Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

Hello experts,

I am trying to use solve to find a solution to a system of two equations. The two equations involved are quite complicated, and so sometimes Maple has difficulty with this. In particular, the solve command tries evaluating but never comes up with a solution (I've waited at least an hour, before giving up). 

I recently learned about fsolve, which gives approximate numeric solutions (which would be fine for my purposes), but fsolve too struggles with a solution and simply returns my input to me. I tried plotting the system of equations using plots:-implictplot to see if a solution existed, and as expected it does. I was hoping to get some tips on trying to solve a difficult system like this, perhaps given the knowledge that a solution definitely exists. Unfortunately, I need a solution for many variations of the same system, so simply reading off the approximate solution isn't really an option.

In my attatched code, the system with W = 49 is the first one where Maple really begins to struggle, and I believe that solutions for W>49 are also difficult.

06042020_Predicting_w_AB_Ratio_Maple_Primes.mw

Thanks!

Hello again, it's my first time using maple, so I have more problems :(

I need solve three equations, but maple shows an error:

Error, (in solve) a constant is invalid as a variable, gamma

gamma.mw

I have used g instead of gamma and solve works, but I don't understand what happen.

 

The second problem is when I use g instead of gamma. In some tau values solve() doesn't show the solution. In each solve() always there are one unnecessary equation. Maybe could be that. But I don't know.

g.mw

 

Thank you in advance!!!

 

P.S. Sorry for my bad English

 Hello! I'm trying to solve the following: 

pde1 := (y+z)*(diff(u(x, y, z), x))+(z+x)*(diff(u(x, y, z), y))+(x+y)*(diff(u(x, y, z), z)) = 0;
{pdsolve(pde1,u(x,y,z))}

Unfortunately, after calling pdsolve , I get an empty result set . Can you help me figure out what's going on?  Does it  really have no solution? 

 

 

 

 

 

Hello, I have this:

maple.mw

I need save the three solutions in three different variables.

Thanks a lot!!!

I am using Maple to load well-behaved function data (512 points) and using ArrayInterpolation integrate it:

P:= r -> CurveFitting:-ArrayInterpolation(xydata, Array(1 .. 1, 1 .. 1, [r]), method = spline)[1];.

While the simple integral    int(P, 0 .. 100, numeric, digits = 4)    outputs a number, if I add another variable like   int(P*a, [r = 0 .. 1, a = 0 .. 1], numeric)    it just outputs      int(P*a, [r = 0 .. 1, a = 0 .. 1], numeric)  (obviously the integral is more complex but this just shows the principle).

int(P(r)*a, [r = 0 .. 1, a = 0 .. 1], numeric)  gives and error 'invalid input: coordinates of xvalues must be of type numeric'. Does anyone know the syntax to make this integral evaluate numerically?

I really wouldn't want to use   spline()  or interpolation()  because as far as I have tried they are really slow and incompatable respectively. Actual document below.


Much thanks in advance.

restart; with(LinearAlgebra); with(CurveFitting); with(Interpolation); with(plots)

NULL

NULL

data := Import("C:/Users/Ingvars/Desktop/data.csv", output = Matrix)

NULL

NULL``

P := proc (r) options operator, arrow; CurveFitting:-ArrayInterpolation(`<|>`(Column(data, 1), `~`[`^`](Column(data, 15), 2)), Array(1 .. 1, 1 .. 1, [[r]]), method = spline)[1] end proc
``

``

NULLNULL

display(plot(P, 0 .. 10), pointplot(Column(data, 1)[1 .. 450], `~`[`^`](Column(data, 15)[1 .. 450], 2), symbolsize = 2, color = red))

 

NULL

int(P, 0 .. 100, numeric, digits = 4)

1.000

(1)

NULL

"F_R(m,l,q):=2*int(P*sin(q r cos(theta))^(2)*sin(theta)*|(Y)[l]^(m)(theta,phi)|^(2),[theta=0..Pi,phi=0..2 Pi,r=0..100],numeric,digits=4):"NULL

"F_I(m,l,q):=int(P*sin(q r cos(theta))*sin(theta)*|(Y)[l]^(m)(theta,phi)|^(2),[theta=0..Pi,phi=0..2 Pi,r=0..100],numeric,digits=4):" 

 

"F(m,l,q):=|F_R(m,l,q)-i*F_I(m,l,q)|:"

 

 

evalf(F(1, 2, 1))

abs(-2.*(Int(Int(Int(P*sin(r*cos(theta))^2*sin(theta)*abs(SphericalY(2., 1., theta, phi))^2, theta = 0. .. 3.142), phi = 0. .. 6.284), r = 0. .. 100.))+(1.*I)*(Int(Int(Int(P*sin(r*cos(theta))*sin(theta)*abs(SphericalY(2., 1., theta, phi))^2, theta = 0. .. 3.142), phi = 0. .. 6.284), r = 0. .. 100.)))

(2)

``


 

Download Au_Scattering.mw

Hi, when trying to solve 2 equations with 2 variables the fsolve function reutrns just expression instead of numerical solution. Can someone please help with this? Thanks a lot

 

NRTL.mw
 

restart

T:=325:

a12:=2305.28444347652 - 9.14490843016421*T + 0.00680052257590234*T^2:

a21:=-6665.24838284836 + 46.0897018087247*T - 0.0694991633494123*T^2:

alfa:=0.3:

x2:=1-x1:

tau12:=a12/T:

tau21:=a21/T:

G12:=exp(-alfa*tau12):

G21:=exp(-alfa*tau21):

lng1:=x2^2*(tau21*(G21/(x1+x2*G21))^2+tau12*(G12/((x2+x1*G12)^2))):

lng2:=x1^2*(tau12*(G12/(x2+x1*G12))^2+tau21*(G21/((x1+x2*G21)^2))):

lnga1:=subs(x1=xa1,lng1):

lngb1:=subs(x1=xb1,lng1):

lnga2:=subs(x1=xa1,lng2):

lngb2:=subs(x1=xb1,lng2):

r1:=lnga1+ln(xa1)=lngb1+ln(xb1)

(1-xa1)^2*(.4966874722/(.4073000470+.5926999530*xa1)^2+.1510891213/(-0.464212743e-1*xa1+1)^2)+ln(xa1) = (1-xb1)^2*(.4966874722/(.4073000470+.5926999530*xb1)^2+.1510891213/(-0.464212743e-1*xb1+1)^2)+ln(xb1)

