916559512568554, (348, 2) = 1.2485435894628902, (349, 1) = 17.75424411594547, (349, 2) = 2.987904320567638, (350, 1) = -17.01653679614409, (350, 2) = 1.2464122122428551, (351, 1) = 17.85393403406965, (351, 2) = 2.99577326105489, (352, 1) = -17.116513727672398, (352, 2) = 1.244264384926145, (353, 1) = 17.953625238211966, (353, 2) = 3.003625892247887, (354, 1) = -17.216490308495736, (354, 2) = 1.2421002946153439, (355, 1) = 18.053317711168198, (355, 2) = 3.011462398859227, (356, 1) = -17.316466539978496, (356, 2) = 1.2399201252402174, (357, 1) = 18.153011436069086, (357, 2) = 3.019282962482459, (358, 1) = -17.416442423505703, (358, 2) = 1.2377240576290238, (359, 1) = 18.25270639637184, (359, 2) = 3.027087761661891, (360, 1) = -17.516417960481583, (360, 2) = 1.235512269577829, (361, 1) = 18.352402575851915, (361, 2) = 3.0348769719604447, (362, 1) = -17.61639315232819, (362, 2) = 1.233284935917888, (363, 1) = 18.452099958595046, (363, 2) = 3.0426507660256434, (364, 1) = -17.716368000484113, (364, 2) = 1.2310422285811824, (365, 1) = 18.55179852898951, (365, 2) = 3.0504093136537844, (366, 1) = -17.816342506403238, (366, 2) = 1.2287843166641488, (367, 1) = 18.651498271718648, (367, 2) = 3.0581527818523537, (368, 1) = -17.916316671553552, (368, 2) = 1.2265113664896643, (369, 1) = 18.751199171753584, (369, 2) = 3.0658813349007423, (370, 1) = -18.016290497416026, (370, 2) = 1.2242235416673544, (371, 1) = 18.850901214346198, (371, 2) = 3.073595134409324, (372, 1) = -18.11626398548354, (372, 2) = 1.2219210031522638, (373, 1) = 18.950604385022288, (373, 2) = 3.0812943393769356, (374, 1) = -18.216237137259842, (374, 2) = 1.219603909301958, (375, 1) = 19.05030866957493, (375, 2) = 3.088979106246827, (376, 1) = -18.316209954258593, (376, 2) = 1.217272415932095, (377, 1) = 19.15001405405806, (377, 2) = 3.096649588961116, (378, 1) = -18.416182438002412, (378, 2) = 1.2149266763705149, (379, 1) = 19.249720524780226, (379, 2) = 3.1043059390138033, (380, 1) = -18.516154590022012, (380, 2) = 1.2125668415099065, (381, 1) = 19.349428068298526, (381, 2) = 3.1119483055023873, (382, 1) = -18.616126411855333, (382, 2) = 1.2101930598590847, (383, 1) = 19.449136671412727, (383, 2) = 3.119576835178133, (384, 1) = -18.716097905046748, (384, 2) = 1.2078054775929261, (385, 1) = 19.54884632115956, (385, 2) = 3.1271916724950226, (386, 1) = -18.81606907114629, (386, 2) = 1.2054042386009987, (387, 1) = 19.648557004807166, (387, 2) = 3.134792959657441, (388, 1) = -18.916039911708925, (388, 2) = 1.202989484534943, (389, 1) = 19.748268709849718, (389, 2) = 3.142380836666629, (390, 1) = -19.01601042829384, (390, 2) = 1.2005613548546221, (391, 1) = 19.847981424002167, (391, 2) = 3.1499554413659463, (392, 1) = -19.11598062246379, (392, 2) = 1.1981199868730976, (393, 1) = 19.947695135195183, (393, 2) = 3.1575169094849778, (394, 1) = -19.21595049578447, (394, 2) = 1.195665515800449, (395, 1) = 20.047409831570192, (395, 2) = 3.1650653746825133, (396, 1) = -19.315920049823895, (396, 2) = 1.1931980747864839, (397, 1) = 20.147125501474594, (397, 2) = 3.1726009685884518, (398, 1) = -19.41588928615184, (398, 2) = 1.1907177949623766, (399, 1) = 20.24684213345708, (399, 2) = 3.1801238208446416, (400, 1) = -19.515858206339296, (400, 2) = 1.18822480548125}, datatype = float[8])

