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Sharing content between worksheets...

Asked by: mskalsi 290
worksheet import
May 30 2016
2  5

Is it possible to share contents between two different Maple worksheets ? Suppose for example, I want to use certain expression number (10) of  Worksheet 1 in worksheet 2, can I call that expression (10) in worksheet 2 ? I am asking this question because copying expressions between different worksheets is not easy task, sometime we unable copy expressions when they are too large. In my case after carrying out very tedious and lengthy calculations Maple stopped responding, now I have an idea that if I import last output of present worksheet in new worksheet may be I could continue my calculations.

Regards

Displaying 2D plot and 3D plot together?...

Asked by: J4James 355
May 30 2016
0  11

I am having trouble to display a 3d and a 2d plots in a same figure. I tried with the display command but no luck.

f1:=exp(x*y);

plot3d(f1,x=0..1,y=0..1);

p1:=%:

f2:=exp(x);

plot(f2,x=0..1);

p2:=%:

To combine both I used display

display(p1,p2);

I ends up with a structure error

The second question is how to plot f(x,y,z)=exp(x+y+z)?

Thanks

Forcing Maple to give desired output...

Asked by: mskalsi 290
output
May 30 2016
0  2


Suppose I type certain math expression like as follow:

> 

F^5*alpha[5]+F^4*G*gamma[1]+F*G^4*gamma[3]+G^5*beta[5]+F^4*alpha[4]+G^4*beta[4]+F^3*alpha[3]+F^2*G*gamma[2]+F*G^2*gamma[4]+G^3*beta[3]+F^2*alpha[2]+F*G*gamma[5]+G^2*beta[2]+F*alpha[1]+G*beta[1]+delta[0]

F^5*alpha[5]+F^4*G*gamma[1]+F*G^4*gamma[3]+G^5*beta[5]+F^4*alpha[4]+G^4*beta[4]+F^3*alpha[3]+F^2*G*gamma[2]+F*G^2*gamma[4]+G^3*beta[3]+F^2*alpha[2]+F*G*gamma[5]+G^2*beta[2]+F*alpha[1]+G*beta[1]+delta[0]

 (1)

But when I enter this expression, Maple gives totally different look to this expression, can I force Maple to print similar looking expression as I typed in command line ? I mean without change of  position of intermediates and coefficients.


Download Forcing_Maple_Output.mw

Regards

How to do composite differentiaition? ...

Asked by: mskalsi 290
differentiation
May 26 2016
1  7

Please help me to differentiate function "u" wrt t in following manner:

 

> 

with(PDEtools):

-t*c[2]*k[2]+x*k[2]

 (1)
> 

DepVars := [F(xi), G(xi)]

[F(xi), G(xi)]

 (2)
> 

alias(F = F(xi), G = G(eta))

F, G

 (3)
> 

declare(F, G(xi))

F(xi)*`will now be displayed as`*F

  

G(xi)*`will now be displayed as`*G

 (4)
> 

u := a[0]+(F*a[1]+G*a[2]+kappa[1])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))+(F^2*a[3]+F*G*a[4]+G^2*a[5]+kappa[2])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))^2

a[0]+(a[1]*F+a[2]*G+kappa[1])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))+(a[3]*F^2+a[4]*F*G+a[5]*G^2+kappa[2])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))^2

 (5)
> 

xi := -t*c[1]*k[1]+x*k[1]; 1; eta := -t*c[2]*k[2]+x*k[2]

-t*c[1]*k[1]+x*k[1]

  

-t*c[2]*k[2]+x*k[2]

 (6)
> 

diff(u, t)

Error, invalid input: diff received -t*c[1]*k[1]+x*k[1], which is not valid for its 2nd argument

  
> 

``

 

Download [1063]_Sub-equation_Method.mw

Regards

Shaded region ...

Asked by: kelvin goh 25
region
May 25 2016
1  3

I had another problem whereby I need to shaded a region between y=ln(x+2) , y-axis and y=-1 to y= 2. What is the suitable comand I shall apply ( Maple 18)

Block Matrix assembly problem...

Asked by: Ronan 1022
syntax
May 24 2016
1  10


Trying to build a block matrix. Having a problem getting the syntax correct. Can't add in the predefind matrices to the lower band.

restart

with(LinearAlgebra):

interface(displayprecision = 5)

5

 (1)

interface(rtablesize = 81)

10

 (2)

S := 2

2

 (3)

dmax := 7

7

 (4)

CCnew0 := Matrix(2, 2, {(1, 1) = 336750255587/3769550688757, (1, 2) = -14853552191797/1696297809940650, (2, 1) = 665096091/76929605893, (2, 2) = 1328910382993/11539440883950})

CCnew0 := Matrix(2, 2, {(1, 1) = 336750255587/3769550688757, (1, 2) = -14853552191797/1696297809940650, (2, 1) = 665096091/76929605893, (2, 2) = 1328910382993/11539440883950})

 (5)

CCnew1 := Matrix(2, 2, {(1, 1) = 49655436033349/56543260331355, (1, 2) = -75647656451147/1413581508283875, (2, 1) = 29849106694/384648029465, (2, 2) = 10591394356218/9616200736625})

CCnew1 := Matrix(2, 2, {(1, 1) = 49655436033349/56543260331355, (1, 2) = -75647656451147/1413581508283875, (2, 1) = 29849106694/384648029465, (2, 2) = 10591394356218/9616200736625})

 (6)

CCnew2 := Matrix(2, 2, {(1, 1) = 299962512141959/80776086187650, (1, 2) = -1231816081155781/8481489049703250, (2, 1) = 155175716729/549497184950, (2, 2) = 260449617208489/57697204419750})

CCnew2 := Matrix(2, 2, {(1, 1) = 299962512141959/80776086187650, (1, 2) = -1231816081155781/8481489049703250, (2, 1) = 155175716729/549497184950, (2, 2) = 260449617208489/57697204419750})

 (7)

CCnew3 := Matrix(2, 2, {(1, 1) = 50445725001719/5769720441975, (1, 2) = -9065291388901/40388043093825, (2, 1) = 21111399914/39249798925, (2, 2) = 2819495262394/274748592475})