(1)

r2:=lnga2+ln(1-xa1)=lngb2+ln(1-xb1)

xa1^2*(.1440753718/(-0.464212743e-1*xa1+1)^2+1.219463331/(.4073000470+.5926999530*xa1)^2)+ln(1-xa1) = xb1^2*(.1440753718/(-0.464212743e-1*xb1+1)^2+1.219463331/(.4073000470+.5926999530*xb1)^2)+ln(1-xb1)

(2)

fsolve({r1,r2})

fsolve({xa1^2*(.1440753718/(-0.464212743e-1*xa1+1)^2+1.219463331/(.4073000470+.5926999530*xa1)^2)+ln(1-xa1) = xb1^2*(.1440753718/(-0.464212743e-1*xb1+1)^2+1.219463331/(.4073000470+.5926999530*xb1)^2)+ln(1-xb1), (1-xa1)^2*(.4966874722/(.4073000470+.5926999530*xa1)^2+.1510891213/(-0.464212743e-1*xa1+1)^2)+ln(xa1) = (1-xb1)^2*(.4966874722/(.4073000470+.5926999530*xb1)^2+.1510891213/(-0.464212743e-1*xb1+1)^2)+ln(xb1)}, {xa1, xb1})

(3)

 


 

Download NRTL.mw

 

Hello,

I obtained a mode shape from a vibration problem.

I want to normalized mode shape for the comparison of responses corresponding to different modes.

How I can normalize the mode shape that provided in the maple file?

The figure corresponds to this mode shape is plotted that is attached.

Thanks

mode_shapes.mw


 

a := Vector(325, {(1) = 0, (2) = 0., (3) = 0., (4) = 0.1e-3, (5) = 0.1e-3, (6) = 0.2e-3, (7) = 0.4e-3, (8) = 0.7e-3, (9) = 0.10e-2, (10) = 0.16e-2, (11) = 0.23e-2, (12) = 0.33e-2, (13) = 0.44e-2, (14) = 0.65e-2, (15) = 0.89e-2, (16) = 0.114e-1, (17) = 0.139e-1, (18) = 0.162e-1, (19) = 0.178e-1, (20) = 0.186e-1, (21) = 0.183e-1, (22) = 0.171e-1, (23) = 0.150e-1, (24) = 0.120e-1, (25) = 0.85e-2, (26) = 0.51e-2, (27) = 0.16e-2, (28) = -0.19e-2, (29) = -0.51e-2, (30) = -0.79e-2, (31) = -0.103e-1, (32) = -0.120e-1, (33) = -0.132e-1, (34) = -0.138e-1, (35) = -0.136e-1, (36) = -0.129e-1, (37) = -0.118e-1, (38) = -0.106e-1, (39) = -0.94e-2, (40) = -0.83e-2, (41) = -0.75e-2, (42) = -0.71e-2, (43) = -0.69e-2, (44) = -0.71e-2, (45) = -0.75e-2, (46) = -0.79e-2, (47) = -0.83e-2, (48) = -0.84e-2, (49) = -0.81e-2, (50) = -0.73e-2, (51) = -0.60e-2, (52) = -0.43e-2, (53) = -0.20e-2, (54) = 0.11e-2, (55) = 0.46e-2, (56) = 0.82e-2, (57) = 0.117e-1, (58) = 0.149e-1, (59) = 0.174e-1, (60) = 0.191e-1, (61) = 0.200e-1, (62) = 0.198e-1, (63) = 0.187e-1, (64) = 0.167e-1, (65) = 0.139e-1, (66) = 0.103e-1, (67) = 0.65e-2, (68) = 0.28e-2, (69) = -0.5e-3, (70) = -0.27e-2, (71) = -0.45e-2, (72) = -0.56e-2, (73) = -0.62e-2, (74) = -0.64e-2, (75) = -0.64e-2, (76) = -0.62e-2, (77) = -0.60e-2, (78) = -0.58e-2, (79) = -0.57e-2, (80) = -0.59e-2, (81) = -0.62e-2, (82) = -0.69e-2, (83) = -0.78e-2, (84) = -0.90e-2, (85) = -0.103e-1, (86) = -0.122e-1, (87) = -0.138e-1, (88) = -0.150e-1, (89) = -0.153e-1, (90) = -0.147e-1, (91) = -0.133e-1, (92) = -0.111e-1, (93) = -0.82e-2, (94) = -0.49e-2, (95) = -0.13e-2, (96) = 0.25e-2, (97) = 0.62e-2, (98) = 0.96e-2, (99) = 0.126e-1, (100) = 0.150e-1, (101) = 0.167e-1, (102) = 0.176e-1, (103) = 0.176e-1, (104) = 0.169e-1, (105) = 0.155e-1, (106) = 0.135e-1, (107) = 0.112e-1, (108) = 0.89e-2, (109) = 0.68e-2, (110) = 0.50e-2, (111) = 0.37e-2, (112) = 0.28e-2, (113) = 0.23e-2, (114) = 0.22e-2, (115) = 0.21e-2, (116) = 0.22e-2, (117) = 0.22e-2, (118) = 0.21e-2, (119) = 0.19e-2, (120) = 0.15e-2, (121) = 0.8e-3, (122) = -0., (123) = -0.11e-2, (124) = -0.25e-2, (125) = -0.40e-2, (126) = -0.68e-2, (127) = -0.97e-2, (128) = -0.127e-1, (129) = -0.154e-1, (130) = -0.175e-1, (131) = -0.189e-1, (132) = -0.193e-1, (133) = -0.187e-1, (134) = -0.171e-1, (135) = -0.146e-1, (136) = -0.113e-1, (137) = -0.76e-2, (138) = -0.42e-2, (139) = -0.9e-3, (140) = 