(2)

ATTENTION TO INITIAL VALUES

crv[1 .. 3]

Matrix([[0., 0.], [1., 0.], [1., .100000000000000]])

(3)

CYCLE EXCEPTIONS

hlf(crv[1], crv[2], crv[3], 4);

hlf(crv[3], crv[1], crv[4], 5)

ds1, ds2, ds3, tt1, dss, pb, ds4

 

ds1, ds2, ds3, tt1, dss, pb, ds4

(4)

GENERATED DATA SAMPLES

seq(hlf(crv[i-2], crv[i-3], crv[i-1], i), i = 6 .. 400):

MERGING SECTIONS

plots[display](seq(plots[polygonplot](crv[i .. i+2], scaling = constrained, color = [blue, green][irem(i, 2)+1], axes = none), i = 3 .. 10))

 

PLOT OF CURVES

plots[pointplot](crv[1 .. 300], axes = none, symbol = point, symbolsize = 20, color = red, scaling = constrained, connect = false)

 

plots[pointplot](crv[1 .. 10], axes = none, symbol = asterisk, symbolsize = 20, color = red, scaling = constrained, connect = false)

 

plots[display](seq(plots[polygonplot]([[0, 0], [1, (1/10)*i], [1, (i+1)*(1/10)]], scaling = constrained, color = [blue, green][irem(i, 2)+1], axes = none), i = 0 .. 10))

 

``

``


 

Download unknown_curve_by_shekofte.mw

 


 

"I am trying to solve these two algebraic equations for A and B "

 

eq1 := -(64*A*B^2*k[1]+28*B^2*k[2]+112*A*k[1]+105*k[2])*A/(105*B)-(32*A^2*B^2*k[1]+28*A*B^2*k[2]+56*A^2*k[1]+105*A*k[2]+210*a)/(105*B) = 0

-(1/105)*(64*A*B^2*k[1]+28*B^2*k[2]+112*A*k[1]+105*k[2])*A/B-(1/105)*(32*A^2*B^2*k[1]+28*A*B^2*k[2]+56*A^2*k[1]+105*A*k[2]+210*a)/B = 0

(1)

eq2 := -(64*A^2*B*k[1]+56*A*B*k[2])*A/(105*B)+(32*A^2*B^2*k[1]+28*A*B^2*k[2]+56*A^2*k[1]+105*A*k[2]+210*a)*A/(105*B^2) = 0

-(1/105)*(64*A^2*B*k[1]+56*A*B*k[2])*A/B+(1/105)*(32*A^2*B^2*k[1]+28*A*B^2*k[2]+56*A^2*k[1]+105*A*k[2]+210*a)*A/B^2 = 0

(2)

solve({eq1, eq2}, {A, B})

{A = RootOf(192*k[1]^2*_Z^3+440*k[1]*k[2]*_Z^2+(480*a*k[1]+210*k[2]^2)*_Z+315*a*k[2]), B = (1/2)*RootOf(1536*k[1]^2*RootOf(192*k[1]^2*_Z^3+440*k[1]*k[2]*_Z^2+(480*a*k[1]+210*k[2]^2)*_Z+315*a*k[2])^2+2512*k[1]*k[2]*RootOf(192*k[1]^2*_Z^3+440*k[1]*k[2]*_Z^2+(480*a*k[1]+210*k[2]^2)*_Z+315*a*k[2])+21*_Z^2+3840*a*k[1]+105*k[2]^2)/k[2]}

(3)

``

How can I find A and B explicitly

 

 

``


 

Download solve_equattion.mw

hi

in every math software there is a page which we could find our results in tabels  as numerical output ..is there like this in maple?

Hello guys, I want to compute Einstein tensor components of Kerr metric, but it seems there are some problems with computing.

 

Thank you for your help.Kerr.mw

simplify_question.mws
Am trying to teach myself about lines and circles and inversion.  In the code below I'd like to put textt on the circles eg c1 to identify circle c1 etc.I'm more familiar with the textplot command & plottools, but want to use the draw command.  I've tried some options with the circle statement without success.
circle(c1,x^2+(y-2*R*cos(Pi/6))^2=R^2):  # 'ctext'=c1):

Is it possible to position text in a draw statement, similar to the textplot statement (that uses plot)?  