CCnew3 := Matrix(2, 2, {(1, 1) = 50445725001719/5769720441975, (1, 2) = -9065291388901/40388043093825, (2, 1) = 21111399914/39249798925, (2, 2) = 2819495262394/274748592475})

 (8)

CCnew4 := Matrix(2, 2, {(1, 1) = 142685068141037/11539440883950, (1, 2) = -116560067351321/565432603313550, (2, 1) = 44654487647/78499597850, (2, 2) = 53741323977599/3846480294650})

CCnew4 := Matrix(2, 2, {(1, 1) = 142685068141037/11539440883950, (1, 2) = -116560067351321/565432603313550, (2, 1) = 44654487647/78499597850, (2, 2) = 53741323977599/3846480294650})

 (9)

CCnew5 := Matrix(2, 2, {(1, 1) = 60560690824604/5769720441975, (1, 2) = -88774498025543/848148904970325, (2, 1) = 12484906049/39249798925, (2, 2) = 65745570806567/5769720441975})

CCnew5 := Matrix(2, 2, {(1, 1) = 60560690824604/5769720441975, (1, 2) = -88774498025543/848148904970325, (2, 1) = 12484906049/39249798925, (2, 2) = 65745570806567/5769720441975})

 (10)

CCnew6 := Matrix(2, 2, {(1, 1) = 20398649489879/4121228887125, (1, 2) = -5446073753219/242328258562950, (2, 1) = 14465459393/196248994625, (2, 2) = 8502096238511/1648491554850})

CCnew6 := Matrix(2, 2, {(1, 1) = 20398649489879/4121228887125, (1, 2) = -5446073753219/242328258562950, (2, 1) = 14465459393/196248994625, (2, 2) = 8502096238511/1648491554850})

 (11)

S*dmax

14

 (12)

M1 := Matrix(S*dmax, S*dmax, [Matrix(S*(dmax-1), S), Matrix(S*(dmax-1), shape = identity), Matrix(S, S*dmax, [seq(-CCnew || n, n = 0 .. dmax-1)])])

Error, (in Matrix) this entry is too tall or too short: Matrix(2, 14, {(1, 1) = -336750255587/3769550688757, (1, 2) = 14853552191797/1696297809940650, (1, 3) = -49655436033349/56543260331355, (1, 4) = 75647656451147/1413581508283875, (1, 5) = -299962512141959/80776086187650, (1, 6) = 1231816081155781/8481489049703250, (1, 7) = -50445725001719/5769720441975, (1, 8) = 9065291388901/40388043093825, (1, 9) = -142685068141037/11539440883950, (1, 10) = 116560067351321/565432603313550, (1, 11) = -60560690824604/5769720441975, (1, 12) = 88774498025543/848148904970325, (1, 13) = -20398649489879/4121228887125, (1, 14) = 5446073753219/242328258562950, ...

  

M2 := Matrix(S*dmax, S*dmax, [Matrix(S*(dmax-1), S), Matrix(S*(dmax-1), shape = identity)])

M2 := Matrix(14, 14, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 1, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 1, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 1, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 1, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (5, 7) = 1, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 0, (6, 8) = 1, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 1, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (8, 10) = 1, (8, 11) = 0, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 1, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = 0, (10, 12) = 1, (10, 13) = 0, (10, 14) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 1, (11, 14) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = 0, (12, 13) = 0, (12, 14) = 1, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = 0})

 (13)

lowerband := Matrix(S, S*dmax, [seq(-evalf(CCnew || n), n = 0 .. dmax-1)])

lowerband := Matrix(2, 14, {(1, 1) = -0.893343e-1, (1, 2) = 0.875645e-2, (1, 3) = -.878185, (1, 4) = 0.535149e-1, (1, 5) = -3.71351, (1, 6) = .145236, (1, 7) = -8.74318, (1, 8) = .224455, (1, 9) = -12.36499, (1, 10) = .206143, (1, 11) = -10.49630, (1, 12) = .104669, (1, 13) = -4.94965, (1, 14) = 0.224740e-1, (2, 1) = -0.864552e-2, (2, 2) = -.115162, (2, 3) = -0.776011e-1, (2, 4) = -1.10141, (2, 5) = -.282396, (2, 6) = -4.51408, (2, 7) = -.537873, (2, 8) = -10.26209, (2, 9) = -.568850, (2, 10) = -13.97156, (2, 11) = -.318088, (2, 12) = -11.39493, (2, 13) = -0.737097e-1, (2, 14) = -5.15750})

 (14)

M3 := Matrix(S*dmax, S*dmax, [Matrix(S*(dmax-1), S), Matrix(S*(dmax-1), shape = identity), lowerband])

Error, (in Matrix) this entry is too tall or too short: Matrix(2, 14, {(1, 1) = -0.8933432215e-1, (1, 2) = 0.8756453086e-2, (1, 3) = -.8781848755, (1, 4) = 0.5351488825e-1, (1, 5) = -3.713506389, (1, 6) = .1452358276, (1, 7) = -8.743183575, (1, 8) = .224454831, (1, 9) = -12.36498974, (1, 10) = .2061431666, (1, 11) = -10.49629552, (1, 12) = .1046685287, (1, 13) = -4.949652167, (1, 14) = 0.2247395242e-1, (2, 1) = -0.8645515381e-2, (2, 2) = -.1151624586, (2, 3) = -0.7760109089e-1, (2, 4) = -1.101411529, (2, 5) = -.2823958356, (2, 6) = -4.514076892, (2, 7) = -.537872817, (2, 8) = -10.26209174, (2, 9) = -.5688498906, (2, 10) = -13.97155838, (2, 1...