0.23e-2, (141) = 0.52e-2, (142) = 0.76e-2, (143) = 0.96e-2, (144) = 0.110e-1, (145) = 0.118e-1, (146) = 0.121e-1, (147) = 0.118e-1, (148) = 0.110e-1, (149) = 0.100e-1, (150) = 0.91e-2, (151) = 0.84e-2, (152) = 0.78e-2, (153) = 0.75e-2, (154) = 0.76e-2, (155) = 0.79e-2, (156) = 0.85e-2, (157) = 0.92e-2, (158) = 0.98e-2, (159) = 0.103e-1, (160) = 0.103e-1, (161) = 0.98e-2, (162) = 0.88e-2, (163) = 0.72e-2, (164) = 0.51e-2, (165) = 0.24e-2, (166) = -0.15e-2, (167) = -0.57e-2, (168) = -0.99e-2, (169) = -0.137e-1, (170) = -0.164e-1, (171) = -0.184e-1, (172) = -0.196e-1, (173) = -0.197e-1, (174) = -0.189e-1, (175) = -0.171e-1, (176) = -0.146e-1, (177) = -0.115e-1, (178) = -0.81e-2, (179) = -0.47e-2, (180) = -0.16e-2, (181) = 0.8e-3, (182) = 0.24e-2, (183) = 0.34e-2, (184) = 0.40e-2, (185) = 0.43e-2, (186) = 0.43e-2, (187) = 0.42e-2, (188) = 0.41e-2, (189) = 0.41e-2, (190) = 0.43e-2, (191) = 0.47e-2, (192) = 0.53e-2, (193) = 0.62e-2, (194) = 0.76e-2, (195) = 0.92e-2, (196) = 0.109e-1, (197) = 0.127e-1, (198) = 0.146e-1, (199) = 0.160e-1, (200) = 0.166e-1, (201) = 0.162e-1, (202) = 0.149e-1, (203) = 0.128e-1, (204) = 0.99e-2, (205) = 0.65e-2, (206) = 0.28e-2, (207) = -0.10e-2, (208) = -0.47e-2, (209) = -0.82e-2, (210) = -0.112e-1, (211) = -0.137e-1, (212) = -0.154e-1, (213) = -0.164e-1, (214) = -0.166e-1, (215) = -0.159e-1, (216) = -0.147e-1, (217) = -0.129e-1, (218) = -0.110e-1, (219) = -0.90e-2, (220) = -0.73e-2, (221) = -0.59e-2, (222) = -0.49e-2, (223) = -0.44e-2, (224) = -0.41e-2, (225) = -0.41e-2, (226) = -0.42e-2, (227) = -0.43e-2, (228) = -0.43e-2, (229) = -0.41e-2, (230) = -0.36e-2, (231) = -0.29e-2, (232) = -0.18e-2, (233) = -0.3e-3, (234) = 0.16e-2, (235) = 0.38e-2, (236) = 0.62e-2, (237) = 0.88e-2, (238) = 0.121e-1, (239) = 0.151e-1, (240) = 0.175e-1, (241) = 0.192e-1, (242) = 0.198e-1, (243) = 0.194e-1, (244) = 0.181e-1, (245) = 0.159e-1, (246) = 0.122e-1, (247) = 0.80e-2, (248) = 0.34e-2, (249) = -0.9e-3, (250) = -0.41e-2, (251) = -0.68e-2, (252) = -0.87e-2, (253) = -0.98e-2, (254) = -0.103e-1, (255) = -0.103e-1, (256) = -0.98e-2, (257) = -0.92e-2, (258) = -0.86e-2, (259) = -0.80e-2, (260) = -0.76e-2, (261) = -0.75e-2, (262) = -0.77e-2, (263) = -0.82e-2, (264) = -0.89e-2, (265) = -0.98e-2, (266) = -0.109e-1, (267) = -0.117e-1, (268) = -0.121e-1, (269) = -0.119e-1, (270) = -0.111e-1, (271) = -0.96e-2, (272) = -0.74e-2, (273) = -0.46e-2, (274) = -0.7e-3, (275) = 0.36e-2, (276) = 0.80e-2, (277) = 0.121e-1, (278) = 0.150e-1, (279) = 0.173e-1, (280) = 0.188e-1, (281) = 0.193e-1, (282) = 0.189e-1, (283) = 0.176e-1, (284) = 0.155e-1, (285) = 0.128e-1, (286) = 0.98e-2, (287) = 0.67e-2, (288) = 0.38e-2, (289) = 0.15e-2, (290) = -0.1e-3, (291) = -0.12e-2, (292) = -0.18e-2, (293) = -0.21e-2, (294) = -0.22e-2, (295) = -0.22e-2, (296) = -0.21e-2, (297) = -0.22e-2, (298) = -0.24e-2, (299) = -0.27e-2, (300) = -0.33e-2, (301) = -0.42e-2, (302) = -0.54e-2, (303) = -0.68e-2, (304) = -0.85e-2, (305) = -0.103e-1, (306) = -0.130e-1, (307) = -0.154e-1, (308) = -0.170e-1, (309) = -0.177e-1, (310) = -0.173e-1, (311) = -0.160e-1, (312) = -0.138e-1, (313) = -0.108e-1, (314) = -0.75e-2, (315) = -0.38e-2, (316) = -0., (317) = 0.37e-2, (318) = 0.71e-2, (319) = 0.101e-1, (320) = 0.124e-1, (321) = 0.141e-1, (322) = 0.149e-1, (323) = 0.152e-1, (324) = 0.152e-1, (325) = 0.149e-1})