  I was amused by an idiosincracy of Maple 7.  The last line of my code uses the simplify command, yet I have had to resort to the simplification myself - (on the previous lines).   I was surprised and curious about this.  The Help section on simplify mentions several high power simplification procedures, yet fails to simplify a simple expression.  Any comments on this?

   I'm interested in learning more about circle inversion and wondered if anyone knew of some elementary books on this.  Geometry Inversion was never taught to me at school, nor university, despite it being a topic over 1000 years old.

   Thanks for your time.  Any comments, answers, gladly appreciated.      

  

restart:
# # # # # # # # # # # # # # # # # # # # # # # # # # # #
# Test of geometry, radical axis.
# # # # # # # # # # # # # # # # # # # # # # # # # # # #
with(geometry):
with(plots):
_EnvHorizontalName := x: _EnvVerticalName := y:

R:=5:
circle(c1,x^2+(y-2*R*cos(Pi/6))^2=R^2):  # 'ctext'=c1):
circle(c2,(x-R)^2+y^2=R^2):
circle(c3,(x+R)^2+y^2=R^2):
RadicalAxis(ra12,c1,c2):
RadicalAxis(ra13,c1,c3):

printf("Colors:  c1=red c2=blue  c3=gold\n");
printf("       ra12=magenta    ra23=grey\n");
t1:=textplot([0, 1.8*R, `Circle c1`]):
draw([c1,c2, c3, ra12,ra13], axes=normal, color=[red, blue,gold, magenta,grey]);

#draw([c1,c2, c3, ra12,ra13,t1], axes=normal, color=[red, blue,gold, magenta,grey, black], printtext=true);
if AreTangent(c1,c2) then
   printf("Circles c1 and c2 are tangential, (as they all are!)\n");
end if:
testp:=Equation(ra12):
#print(whattype(testp));
printf("Equation of radical axis for c1 & c2 is %A or\n", testp);
simplify(Equation(ra12)/10);
simplify(Equation(ra12));

Warning, the name changecoords has been redefined

Colors:  c1=red c2=blue  c3=gold

       ra12=magenta    ra23=grey

Circles c1 and c2 are tangential, (as they all are!)

Equation of radical axis for c1 & c2 is 50+10*x-10*3^(1/2)*y = 0 or

5+x-sqrt(3)*y = 0

50+10*x-10*sqrt(3)*y = 0

 

 


 

Download simplify_question.mws

 

I have been computing curvature etc of a four-dimensional metric that invloves three arbitary functions using the DifferentialGeometry package. I am now intereted in whether Maple can compute the Killing vectors. I have used the code of Example 3 from the Maple help page on KillingVectors in the  Tensor subpackage of the package DifferentialGeoemtry. If I set the arbitrary functions to be constants using the' auxiliaryequations' part of the code, then Maple outputs Killing vectors, so all good so far. If I leave the three arbitary functions to be arbitrary, however, specifying only that they be nonzero (as in Example 3) Maple had not produced any output after five hours, though when I moved the cursor over the tool bars at the top of the screen it turned to an hour glass, indicating that Maple was busy. Does anyone have experience with whether I am asking too much of Maple or whether I just need to give it more time to produce answers? If the latter, how long? The Example 3 indicates Maple will consider several possibilties including the completely arbitrary option, though that example only involves one arbitary function, so having multiple arbitary functions obviously increases the complexity.

Hi, how can you compute the normal distribution value (in my case the standard normal distribution) of a value and likewise the inverse normal distribution for a given random number in Maple?

I haven't really found any way to do this easily like you can in e.g. Excel or Matlab.

For example if I have a value z = 2.7102, I can in Matlab find the standard normal distribution value as:

Φ(z) = cdf('normal',z,0,1) and inversely z = norminv(Φ(z) ,0,1)

Or in Excel: Φ(z) = normdist(z,0,1) and z = norminv(Φ(z) ,0,1)

 

How to do this in Maple?

 

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