  

``


Download Test_Block_matrix.mw

restart

with(LinearAlgebra):

interface(displayprecision = 5)

5

 (1)

interface(rtablesize = 81)

10

 (2)

S := 2

2

 (3)

dmax := 7

7

 (4)

CCnew0 := Matrix(2, 2, {(1, 1) = 336750255587/3769550688757, (1, 2) = -14853552191797/1696297809940650, (2, 1) = 665096091/76929605893, (2, 2) = 1328910382993/11539440883950})

CCnew0 := Matrix(2, 2, {(1, 1) = 336750255587/3769550688757, (1, 2) = -14853552191797/1696297809940650, (2, 1) = 665096091/76929605893, (2, 2) = 1328910382993/11539440883950})

 (5)

CCnew1 := Matrix(2, 2, {(1, 1) = 49655436033349/56543260331355, (1, 2) = -75647656451147/1413581508283875, (2, 1) = 29849106694/384648029465, (2, 2) = 10591394356218/9616200736625})

CCnew1 := Matrix(2, 2, {(1, 1) = 49655436033349/56543260331355, (1, 2) = -75647656451147/1413581508283875, (2, 1) = 29849106694/384648029465, (2, 2) = 10591394356218/9616200736625})

 (6)

CCnew2 := Matrix(2, 2, {(1, 1) = 299962512141959/80776086187650, (1, 2) = -1231816081155781/8481489049703250, (2, 1) = 155175716729/549497184950, (2, 2) = 260449617208489/57697204419750})

CCnew2 := Matrix(2, 2, {(1, 1) = 299962512141959/80776086187650, (1, 2) = -1231816081155781/8481489049703250, (2, 1) = 155175716729/549497184950, (2, 2) = 260449617208489/57697204419750})

 (7)

CCnew3 := Matrix(2, 2, {(1, 1) = 50445725001719/5769720441975, (1, 2) = -9065291388901/40388043093825, (2, 1) = 21111399914/39249798925, (2, 2) = 2819495262394/274748592475})

CCnew3 := Matrix(2, 2, {(1, 1) = 50445725001719/5769720441975, (1, 2) = -9065291388901/40388043093825, (2, 1) = 21111399914/39249798925, (2, 2) = 2819495262394/274748592475})

 (8)

CCnew4 := Matrix(2, 2, {(1, 1) = 142685068141037/11539440883950, (1, 2) = -116560067351321/565432603313550, (2, 1) = 44654487647/78499597850, (2, 2) = 53741323977599/3846480294650})

CCnew4 := Matrix(2, 2, {(1, 1) = 142685068141037/11539440883950, (1, 2) = -116560067351321/565432603313550, (2, 1) = 44654487647/78499597850, (2, 2) = 53741323977599/3846480294650})

 (9)

CCnew5 := Matrix(2, 2, {(1, 1) = 60560690824604/5769720441975, (1, 2) = -88774498025543/848148904970325, (2, 1) = 12484906049/39249798925, (2, 2) = 65745570806567/5769720441975})

CCnew5 := Matrix(2, 2, {(1, 1) = 60560690824604/5769720441975, (1, 2) = -88774498025543/848148904970325, (2, 1) = 12484906049/39249798925, (2, 2) = 65745570806567/5769720441975})

 (10)

CCnew6 := Matrix(2, 2, {(1, 1) = 20398649489879/4121228887125, (1, 2) = -5446073753219/242328258562950, (2, 1) = 14465459393/196248994625, (2, 2) = 8502096238511/1648491554850})

CCnew6 := Matrix(2, 2, {(1, 1) = 20398649489879/4121228887125, (1, 2) = -5446073753219/242328258562950, (2, 1) = 14465459393/196248994625, (2, 2) = 8502096238511/1648491554850})

 (11)

S*dmax

14

 (12)

M1 := Matrix(S*dmax, S*dmax, [Matrix(S*(dmax-1), S), Matrix(S*(dmax-1), shape = identity), Matrix(S, S*dmax, [seq(-CCnew || n, n = 0 .. dmax-1)])])

Error, (in Matrix) this entry is too tall or too short: Matrix(2, 14, {(1, 1) = -336750255587/3769550688757, (1, 2) = 14853552191797/1696297809940650, (1, 3) = -49655436033349/56543260331355, (1, 4) = 75647656451147/1413581508283875, (1, 5) = -299962512141959/80776086187650, (1, 6) = 1231816081155781/8481489049703250, (1, 7) = -50445725001719/5769720441975, (1, 8) = 9065291388901/40388043093825, (1, 9) = -142685068141037/11539440883950, (1, 10) = 116560067351321/565432603313550, (1, 11) = -60560690824604/5769720441975, (1, 12) = 88774498025543/848148904970325, (1, 13) = -20398649489879/4121228887125, (1, 14) = 5446073753219/242328258562950, ...

  

M2 := Matrix(S*dmax, S*dmax, [Matrix(S*(dmax-1), S), Matrix(S*(dmax-1), shape = identity)])

M2 := Matrix(14, 14, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 1, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 1, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 1, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 1, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (5, 7) = 1, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 0, (6, 8) = 1, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 1, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (8, 10) = 1, (8, 11) = 0, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 1, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = 0, (10, 12) = 1, (10, 13) = 0, (10, 14) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 1, (11, 14) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = 0, (12, 13) = 0, (12, 14) = 1, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = 0})

 (13)

lowerband := Matrix(S, S*dmax, [seq(-evalf(CCnew || n), n = 0 .. dmax-1)])

lowerband := Matrix(2, 14, {(1, 1) = -0.893343e-1, (1, 2) = 0.875645e-2, (1, 3) = -.878185, (1, 4) = 0.535149e-1, (1, 5) = -3.71351, (1, 6) = .145236, (1, 7) = -8.74318, (1, 8) = .224455, (1, 9) = -12.36499, (1, 10) = .206143, (1, 11) = -10.49630, (1, 12) = .104669, (1, 13) = -4.94965, (1, 14) = 0.224740e-1, (2, 1) = -0.864552e-2, (2, 2) = -.115162, (2, 3) = -0.776011e-1, (2, 4) = -1.10141, (2, 5) = -.282396, (2, 6) = -4.51408, (2, 7) = -.537873, (2, 8) = -10.26209, (2, 9) = -.568850, (2, 10) = -13.97156, (2, 11) = -.318088, (2, 12) = -11.39493, (2, 13) = -0.737097e-1, (2, 14) = -5.15750})

 (14)

M3 := Matrix(S*dmax, S*dmax, [Matrix(S*(dmax-1), S), Matrix(S*(dmax-1), shape = identity), lowerband])

Error, (in Matrix) this entry is too tall or too short: Matrix(2, 14, {(1, 1) = -0.8933432215e-1, (1, 2) = 0.8756453086e-2, (1, 3) = -.8781848755, (1, 4) = 0.5351488825e-1, (1, 5) = -3.713506389, (1, 6) = .1452358276, (1, 7) = -8.743183575, (1, 8) = .224454831, (1, 9) = -12.36498974, (1, 10) = .2061431666, (1, 11) = -10.49629552, (1, 12) = .1046685287, (1, 13) = -4.949652167, (1, 14) = 0.2247395242e-1, (2, 1) = -0.8645515381e-2, (2, 2) = -.1151624586, (2, 3) = -0.7760109089e-1, (2, 4) = -1.101411529, (2, 5) = -.2823958356, (2, 6) = -4.514076892, (2, 7) = -.537872817, (2, 8) = -10.26209174, (2, 9) = -.5688498906, (2, 10) = -13.97155838, (2, 1...