_rtable[18446746442173411926]

(1)

``

t := Vector(325, {(1) = 0, (2) = 0.67e-2, (3) = 0.134e-1, (4) = 0.202e-1, (5) = 0.269e-1, (6) = 0.336e-1, (7) = 0.403e-1, (8) = 0.471e-1, (9) = 0.538e-1, (10) = 0.637e-1, (11) = 0.736e-1, (12) = 0.836e-1, (13) = 0.935e-1, (14) = .1098, (15) = .1261, (16) = .1424, (17) = .1586, (18) = .1764, (19) = .1943, (20) = .2121, (21) = .2299, (22) = .2465, (23) = .2632, (24) = .2798, (25) = .2965, (26) = .3109, (27) = .3253, (28) = .3397, (29) = .3542, (30) = .3686, (31) = .3830, (32) = .3974, (33) = .4118, (34) = .4284, (35) = .4450, (36) = .4615, (37) = .4781, (38) = .4938, (39) = .5095, (40) = .5253, (41) = .5410, (42) = .5567, (43) = .5724, (44) = .5882, (45) = .6039, (46) = .6204, (47) = .6368, (48) = .6533, (49) = .6697, (50) = .6843, (51) = .6989, (52) = .7135, (53) = .7281, (54) = .7448, (55) = .7615, (56) = .7781, (57) = .7948, (58) = .8113, (59) = .8278, (60) = .8442, (61) = .8607, (62) = .8775, (63) = .8943, (64) = .9112, (65) = .9280, (66) = .9468, (67) = .9655, (68) = .9843, (69) = 1.0031, (70) = 1.0190, (71) = 1.0348, (72) = 1.0507, (73) = 1.0665, (74) = 1.0794, (75) = 1.0924, (76) = 1.1053, (77) = 1.1183, (78) = 1.1312, (79) = 1.1442, (80) = 1.1571, (81) = 1.1700, (82) = 1.1842, (83) = 1.1984, (84) = 1.2126, (85) = 1.2268, (86) = 1.2459, (87) = 1.2651, (88) = 1.2842, (89) = 1.3034, (90) = 1.3198, (91) = 1.3362, (92) = 1.3527, (93) = 1.3691, (94) = 1.3844, (95) = 1.3996, (96) = 1.4149, (97) = 1.4302, (98) = 1.4454, (99) = 1.4607, (100) = 1.4760, (101) = 1.4913, (102) = 1.5075, (103) = 1.5238, (104) = 1.5400, (105) = 1.5563, (106) = 1.5733, (107) = 1.5904, (108) = 1.6075, (109) = 1.6246, (110) = 1.6410, (111) = 1.6574, (112) = 1.6739, (113) = 1.6903, (114) = 1.7021, (115) = 1.7140, (116) = 1.7258, (117) = 1.7377, (118) = 1.7495, (119) = 1.7614, (120) = 1.7732, (121) = 1.7851, (122) = 1.7964, (123) = 1.8076, (124) = 1.8189, (125) = 1.8302, (126) = 1.8475, (127) = 1.8649, (128) = 1.8822, (129) = 1.8995, (130) = 1.9168, (131) = 1.9341, (132) = 1.9514, (133) = 1.9687, (134) = 1.9856, (135) = 2.0026, (136) = 2.0195, (137) = 2.0365, (138) = 2.0507, (139) = 2.0649, (140) = 2.0791, (141) = 2.0933, (142) = 2.1075, (143) = 2.1217, (144) = 2.1359, (145) = 2.1501, (146) = 2.1674, (147) = 2.1846, (148) = 2.2018, (149) = 2.2191, (150) = 2.2341, (151) = 2.2492, (152) = 2.2643, (153) = 2.2793, (154) = 2.2949, (155) = 2.3105, (156) = 2.3261, (157) = 2.3417, (158) = 2.3576, (159) = 2.3735, (160) = 2.3895, (161) = 2.4054, (162) = 2.4203, (163) = 2.4353, (164) = 2.4503, (165) = 2.4653, (166) = 2.4839, (167) = 2.5025, (168) = 2.5211, (169) = 2.5397, (170) = 2.5561, (171) = 2.5725, (172) = 2.5888, (173) = 2.6052, (174) = 2.6226, (175) = 2.6399, (176) = 2.6572, (177) = 2.6746, (178) = 2.6930, (179) = 2.7114, (180) = 2.7297, (181) = 2.7481, (182) = 2.7634, (183) = 2.7787, (184) = 2.7940, (185) = 2.8094, (186) = 2.8226, (187) = 2.8358, (188) = 2.8490, (189) = 2.8622, (190) = 2.8755, (191) = 2.8887, (192) = 2.9019, (193) = 2.9151, (194) = 2.9302, (195) = 2.9453, (196) = 2.9604, (197) = 2.9755, (198) = 2.9940, (199) = 3.0126, (200) = 3.0311, (201) = 3.0496, (202) = 3.0659, (203) = 3.0822, (204) = 3.0985, (205) = 3.1149, (206) = 3.1302, (207) = 3.1455, (208) = 3.1609, (209) = 3.1762, (210) = 3.1915, (211) = 3.2069, (212) = 3.2222, (213) = 3.2375, (214) = 3.2545, (215) = 3.2715, (216) = 3.2885, (217) = 3.3055, (218) = 3.3223, (219) = 3.3391, (220) = 3.3560, (221) = 3.3728, (222) = 3.3888, (223) = 3.4047, (224) = 3.4206, (225) = 3.4365, (226) = 3.4494, (227) = 3.4622, (228) = 3.4750, (229) = 3.4879, (230) = 3.5007, (231) = 3.5136, (232) = 3.5264, (233) = 3.5392, (234) = 3.5529, (235) = 3.5667, (236) = 3.5804, (237) = 3.5941, (238) = 3.6116, (239) = 3.6292, (240) = 3.6468, (241) = 3.6644, (242) = 3.6810, (243) = 3.6976, (244) = 3.7143, (245) = 3.7309, (246) = 3.7508, (247) = 3.7707, (248) = 3.7905, (249) = 3.8104, (250) = 3.8273, (251) = 3.8442, (252) = 3.8610, (253) = 3.8779, (254) = 3.8938, (255) = 3.9096, (256) = 3.9255, (257) = 3.9414, (258) = 3.9559, (259) = 3.9705, (260) = 3.9851, (261) = 3.9997, (262) = 4.0149, (263) = 4.0301, (264) = 4.0452, (265) = 4.0604, (266) = 4.0779, (267) = 4.0953, (268) = 4.1128, (269) = 4.1302, (270) = 4.1459, (271) = 4.1615, (272) = 4.1771, (273) = 4.1927, (274) = 4.2114, (275) = 4.2300, (276) = 4.2486, (277) = 4.2673, (278) = 4.2833, (279) = 4.2993, (280) = 4.3153, (281) = 4.3313, (282) = 4.3485, (283) = 4.3657, (284) = 4.3829, (285) = 4.4001, (286) = 4.4182, (287) = 4.4362, (288) = 4.4543, (289) = 4.4724, (290) = 4.4881, (291) = 4.5037, (292) = 4.5194, (293) = 4.5351, (294) = 4.5472, (295) = 4.5593, (296) = 4.5715, (297) = 4.5836, (298) = 4.5957, (299) = 4.6079, (300) = 4.6200, (301) = 4.6321, (302) = 4.6456, (303) = 4.6591, (304) = 4.6726, (305) = 4.6861, (306) = 4.7059, (307) = 4.7256, (308) = 4.7454, (309) = 4.7652, (310) = 4.7819, (311) = 4.7986, (312) = 4.8153, (313) = 4.8320, (314) = 4.8474, (315) = 4.8627, (316) = 4.8781, (317) = 4.8935, (318) = 4.9088, (319) = 4.9242, (320) = 4.9396, (321) = 4.9550, (322) = 4.9662, (323) = 4.9775, (324) = 4.9887, (325) = 5.0000})

_rtable[18446746442112534638]

(2)

``


 

Download mode_shapes.mw


 

a := Vector(325, {(1) = 0, (2) = 0., (3) = 0., (4) = 0.1e-3, (5) = 0.1e-3, (6) = 0.2e-3, (7) = 0.4e-3, (8) = 0.7e-3, (9) = 0.10e-2, (10) = 0.16e-2, (11) = 0.23e-2, (12) = 0.33e-2, (13) = 0.44e-2, (14) = 0.65e-2, (15) = 0.89e-2, (16) = 0.114e-1, (17) = 0.139e-1, (18) = 0.162e-1, (19) = 0.178e-1, (20) = 0.186e-1, (21) = 0.183e-1, (22) = 0.171e-1, (23) = 0.150e-1, (24) = 0.120e-1, (25) = 0.85e-2, (26) = 0.51e-2, (27) = 0.16e-2, (28) = -0.19e-2, (29) = -0.51e-2, (30) = -0.79e-2, (31) = -0.103e-1, (32) = -0.120e-1, (33) = -0.132e-1, (34) = -0.138e-1, (35) = -0.136e-1, (36) = -0.129e-1, (37) = -0.118e-1, (38) = -0.106e-1, (39) = -0.94e-2, (40) = -0.83e-2, (41) = -0.75e-2, (42) = -0.71e-2, (43) = -0.69e-2, (44) = -0.71e-2, (45) = -0.75e-2, (46) = -0.79e-2, (47) = -0.83e-2, (48) = -0.84e-2, (49) = -0.81e-2, (50) = -0.73e-2, (51) = -0.60e-2, (52) = -0.43e-2, (53) = -0.20e-2, (54) = 0.11e-2, (55) = 0.46e-2, (56) = 0.82e-2, (57) = 0.117e-1, (58) = 0.149e-1, (59) = 0.174e-1, (60) = 0.191e-1, (61) = 0.200e-1, (62) = 0.198e-1, (63) = 0.187e-1, (64) = 0.167e-1, (65) = 0.139e-1, (66) = 0.103e-1, (67) = 0.65e-2, (68) = 0.28e-2, (69) = -0.5e-3, (70) = -0.27e-2, (71) = -0.45e-2, (72) = -0.56e-2, (73) = -0.62e-2, (74) = -0.64e-2, (75) = -0.64e-2, (76) = -0.62e-2, (77) = -0.60e-2, (78) = -0.58e-2, (79) = -0.57e-2, (80) = -0.59e-2, (81) = -0.62e-2, (82) = -0.69e-2, (83) = -0.78e-2, (84) = -0.90e-2, (85) = -0.103e-1, (86) = -0.122e-1, (87) = -0.138e-1, (88) = -0.150e-1, (89) = -0.153e-1, (90) = -0.147e-1, (91) = -0.133e-1, (92) = -0.111e-1, (93) = -0.82e-2, (94) = -0.49e-2, (95) = -0.13e-2, (96) = 0.25e-2, (97) = 0.62e-2, (98) = 0.96e-2, (99) = 0.126e-1, (100) = 0.150e-1, (101) = 0.167e-1, (102) = 0.176e-1, (103) = 0.176e-1, (104) = 0.169e-1, (105) = 0.155e-1, (106) = 0.135e-1, (107) = 0.112e-1, (108) = 0.89e-2, (109) = 0.68e-2, (110) = 0.50e-2, (111) = 0.37e-2, (112) = 0.28e-2, (113) = 0.23e-2, (114) = 0.22e-2, (115) = 0.21e-2, (116) = 0.22e-2, (117) = 0.22e-2, (118) = 0.21e-2, (119) = 0.19e-2, (120) = 0.15e-2, (121) = 0.8e-3, (122) = -0., (123) = -0.11e-2, (124) = -0.25e-2, (125) = -0.40e-2, (126) = -0.68e-2, (127) = -0.97e-2, (128) = -0.127e-1, (129) = -0.154e-1, (130) = -0.175e-1, (131) = -0.189e-1, (132) = -0.193e-1, (133) = -0.187e-1, (134) = -0.171e-1, (135) = -0.146e-1, (136) = -0.113e-1, (137) = -0.76e-2, (138) = -0.42e-2, (139) = -0.9e-3, (140) = 0.23e-2, (141) = 0.52e-2, (142) = 0.76e-2, (143) = 0.96e-2, (144) = 0.110e-1, (145) = 0.118e-1, (146) = 0.121e-1, (147) = 0.118e-1, (148) = 0.110e-1, (149) = 0.100e-1, (150) = 0.91e-2, (151) = 0.84e-2, (152) = 0.78e-2, (153) = 0.75e-2, (154) = 0.76e-2, (155) = 0.79e-2, (156) = 0.85e-2, (157) = 0.92e-2, (158) = 0.98e-2, (159) = 0.103e-1, (160) = 0.103e-1, (161) = 0.98e-2, (162) = 0.88e-2, (163) = 0.72e-2, (164) = 0.51e-2, (165) = 0.24e-2, (166) = -0.15e-2, (167) = -0.57e-2, (168) = -0.99e-2, (169) = -0.137e-1, (170) = -0.164e-1, (171) = -0.184e-1, (172) = -0.196e-1, (173) = -0.197e-1, (174) = -0.189e-1, (175) = -0.171e-1, (176) = -0.146e-1, (177) = -0.115e-1, (178) = -0.81e-2, (179) = -0.47e-2, (180) = -0.16e-2, (181) = 0.8e-3, (182) = 0.24e-2, (183) = 0.34e-2, (184) = 0.40e-2, (185) = 0.43e-2, (186) = 0.43e-2, (187) = 0.42e-2, (188) = 0.41e-2, (189) = 0.41e-2, (190) = 0.43e-2, (191) = 0.47e-2, (192) = 0.53e-2, (193) = 0.62e-2, (194) = 0.76e-2, (195) = 0.92e-2, (196) = 0.109e-1, (197) = 0.127e-1, (198) = 0.146e-1, (199) = 0.160e-1, (200) = 0.166e-1, (201) = 0.162e-1, (202) = 0.149e-1, (203) = 0.128e-1, (204) = 0.99e-2, (205) = 0.65e-2, (206) = 0.28e-2, (207) = -0.10e-2, (208) = -0.47e-2, (209) = -0.82e-2, (210) = -0.112e-1, (211) = -0.137e-1, (212) = -0.154e-1, (213) = -0.164e-1, (214) = -0.166e-1, (215) = -0.159e-1, (216) = -0.147e-1, (217) = -0.129e-1, (218) = -0.110e-1, (219) = -0.90e-2, (220) = -0.73e-2, (221) = -0.59e-2, (222) = -0.49e-2, (223) = -0.44e-2, (224) = -0.41e-2, (225) = -0.41e-2, (226) = -0.42e-2, (227) = -0.43e-2, (228) = -0.43e-2, (229) = -0.41e-2, (230) = -0.36e-2, (231) = -0.29e-2, (232) = -0.18e-2, (233) = -0.3e-3, (234) = 0.16e-2, (235) = 0.38e-2, (236) = 0.62e-2, (237) = 0.88e-2, (238) = 0.121e-1, (239) = 0.151e-1, (240) = 0.175e-1, (241) = 0.192e-1, (242) = 0.198e-1, (243) = 0.194e-1, (244) = 0.181e-1, (245) = 0.159e-1, (246) = 0.122e-1, (247) = 0.80e-2, (248) = 0.34e-2, (249) = -0.9e-3, (250) = -0.41e-2, (251) = -0.68e-2, (252) = -0.87e-2, (253) = -0.98e-2, (254) = -0.103e-1, (255) = -0.103e-1, (256) = -0.98e-2, (257) = -0.92e-2, (258) = -0.86e-2, (259) = -0.80e-2, (260) = -0.76e-2, (261) = -0.75e-2, (262) = -0.77e-2, (263) = -0.82e-2, (264) = -0.89e-2, (265) = -0.98e-2, (266) = -0.109e-1, (267) = -0.117e-1, (268) = -0.121e-1, (269) = -0.119e-1, (270) = -0.111e-1, (271) = -0.96e-2, (272) = -0.74e-2, (273) = -0.46e-2, (274) = -0.7e-3, (275) = 0.36e-2, (276) = 0.80e-2, (277) = 0.121e-1, (278) = 0.150e-1, (279) = 0.173e-1, (280) = 0.188e-1, (281) = 0.193e-1, (282) = 0.189e-1, (283) = 0.176e-1, (284) = 0.155e-1, (285) = 0.128e-1, (286) = 0.98e-2, (287) = 0.67e-2, (288) = 0.38e-2, (289) = 0.15e-2, (290) = -0.1e-3, (291) = -0.12e-2, (292) = -0.18e-2, (293) = -0.21e-2, (294) = -0.22e-2, (295) = -0.22e-2, (296) = -0.21e-2, (297) = -0.22e-2, (298) = -0.24e-2, (299) = -0.27e-2, (300) = -0.33e-2, (301) = -0.42e-2, (302) = -0.54e-2, (303) = -0.68e-2, (304) = -0.85e-2, (305) = -0.103e-1, (306) = -0.130e-1, (307) = -0.154e-1, (308) = -0.170e-1, (309) = -0.177e-1, (310) = -0.173e-1, (311) = -0.160e-1, (312) = -0.138e-1, (313) = -0.108e-1, (314) = -0.75e-2, (315) = -0.38e-2, (316) = -0., (317) = 0.37e-2, (318) = 0.71e-2, (319) = 0.101e-1, (320) = 0.124e-1, (321) = 0.141e-1, (322) = 0.149e-1, (323) = 0.152e-1, (324) = 0.152e-1, (325) = 0.149e-1})