  

``


Download Test_Block_matrix.mw

The factor option for implicitplot3d?...

Asked by: abhilashun 20
options factor implicitplot3d
May 21 2016
1  5

For implicitplot of say (cos(\theta))^2, I had to use 'factor' in the options for the plot so that it considers cos(theta) also while plotting. But I couldn't do the same in implicitplot3d. How can I achieve this plotting of all factors of a function for implicitplot3d?

How to find all ideals in this?...

Asked by: mskalsi 290
radical series ideal
May 18 2016
2  0

Dear All

Using Lie algebra package in Maple we can easily find nilradical for given abstract algebra, but how we can find all the ideal in lower central series by taking new basis as nilradical itself?

Please see following;

 

> 

with(DifferentialGeometry); with(LieAlgebras)
> 

DGsetup([x, y, t, u, v])

`frame name: Euc`

 (1)
Euc > 

VectorFields := evalDG([D_v, D_v*x+D_y*t, 2*D_t*t-2*D_u*u-D_v*v+D_y*y, t*D_v, D_v*y+D_u, D_t, D_x, D_x*t+D_u, 2*D_v*x+D_x*y, -D_t*t+2*D_u*u+2*D_v*v+D_x*x, D_y])

[_DG([["vector", "Euc", []], [[[5], 1]]]), _DG([["vector", "Euc", []], [[[2], t], [[5], x]]]), _DG([["vector", "Euc", []], [[[2], y], [[3], 2*t], [[4], -2*u], [[5], -v]]]), _DG([["vector", "Euc", []], [[[5], t]]]), _DG([["vector", "Euc", []], [[[4], 1], [[5], y]]]), _DG([["vector", "Euc", []], [[[3], 1]]]), _DG([["vector", "Euc", []], [[[1], 1]]]), _DG([["vector", "Euc", []], [[[1], t], [[4], 1]]]), _DG([["vector", "Euc", []], [[[1], y], [[5], 2*x]]]), _DG([["vector", "Euc", []], [[[1], x], [[3], -t], [[4], 2*u], [[5], 2*v]]]), _DG([["vector", "Euc", []], [[[2], 1]]])]

 (2)
Euc > 

L1 := LieAlgebraData(VectorFields)

_DG([["LieAlgebra", "L1", [11]], [[[1, 3, 1], -1], [[1, 10, 1], 2], [[2, 3, 2], -1], [[2, 5, 4], 1], [[2, 6, 11], -1], [[2, 7, 1], -1], [[2, 8, 4], -1], [[2, 9, 5], -1], [[2, 9, 8], 1], [[2, 10, 2], 1], [[3, 4, 4], 3], [[3, 5, 5], 2], [[3, 6, 6], -2], [[3, 8, 8], 2], [[3, 9, 9], 1], [[3, 11, 11], -1], [[4, 6, 1], -1], [[4, 10, 4], 3], [[5, 10, 5], 2], [[5, 11, 1], -1], [[6, 8, 7], 1], [[6, 10, 6], -1], [[7, 9, 1], 2], [[7, 10, 7], 1], [[8, 9, 4], 2], [[8, 10, 8], 2], [[9, 10, 9], 1], [[9, 11, 7], -1]]])

 (3)
Euc > 

DGsetup(L1)

`Lie algebra: L1`

 (4)
L1 > 

MultiplicationTable("LieTable"):
L1 > 

N := Nilradical(L1)

[_DG([["vector", "L1", []], [[[1], 1]]]), _DG([["vector", "L1", []], [[[2], 1]]]), _DG([["vector", "L1", []], [[[4], 1]]]), _DG([["vector", "L1", []], [[[5], 1]]]), _DG([["vector", "L1", []], [[[6], 1]]]), _DG([["vector", "L1", []], [[[7], 1]]]), _DG([["vector", "L1", []], [[[8], 1]]]), _DG([["vector", "L1", []], [[[9], 1]]]), _DG([["vector", "L1", []], [[[11], 1]]])]

 (5)
L1 > 

Query(N, "Nilpotent")

true

 (6)
L1 > 

Query(N, "Solvable")

true

 (7)

Taking N as new basis , how we can find all ideals in lower central series of this solvable ideal N?

 

Download [944]_Structure_of_Lie_algebra.mw

Regards

How to fill a region between three lines?...

Asked by: abhilashun 20
May 16 2016
1  2

Hi all,

I have three points in 3d space say A1=[a11, a12, a13]; A2=[a21, a22, a23] and A3=[a31, a32, a33]. I want to fill the triangle formed by these points. How can I do that?

Thanks is advance.

Delete Matrix rows with complex values...

Asked by: Ronan 1022
delete
May 16 2016
0  5


I wish to delete the rows that have imaginery components from my results Matrix. Have tried many variants of for loops etc.

restart

``

``

interface(displayprecision = 3)

3

 (1)

(2)

``

interface(rtablesize = 81)

10

 (3)

``

``

Ans := Matrix(17, 15, {(1, 1) = `-`, (1, 2) = u0, (1, 3) = u1, (1, 4) = u2, (1, 5) = u3, (1, 6) = P*x, (1, 7) = Py, (1, 8) = Pz, (1, 9) = g0, (1, 10) = g1, (1, 11) = g2, (1, 12) = g3, (1, 13) = u^2, (1, 14) = g^2, (1, 15) = P, (2, 1) = 1, (2, 2) = -.516501806300516366332207827845271720295699875, (2, 3) = .157087667438024041386330713987768482051008262*I, (2, 4) = .113781789011852812312696505223578179747798329*I, (2, 5) = -.877979905726868500805204485093148911811362591, (2, 6) = -45.5583959992909648360043286735679679113587631, (2, 7) = -49.2104104577498887775211368820566392860712299, (2, 8) = -893.5067837*I, (2, 9) = -.866146675707479268632063873487527071333386044, (2, 10) = 0.392015486681650570173437868256055772345022977e-1*I, (2, 11) = -.1411657646*I, (2, 12) = .520820958366521078324036803446408915170112964, (2, 13) = .999999999999999999999999999999999999997268842, (2, 14) = .999999999999999999999999999999999999974976375, (2, 15) = 890.986610791943203054869284606448158021303178*I, (3, 1) = 0, (3, 2) = -.516501806300516366332207827845271720295699875, (3, 3) = -.1570876674*I, (3, 4) = -.1137817890*I, (3, 5) = -.877979905726868500805204485093148911811362591, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (4, 1) = 2, (4, 2) = 1.37465842397864539997343521056744950913464373, (4, 3) = -.4720070715*I, (4, 4) = 1.04887251334709968989772260444378754238846281*I, (4, 5) = -.658208509656740520048240372814155977066034431, (4, 6) = -139.935858043713569770172241394940432701557933, (4, 7) = 1009.16689416507143999697715965318783801532828, (4, 8) = 35.050637050173061427545252165933711014164793*I, (4, 9) = -1.081758215*I, (4, 10) = -.805172606177376737844957657938233921696306905, (4, 11) = 1.28822588438750284892199202326992770781607054, (4, 12) = .370982506039653923963789326359229665746676298*I, (4, 13) = 1.00000000000000000000000000000000000000004448, (4, 14) = 1.00000000000000000000000000000000000002308483, (4, 15) = 1018.21968036744599747318369866423941656487034, (5, 1) = 0, (5, 2) = 1.37465842397864539997343521056744950913464373, (5, 3) = .472007071498869469711464480852290076392886818*I, (5, 4) = -1.048872513*I, (5, 5) = -.658208509656740520048240372814155977066034431, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (6, 1) = 3, (6, 2) = .888607277416217966051928947403779522572804242, (6, 3) = -.106822611437208274601612056689973427508887756, (6, 4) = .227628951666705815052303897780904267397418654, (6, 5) = -.383602784885339918445575993340862111408067307, (6, 6) = -33.2619224164850716022540679651061384838837392, (6, 7) = -70.5221377558306752001316338827006032187340768, (6, 8) = 520.235208378859672763343647578296600919428272, (6, 9) = .403127155352863813666160452061241985268802920, (6, 10) = -.229875128453580499649930605383626391667210087, (6, 11) = -.249025243344440313757976839460134436215711022, (6, 12) = .850077849442508503270095108095866473994329709, (6, 13) = .999999999999999999999999999999999999999999990, (6, 14) = 1.00000000000000000000000000000000000000001494, (6, 15) = 526.046005054204528169704406776278260629227147, (7, 1) = 0, (7, 2) = .888607277416217966051928947403779522572804242, (7, 3) = .106822611437208274601612056689973427508887756, (7, 4) = -.227628951666705815052303897780904267397418654, (7, 5) = -.383602784885339918445575993340862111408067307, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (8, 1) = 4, (8, 2) = .771395089635626888037058585282289072153672569, (8, 3) = -.251315638632409886572894533969222074089643996, (8, 4) = .494467079738422222368894560870844350373447897, (8, 5) = -.311917252680552965184041884461266972741091408, (8, 6) = -35.3773974809076144493333628813387306219066392, (8, 7) = -261.955262605587133808935304231369552994540307, (8, 8) = 267.817639506339708440220037786669249266668237, (8, 9) = .542590138401669145144489319765760630956089296, (8, 10) = -.207306657051038538831939399741694104211987188, (8, 11) = -.745192226522038608473536679495983480516139685, (8, 12) = .327579665398674149197429570862493923635921752, (8, 13) = 1.00000000000000000000000000000000000000000004, (8, 14) = 1.00000000000000000000000000000000000000000070, (8, 15) = 376.295638946336949362327994692547262453058894, (9, 1) = 0, (9, 2) = .771395089635626888037058585282289072153672569, (9, 3) = .251315638632409886572894533969222074089643996, (9, 4) = -.494467079738422222368894560870844350373447897, (9, 5) = -.311917252680552965184041884461266972741091408, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (10, 