_rtable[18446746442173411926]

(1)

``

t := Vector(325, {(1) = 0, (2) = 0.67e-2, (3) = 0.134e-1, (4) = 0.202e-1, (5) = 0.269e-1, (6) = 0.336e-1, (7) = 0.403e-1, (8) = 0.471e-1, (9) = 0.538e-1, (10) = 0.637e-1, (11) = 0.736e-1, (12) = 0.836e-1, (13) = 0.935e-1, (14) = .1098, (15) = .1261, (16) = .1424, (17) = .1586, (18) = .1764, (19) = .1943, (20) = .2121, (21) = .2299, (22) = .2465, (23) = .2632, (24) = .2798, (25) = .2965, (26) = .3109, (27) = .3253, (28) = .3397, (29) = .3542, (30) = .3686, (31) = .3830, (32) = .3974, (33) = .4118, (34) = .4284, (35) = .4450, (36) = .4615, (37) = .4781, (38) = .4938, (39) = .5095, (40) = .5253, (41) = .5410, (42) = .5567, (43) = .5724, (44) = .5882, (45) = .6039, (46) = .6204, (47) = .6368, (48) = .6533, (49) = .6697, (50) = .6843, (51) = .6989, (52) = .7135, (53) = .7281, (54) = .7448, (55) = .7615, (56) = .7781, (57) = .7948, (58) = .8113, (59) = .8278, (60) = .8442, (61) = .8607, (62) = .8775, (63) = .8943, (64) = .9112, (65) = .9280, (66) = .9468, (67) = .9655, (68) = .9843, (69) = 1.0031, (70) = 1.0190, (71) = 1.0348, (72) = 1.0507, (73) = 1.0665, (74) = 1.0794, (75) = 1.0924, (76) = 1.1053, (77) = 1.1183, (78) = 1.1312, (79) = 1.1442, (80) = 1.1571, (81) = 1.1700, (82) = 1.1842, (83) = 1.1984, (84) = 1.2126, (85) = 1.2268, (86) = 1.2459, (87) = 1.2651, (88) = 1.2842, (89) = 1.3034, (90) = 1.3198, (91) = 1.3362, (92) = 1.3527, (93) = 1.3691, (94) = 1.3844, (95) = 1.3996, (96) = 1.4149, (97) = 1.4302, (98) = 1.4454, (99) = 1.4607, (100) = 1.4760, (101) = 1.4913, (102) = 1.5075, (103) = 1.5238, (104) = 1.5400, (105) = 1.5563, (106) = 1.5733, (107) = 1.5904, (108) = 1.6075, (109) = 1.6246, (110) = 1.6410, (111) = 1.6574, (112) = 1.6739, (113) = 1.6903, (114) = 1.7021, (115) = 1.7140, (116) = 1.7258, (117) = 1.7377, (118) = 1.7495, (119) = 1.7614, (120) = 1.7732, (121) = 1.7851, (122) = 1.7964, (123) = 1.8076, (124) = 1.8189, (125) = 1.8302, (126) = 1.8475, (127) = 1.8649, (128) = 1.8822, (129) = 1.8995, (130) = 1.9168, (131) = 1.9341, (132) = 1.9514, (133) = 1.9687, (134) = 1.9856, (135) = 2.0026, (136) = 2.0195, (137) = 2.0365, (138) = 2.0507, (139) = 2.0649, (140) = 2.0791, (141) = 2.0933, (142) = 2.1075, (143) = 2.1217, (144) = 2.1359, (145) = 2.1501, (146) = 2.1674, (147) = 2.1846, (148) = 2.2018, (149) = 2.2191, (150) = 2.2341, (151) = 2.2492, (152) = 2.2643, (153) = 2.2793, (154) = 2.2949, (155) = 2.3105, (156) = 2.3261, (157) = 2.3417, (158) = 2.3576, (159) = 2.3735, (160) = 2.3895, (161) = 2.4054, (162) = 2.4203, (163) = 2.4353, (164) = 2.4503, (165) = 2.4653, (166) = 2.4839, (167) = 2.5025, (168) = 2.5211, (169) = 2.5397, (170) = 2.5561, (171) = 2.5725, (172) = 2.5888, (173) = 2.6052, (174) = 2.6226, (175) = 2.6399, (176) = 2.6572, (177) = 2.6746, (178) = 2.6930, (179) = 2.7114, (180) = 2.7297, (181) = 2.7481, (182) = 2.7634, (183) = 2.7787, (184) = 2.7940, (185) = 2.8094, (186) = 2.8226, (187) = 2.8358, (188) = 2.8490, (189) = 2.8622, (190) = 2.8755, (191) = 2.8887, (192) = 2.9019, (193) = 2.9151, (194) = 2.9302, (195) = 2.9453, (196) = 2.9604, (197) = 2.9755, (198) = 2.9940, (199) = 3.0126, (200) = 3.0311, (201) = 3.0496, (202) = 3.0659, (203) = 3.0822, (204) = 3.0985, (205) = 3.1149, (206) = 3.1302, (207) = 3.1455, (208) = 3.1609, (209) = 3.1762, (210) = 3.1915, (211) = 3.2069, (212) = 3.2222, (213) = 3.2375, (214) = 3.2545, (215) = 3.2715, (216) = 3.2885, (217) = 3.3055, (218) = 3.3223, (219) = 3.3391, (220) = 3.3560, (221) = 3.3728, (222) = 3.3888, (223) = 3.4047, (224) = 3.4206, (225) = 3.4365, (226) = 3.4494, (227) = 3.4622, (228) = 3.4750, (229) = 3.4879, (230) = 3.5007, (231) = 3.5136, (232) = 3.5264, (233) = 3.5392, (234) = 3.5529, (235) = 3.5667, (236) = 3.5804, (237) = 3.5941, (238) = 3.6116, (239) = 3.6292, (240) = 3.6468, (241) = 3.6644, (242) = 3.6810, (243) = 3.6976, (244) = 3.7143, (245) = 3.7309, (246) = 3.7508, (247) = 