1) = 5, (10, 2) = -.771395089635626888037058585282289072153672569, (10, 3) = -.251315638632409886572894533969222074089643996, (10, 4) = .494467079738422222368894560870844350373447897, (10, 5) = .311917252680552965184041884461266972741091408, (10, 6) = -35.3773974809076144493333628813387306219066392, (10, 7) = -261.955262605587133808935304231369552994540307, (10, 8) = -267.817639506339708440220037786669249266668237, (10, 9) = .542590138401669145144489319765760630956089296, (10, 10) = .207306657051038538831939399741694104211987188, (10, 11) = .745192226522038608473536679495983480516139685, (10, 12) = .327579665398674149197429570862493923635921752, (10, 13) = 1.00000000000000000000000000000000000000000004, (10, 14) = 1.00000000000000000000000000000000000000000070, (10, 15) = 376.295638946336949362327994692547262453058894, (11, 1) = 0, (11, 2) = -.771395089635626888037058585282289072153672569, (11, 3) = .251315638632409886572894533969222074089643996, (11, 4) = -.494467079738422222368894560870844350373447897, (11, 5) = .311917252680552965184041884461266972741091408, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (12, 1) = 6, (12, 2) = -.888607277416217966051928947403779522572804242, (12, 3) = -.106822611437208274601612056689973427508887756, (12, 4) = .227628951666705815052303897780904267397418654, (12, 5) = .383602784885339918445575993340862111408067307, (12, 6) = -33.2619224164850716022540679651061384838837392, (12, 7) = -70.5221377558306752001316338827006032187340768, (12, 8) = -520.235208378859672763343647578296600919428272, (12, 9) = .403127155352863813666160452061241985268802920, (12, 10) = .229875128453580499649930605383626391667210087, (12, 11) = .249025243344440313757976839460134436215711022, (12, 12) = .850077849442508503270095108095866473994329709, (12, 13) = .999999999999999999999999999999999999999999990, (12, 14) = 1.00000000000000000000000000000000000000001494, (12, 15) = 526.046005054204528169704406776278260629227147, (13, 1) = 0, (13, 2) = -.888607277416217966051928947403779522572804242, (13, 3) = .106822611437208274601612056689973427508887756, (13, 4) = -.227628951666705815052303897780904267397418654, (13, 5) = .383602784885339918445575993340862111408067307, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (14, 1) = 7, (14, 2) = -1.37465842397864539997343521056744950913464373, (14, 3) = -.4720070715*I, (14, 4) = 1.04887251334709968989772260444378754238846281*I, (14, 5) = .658208509656740520048240372814155977066034431, (14, 6) = -139.935858043713569770172241394940432701557933, (14, 7) = 1009.16689416507143999697715965318783801532828, (14, 8) = -35.05063705*I, (14, 9) = -1.081758215*I, (14, 10) = .805172606177376737844957657938233921696306905, (14, 11) = -1.28822588438750284892199202326992770781607054, (14, 12) = .370982506039653923963789326359229665746676298*I, (14, 13) = 1.00000000000000000000000000000000000000004448, (14, 14) = 1.00000000000000000000000000000000000002308483, (14, 15) = 1018.21968036744599747318369866423941656487034, (15, 1) = 0, (15, 2) = -1.37465842397864539997343521056744950913464373, (15, 3) = .472007071498869469711464480852290076392886818*I, (15, 4) = -1.048872513*I, (15, 5) = .658208509656740520048240372814155977066034431, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (16, 1) = 8, (16, 2) = .516501806300516366332207827845271720295699875, (16, 3) = .157087667438024041386330713987768482051008262*I, (16, 4) = .113781789011852812312696505223578179747798329*I, (16, 5) = .877979905726868500805204485093148911811362591, (16, 6) = -45.5583959992909648360043286735679679113587631, (16, 7) = -49.2104104577498887775211368820566392860712299, (16, 8) = 893.506783720169698656724304667952267191687315*I, (16, 9) = -.866146675707479268632063873487527071333386044, (16, 10) = -0.3920154867e-1*I, (16, 11) = .141165764599481508540163197537118257205129796*I, (16, 12) = .520820958366521078324036803446408915170112964, (16, 13) = .999999999999999999999999999999999999997268842, (16, 14) = .999999999999999999999999999999999999974976375, (16, 15) = 890.986610791943203054869284606448158021303178*I, (17, 1) = 0, (17, 2) = .516501806300516366332207827845271720295699875, (17, 3) = -.1570876674*I, (17, 4) = -.1137817890*I, (17, 5) = .877979905726868500805204485093148911811362591, (17, 6) = 0, (17, 7) = 0, (17, 8) = 0, (17, 9) = 0, (17, 10) = 0, (17, 11) = 0, (17, 12) = 0, (17, 13) = 0, (17, 14) = 0, (17, 15) = 0})

Ans := Matrix(17, 15, {(1, 1) = `-`, (1, 2) = u0, (1, 3) = u1, (1, 4) = u2, (1, 5) = u3, (1, 6) = P*x, (1, 7) = Py, (1, 8) = Pz, (1, 9) = g0, (1, 10) = g1, (1, 11) = g2, (1, 12) = g3, (1, 13) = u^2, (1, 14) = g^2, (1, 15) = P, (2, 1) = 1, (2, 2) = -.516501806300516366332207827845271720295699875, (2, 3) = .157087667438024041386330713987768482051008262*I, (2, 4) = .113781789011852812312696505223578179747798329*I, (2, 5) = -.877979905726868500805204485093148911811362591, (2, 6) = -45.5583959992909648360043286735679679113587631, (2, 7) = -49.2104104577498887775211368820566392860712299, (2, 8) = -893.5067837*I, (2, 9) = -.866146675707479268632063873487527071333386044, (2, 10) = 0.392015486681650570173437868256055772345022977e-1*I, (2, 11) = -.1411657646*I, (2, 12) = .520820958366521078324036803446408915170112964, (2, 13) = .999999999999999999999999999999999999997268842, (2, 14) = .999999999999999999999999999999999999974976375, (2, 15) = 890.986610791943203054869284606448158021303178*I, (3, 1) = 0, (3, 2) = -.516501806300516366332207827845271720295699875, (3, 3) = -.1570876674*I, (3, 4) = -.1137817890*I, (3, 5) = -.877979905726868500805204485093148911811362591, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (4, 1) = 2, (4, 2) = 1.37465842397864539997343521056744950913464373, (4, 3) = -.4720070715*I, (4, 4) = 1.04887251334709968989772260444378754238846281*I, (4, 5) = -.658208509656740520048240372814155977066034431, (4, 6) = -139.935858043713569770172241394940432701557933, (4, 7) = 1009.16689416507143999697715965318783801532828, (4, 8) = 35.050637050173061427545252165933711014164793*I, (4, 9) = -1.081758215*I, (4, 10) = -.805172606177376737844957657938233921696306905, (4, 11) = 1.28822588438750284892199202326992770781607054, (4, 12) = .370982506039653923963789326359229665746676298*I, (4, 13) = 1.00000000000000000000000000000000000000004448, (4, 14) = 1.00000000000000000000000000000000000002308483, (4, 15) = 1018.21968036744599747318369866423941656487034, (5, 1) = 0, (5, 2) = 1.37465842397864539997343521056744950913464373, (5, 3) = .472007071498869469711464480852290076392886818*I, (5, 4) = -1.048872513*I, (5, 5) = -.658208509656740520048240372814155977066034431, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (6, 1) = 3, (6, 2) = .888607277416217966051928947403779522572804242, (6, 3) = -.106822611437208274601612056689973427508887756, (6, 4) = .227628951666705815052303897780904267397418654, (6, 5) = -.383602784885339918445575993340862111408067307, (6, 6) = -33.2619224164850716022540679651061384838837392, (6, 7) = -70.5221377558306752001316338827006032187340768, (6, 8) = 520.235208378859672763343647578296600919428272, (6, 9) = .403127155352863813666160452061241985268802920, (6, 10) = -.229875128453580499649930605383626391667210087, (6, 11) = -.249025243344440313757976839460134436215711022, (6, 12) = .850077849442508503270095108095866473994329709, (6, 13) = .999999999999999999999999999999999999999999990, (6, 14) = 1.00000000000000000000000000000000000000001494, (6, 15) = 526.046005054204528169704406776278260629227147, (7, 1) = 0, (7, 2) = .888607277416217966051928947403779522572804242, (7, 3) = .106822611437208274601612056689973427508887756, (7, 4) = -.227628951666705815052303897780904267397418654, (7, 5) = -.383602784885339918445575993340862111408067307, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (8, 1) = 4, (8, 2) = .771395089635626888037058585282289072153672569, (8, 3) = -.251315638632409886572894533969222074089643996, (8, 4) = .494467079738422222368894560870844350373447897, (8, 5) = -.311917252680552965184041884461266972741091408, (8, 6) = -35.3773974809076144493333628813387306219066392, (8, 7) = -261.955262605587133808935304231369552994540307, (8, 8) = 267.817639506339708440220037786669249266668237, (8, 9) = .542590138401669145144489319765760630956089296, (8, 10) = -.207306657051038538831939399741694104211987188, (8, 11) = -.745192226522038608473536679495983480516139685, (8, 12) = .327579665398674149197429570862493923635921752, (8, 13) = 1.00000000000000000000000000000000000000000004, (8, 14) = 1.00000000000000000000000000000000000000000070, (8, 15) = 376.295638946336949362327994692547262453058894, (9, 1) = 0, (9, 2) = .771395089635626888037058585282289072153672569, (9, 3) = .251315638632409886572894533969222074089643996, (9, 4) = -.494467079738422222368894560870844350373447897, (9, 5) = -.311917252680552965184041884461266972741091408, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (10, 1) = 5, (10, 2) = -.771395089635626888037058585282289072153672569, (10, 3) = -.251315638632409886572894533969222074089643996, (10, 4) = .494467079738422222368894560870844350373447897, (10, 5) = .311917252680552965184041884461266972741091408, (10, 6) = -35.3773974809076144493333628813387306219066392, (10, 7) = -261.955262605587133808935304231369552994540307, (10, 8) = -267.817639506339708440220037786669249266668237, (10, 9) = .542590138401669145144489319765760630956089296, (10, 10) = .207306657051038538831939399741694104211987188, (10, 11) = .745192226522038608473536679495983480516139685, (10, 12) = .327579665398674149197429570862493923635921752, (10, 13) = 1.00000000000000000000000000000000000000000004, (10, 14) = 1.00000000000000000000000000000000000000000070, (10, 15) = 376.295638946336949362327994692547262453058894, (11, 1) = 0, (11, 2) = -.771395089635626888037058585282289072153672569, (11, 3) = .251315638632409886572894533969222074089643996, (11, 4) = -.494467079738422222368894560870844350373447897, (11, 5) = .311917252680552965184041884461266972741091408, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (12, 1) = 6, (12, 2) = -.888607277416217966051928947403779522572804242, (12, 3) = -.106822611437208274601612056689973427508887756, (12, 4) = .227628951666705815052303897780904267397418654, (12, 5) = .383602784885339918445575993340862111408067307, (12, 6) = -33.2619224164850716022540679651061384838837392, (12, 7) = -70.5221377558306752001316338827006032187340768, (12, 8) = -520.235208378859672763343647578296600919428272, (12, 9) = .403127155352863813666160452061241985268802920, (12, 10) = .229875128453580499649930605383626391667210087, (12, 11) = .249025243344440313757976839460134436215711022, (12, 12) = .850077849442508503270095108095866473994329709, (12, 13) = .999999999999999999999999999999999999999999990, (12, 14) = 1.00000000000000000000000000000000000000001494, (12, 15) = 526.046005054204528169704406776278260629227147, (13, 1) = 0, (13, 2) = -.888607277416217966051928947403779522572804242, (13, 3) = .106822611437208274601612056689973427508887756, (13, 4) = -.227628951666705815052303897780904267397418654, (13, 5) = .383602784885339918445575993340862111408067307, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (14, 1) = 7, (14, 2) = -1.37465842397864539997343521056744950913464373, (14, 3) = -.4720070715*I, (14, 4) = 1.04887251334709968989772260444378754238846281*I, (14, 5) = .658208509656740520048240372814155977066034431, (14, 6) = -139.935858043713569770172241394940432701557933, (14, 7) = 1009.16689416507143999697715965318783801532828, (14, 8) = -35.05063705*I, (14, 9) = -1.081758215*I, (14, 10) = .805172606177376737844957657938233921696306905, (14, 11) = -1.28822588438750284892199202326992770781607054, (14, 12) = .370982506039653923963789326359229665746676298*I, (14, 13) = 1.00000000000000000000000000000000000000004448, (14, 14) = 1.00000000000000000000000000000000000002308483, (14, 15) = 1018.21968036744599747318369866423941656487034, (15, 1) = 0, (15, 2) = -1.37465842397864539997343521056744950913464373, (15, 3) = .472007071498869469711464480852290076392886818*I, (15, 4) = -1.048872513*I, (15, 5) = .658208509656740520048240372814155977066034431, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (16, 1) = 8, (16, 2) = .516501806300516366332207827845271720295699875, (16, 3) = .157087667438024041386330713987768482051008262*I, (16, 4) = .113781789011852812312696505223578179747798329*I, (16, 5) = .877979905726868500805204485093148911811362591, (16, 6) = -45.5583959992909648360043286735679679113587631, (16, 7) = -49.2104104577498887775211368820566392860712299, (16, 8) = 893.506783720169698656724304667952267191687315*I, (16, 9) = -.866146675707479268632063873487527071333386044, (16, 10) = -0.3920154867e-1*I, (16, 11) = .141165764599481508540163197537118257205129796*I, (16, 12) = .520820958366521078324036803446408915170112964, (16, 13) = .999999999999999999999999999999999999997268842, (16, 14) = .999999999999999999999999999999999999974976375, (16, 15) = 890.986610791943203054869284606448158021303178*I, (17, 1) = 0, (17, 2) = .516501806300516366332207827845271720295699875, (17, 3) = -.1570876674*I, (17, 4) = -.1137817890*I, (17, 5) = .877979905726868500805204485093148911811362591, (17, 6) = 0, (17, 7) = 0, (17, 8) = 0, (17, 9) = 0, (17, 10) = 0, (17, 11) = 0, (17, 12) = 0, (17, 13) = 0, (17, 14) = 0, (17, 15) = 0})