3.7707, (248) = 3.7905, (249) = 3.8104, (250) = 3.8273, (251) = 3.8442, (252) = 3.8610, (253) = 3.8779, (254) = 3.8938, (255) = 3.9096, (256) = 3.9255, (257) = 3.9414, (258) = 3.9559, (259) = 3.9705, (260) = 3.9851, (261) = 3.9997, (262) = 4.0149, (263) = 4.0301, (264) = 4.0452, (265) = 4.0604, (266) = 4.0779, (267) = 4.0953, (268) = 4.1128, (269) = 4.1302, (270) = 4.1459, (271) = 4.1615, (272) = 4.1771, (273) = 4.1927, (274) = 4.2114, (275) = 4.2300, (276) = 4.2486, (277) = 4.2673, (278) = 4.2833, (279) = 4.2993, (280) = 4.3153, (281) = 4.3313, (282) = 4.3485, (283) = 4.3657, (284) = 4.3829, (285) = 4.4001, (286) = 4.4182, (287) = 4.4362, (288) = 4.4543, (289) = 4.4724, (290) = 4.4881, (291) = 4.5037, (292) = 4.5194, (293) = 4.5351, (294) = 4.5472, (295) = 4.5593, (296) = 4.5715, (297) = 4.5836, (298) = 4.5957, (299) = 4.6079, (300) = 4.6200, (301) = 4.6321, (302) = 4.6456, (303) = 4.6591, (304) = 4.6726, (305) = 4.6861, (306) = 4.7059, (307) = 4.7256, (308) = 4.7454, (309) = 4.7652, (310) = 4.7819, (311) = 4.7986, (312) = 4.8153, (313) = 4.8320, (314) = 4.8474, (315) = 4.8627, (316) = 4.8781, (317) = 4.8935, (318) = 4.9088, (319) = 4.9242, (320) = 4.9396, (321) = 4.9550, (322) = 4.9662, (323) = 4.9775, (324) = 4.9887, (325) = 5.0000})

_rtable[18446746442112534638]

(2)

``


 

Download mode_shapes.mw

Hi guys, Maple always shows the same result when I use sqrt() function

How can I fix it? Thanks

 

This is a simple model of the covid infection as it applies here, down under, without the use of any de's like

https://www.mapleprimes.com/posts/212100-Exploring-The-CoVid19-Outbreak

I'm told a substantial number of people do recover within 45 days ....
So on the 45th day 1 person has recovered, on day 50 two people have recovered and so on.

Just want to know how to write this sequence...

Covid_dbling.mw

 I have a problem about extremal function.

The function is shown below with restricted condition of x and a:  x>=2 and -1 < a <0.

(x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)

I guess that  it's minimum value is greater than 0.  In other words,  I want prove that  (x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)>0

when I use Minimize function,

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<a, a<0})

I 'm not seeing but Error, (in Optimization:-NLPSolve) strict inequalities are not valid constraints. I cannot but add the condition of equality of a : -1<=a, a<=0.

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<=a, a<=0})

A result is returned with a warning:
Warning, no iterations performed as initial point satisfies first-order conditions
[0.000000, [a = -2.225074*10^(-308), x = 2.000000]]

 

Local or Global ?

When I read recent question post 

https://www.mapleprimes.com/questions/229132-Maximize-Function-Does-Not-Work?ref=Feed:MaplePrimes:New%20Questions

 I'm worrying  that Maple only returns local  extremun. So I use the freely  maple package DirectSearch. We can get it from  https://www.maplesoft.com/applications/view.aspx?SID=101333.

DirectSearch:-GlobalOptima(-((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)),{x>=2, -1<a, a<0},maximize);

 Note: I add a  minus sign to find maximize value .

It returns: [0.002264, [a = -0.000203, x = 1.019590*10^13], 605]

But I substitute the value of a and x  into the function,it returns strange result:   4078.360000 not  -0.002264.

I’m confused.. 

I try to use  Mathematica, 

NMinimize[{(x - 3/2)^a - (x - 1)^
    a + (1 - 2^(a - 1))*((x - 3/2)^a - (x - 1/2)^a) - 
   x*((x - 3/2)^a + x^a - (x - 1/2)^a - (x - 1)^a), 
  x >= 2 && a > -1 && a <= 0}, {x, a}]

It retruns {0., {x -> 13.256, a -> 0.}}  May be well.

 

mimimize.mw

 

i need to create a table with information from plots like how many times x become 0

this is the way to make an null oscillation 

please help!

Any  idea is good for me !

 

According to Wikipedia  https://www.wikidata.org/wiki/Q3115604 ,

Outerplanar graph  is a graph that can be drawn without crossings in the plane (means it is planar graph) with all vertices on the outer face.  

For example 

 

Recently  in my project, I  need to judge whether a planar graph is a  outerplanar graph.

I tried to find some algorithms but failed. 

Maple  only considers how to test wheather a graph is  planar.

like following:

with(GraphTheory):
with(SpecialGraphs)
K4 := CompleteGraph(4)
IsPlanar(K4, 'F')

Hello,

 

 

 

restart; with(Physics); Setup(mathematicalnotation = true); Setup(dimension = 3, metric = Euclidean, spacetimeindices = lowercaselatin); g_[]; Define(X[i], P[k]); Setup(quantumop = {P, X}, algebrarules = {%Commutator(P[i], P[j]) = 0, %Commutator(X[i], X[j]) = 0, %Commutator(X[j], P[k]) = Physics:-`*`(I, g_[j, k])}); L2 := Simplify(Physics:-`^`(Physics:-`*`(Physics:-`*`(LeviCivita[i, j, k], X[j]), P[k]), 2)); L2X := Simplify(Commutator(L2, X[k])); L2L2X__1 := Simplify(Commutator(L2, L2X)); L2L2X__2 := Simplify(Expand(AntiCommutator(Physics:-`*`(2, L2), X[k]))); Simplify(L2L2X__1-L2L2X__2)

[mathematicalnotation = true]

 

`The dimension and signature of the tensor space are set to `[3, `- - +`]

 

`The Euclidean metric in cartesian coordinates`

 

`Changing the signature of the tensor spacetime to: `*`+ + +`

 

[dimension = 3, metric = {(1, 1) = 1, (2, 2) = 1, (3, 3) = 1}, spacetimeindices = lowercaselatin]

 

Physics:-g_[a, b] = Matrix(%id = 18446746397905475934)

 

`Defined objects with tensor properties`

 

{Physics:-Dgamma[a], P[k], Physics:-Psigma[a], X[i], Physics:-d_[a], Physics:-g_[a, b], Physics:-LeviCivita[a, b, c]}

 

`* Partial match of  '`*quantumop*`' against keyword '`*quantumoperators*`' `

 

_______________________________________________________

 

[algebrarules = {%Commutator(P[i], P[j]) = 0, %Commutator(X[i], X[j]) = 0, %Commutator(X[j], P[k]) = I*Physics:-g_[j, k]}, quantumoperators = {P, X}]

 

(2*I)*Physics:-`*`(X[j], P[j])+Physics:-`*`(Physics:-`^`(X[j], 2), Physics:-`^`(P[k], 2))-Physics:-`*`(X[j], X[k], P[j], P[k])

 

2*X[k]-(2*I)*Physics:-`*`(Physics:-`^`(X[b], 2), P[k])+(2*I)*Physics:-`*`(X[c], X[k], P[c])

 

(12*I)*Physics:-`*`(X[c], X[k], P[c])-(4*I)*Physics:-`*`(Physics:-`^`(X[b], 2), P[k])+4*X[k]+4*Physics:-`*`(Physics:-`^`(X[b], 2), X[k], Physics:-`^`(P[h], 2))-4*Physics:-`*`(X[a], Physics:-`^`(X[b], 2), P[a], P[k])+4*Physics:-`*`(Physics:-`^`(X[b], 2), X[f], P[f], P[k])-4*Physics:-`*`(X[f], X[i], X[k], P[f], P[i])

 

4*X[k]+(12*I)*Physics:-`*`(X[c], X[k], P[c])+4*Physics:-`*`(Physics:-`^`(X[b], 2), X[k], Physics:-`^`(P[d], 2))-(4*I)*Physics:-`*`(Physics:-`^`(X[b], 2), P[k])-4*Physics:-`*`(X[e], X[f], X[k], P[e], P[f])

 

0

(1)

NULL

 

 

 

 

Download Commutator_Algebra_with_L2.mw

 

 

 

I have the following issue.

The way it is set at the moment, works kinda in that the final result is 0, which I tried to check.

However, the expression L2L2X[1] is not fully Simplified, since the term

-(4*X[a])*X[b]^2*P[a]*P[k] + (4*X[b]^2)*X[f]*P[f]*P[k]

is actually zero. I suppose that he doesn't manage because of the different indices "a" and "f" here. How can this be fixed?

 

When I comment out "Define" and use "Coordinates(X,P)" instead, it doesn't work. Seems to give the wrong result (Difference is not zero).

 

Hey,

I'm trying to differentiate a function but whenever I do so, it adds new variables for some reason. I think I might be able to copy the new function and just delete the extra but it is not a good solution.

 

So I'm hoping someone could help me to figure out how to remove all this extra that Maple adds to my equation. Thanks in advance.

 

I was working through an old text book, trying to understand a different problem.  I came across this problem in an exercise set and thought it was simple.  Until I tried it.

The difficlty I had was in using subs to substitute all values.  I had to use subs 2 or 3 times to get all substitutions.  How can I avoid this?

## Prove if F is the fibonacci sequence,
restart;
with(combinat, fibonacci):
F := n -> fibonacci(n);  ## F(n+1) = F(n)+F(n-1); F(1) = 1;
## the problem
P := n-> F(n+1)*F(n+2) - F(n)*F(n+3);
##
check_low := proc(n)
    local idx;
    for idx to n do
        print(P(idx),(-1)^idx);
    end do;
end proc;
check_low(1);
check_low(2);
check_low(3);
check_low(4);

## Assume true for n=k
A := P(k) = (-1)^k;

notation := { F(k)   = a,
              F(k+1) = b,
              F(k+2) = c,
              F(k+3) = d,
              F(k+4) = e };

## some fibonacci definitions
fibs := [ e = c + d,  d = b + c, c = a + b ];

eq1 := subs(notation,A);
eq1 := subs(fibs,eq1);
eq1 := subs(fibs,eq1);  ## have to repeat to get only a and b in the expression

eq2 := subs(notation,P(k+1));
eq2 := subs(fibs, eq2);
eq2 := subs(fibs, eq2);
eq2 := subs(fibs, eq2);  ## have to repeat to get only a and b in the expression
## Reduce eq2 to (-1)^(k+1)
simplify(eq2 = -lhs(eq1));
verify(eq2, -lhs(eq1), equal);
evalb(eq2); simplify(%);  ## Ah, this is why I need equal in verify.
evalb(-lhs(eq1)); simplify(%);

testeq(eq2, -lhs(eq1));

 

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