 (4)

``

 (5)

"seq( if 'has'(Ans(n,1..15) ,Im<>0) then DeleteRow (Ans(n) )end if,n=2..17)"

Error, invalid argument sequence

"seq( if 'has'(Ans(n,1..15) ,Im<>0) then DeleteRow (Ans(n) )end if,n=2..17)"

  

Ans

Matrix(17, 15, {(1, 1) = `-`, (1, 2) = u0, (1, 3) = u1, (1, 4) = u2, (1, 5) = u3, (1, 6) = P*x, (1, 7) = Py, (1, 8) = Pz, (1, 9) = g0, (1, 10) = g1, (1, 11) = g2, (1, 12) = g3, (1, 13) = u^2, (1, 14) = g^2, (1, 15) = P, (2, 1) = 1, (2, 2) = -.516501806300516366332207827845271720295699875, (2, 3) = .157087667438024041386330713987768482051008262*I, (2, 4) = .113781789011852812312696505223578179747798329*I, (2, 5) = -.877979905726868500805204485093148911811362591, (2, 6) = -45.5583959992909648360043286735679679113587631, (2, 7) = -49.2104104577498887775211368820566392860712299, (2, 8) = -893.5067837*I, (2, 9) = -.866146675707479268632063873487527071333386044, (2, 10) = 0.392015486681650570173437868256055772345022977e-1*I, (2, 11) = -.1411657646*I, (2, 12) = .520820958366521078324036803446408915170112964, (2, 13) = .999999999999999999999999999999999999997268842, (2, 14) = .999999999999999999999999999999999999974976375, (2, 15) = 890.986610791943203054869284606448158021303178*I, (3, 1) = 0, (3, 2) = -.516501806300516366332207827845271720295699875, (3, 3) = -.1570876674*I, (3, 4) = -.1137817890*I, (3, 5) = -.877979905726868500805204485093148911811362591, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (4, 1) = 2, (4, 2) = 1.37465842397864539997343521056744950913464373, (4, 3) = -.4720070715*I, (4, 4) = 1.04887251334709968989772260444378754238846281*I, (4, 5) = -.658208509656740520048240372814155977066034431, (4, 6) = -139.935858043713569770172241394940432701557933, (4, 7) = 1009.16689416507143999697715965318783801532828, (4, 8) = 35.050637050173061427545252165933711014164793*I, (4, 9) = -1.081758215*I, (4, 10) = -.805172606177376737844957657938233921696306905, (4, 11) = 1.28822588438750284892199202326992770781607054, (4, 12) = .370982506039653923963789326359229665746676298*I, (4, 13) = 1.00000000000000000000000000000000000000004448, (4, 14) = 1.00000000000000000000000000000000000002308483, (4, 15) = 1018.21968036744599747318369866423941656487034, (5, 1) = 0, (5, 2) = 1.37465842397864539997343521056744950913464373, (5, 3) = .472007071498869469711464480852290076392886818*I, (5, 4) = -1.048872513*I, (5, 5) = -.658208509656740520048240372814155977066034431, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (6, 1) = 3, (6, 2) = .888607277416217966051928947403779522572804242, (6, 3) = -.106822611437208274601612056689973427508887756, (6, 4) = .227628951666705815052303897780904267397418654, (6, 5) = -.383602784885339918445575993340862111408067307, (6, 6) = -33.2619224164850716022540679651061384838837392, (6, 7) = -70.5221377558306752001316338827006032187340768, (6, 8) = 520.235208378859672763343647578296600919428272, (6, 9) = .403127155352863813666160452061241985268802920, (6, 10) = -.229875128453580499649930605383626391667210087, (6, 11) = -.249025243344440313757976839460134436215711022, (6, 12) = .850077849442508503270095108095866473994329709, (6, 13) = .999999999999999999999999999999999999999999990, (6, 14) = 1.00000000000000000000000000000000000000001494, (6, 15) = 526.046005054204528169704406776278260629227147, (7, 1) = 0, (7, 2) = .888607277416217966051928947403779522572804242, (7, 3) = .106822611437208274601612056689973427508887756, (7, 4) = -.227628951666705815052303897780904267397418654, (7, 5) = -.383602784885339918445575993340862111408067307, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (8, 1) = 4, (8, 2) = .771395089635626888037058585282289072153672569, (8, 3) = -.251315638632409886572894533969222074089643996, (8, 4) = .494467079738422222368894560870844350373447897, (8, 5) = -.311917252680552965184041884461266972741091408, (8, 6) = -35.3773974809076144493333628813387306219066392, (8, 7) = -261.955262605587133808935304231369552994540307, (8, 8) = 267.817639506339708440220037786669249266668237, (8, 9) = .542590138401669145144489319765760630956089296, (8, 10) = -.207306657051038538831939399741694104211987188, (8, 11) = -.745192226522038608473536679495983480516139685, (8, 12) = .327579665398674149197429570862493923635921752, (8, 13) = 1.00000000000000000000000000000000000000000004, (8, 14) = 1.00000000000000000000000000000000000000000070, (8, 15) = 376.295638946336949362327994692547262453058894, (9, 1) = 0, (9, 2) = .771395089635626888037058585282289072153672569, (9, 3) = .251315638632409886572894533969222074089643996, (9, 4) = -.494467079738422222368894560870844350373447897, (9, 5) = -.311917252680552965184041884461266972741091408, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (10, 1) = 5, (10, 2) = -.771395089635626888037058585282289072153672569, (10, 3) = -.251315638632409886572894533969222074089643996, (10, 4) = .494467079738422222368894560870844350373447897, (10, 5) = .311917252680552965184041884461266972741091408, (10, 6) = -35.3773974809076144493333628813387306219066392, (10, 7) = -261.955262605587133808935304231369552994540307, (10, 8) = -267.817639506339708440220037786669249266668237, (10, 9) = .542590138401669145144489319765760630956089296, (10, 10) = .207306657051038538831939399741694104211987188, (10, 11) = .745192226522038608473536679495983480516139685, (10, 12) = .327579665398674149197429570862493923635921752, (10, 13) = 1.00000000000000000000000000000000000000000004, (10, 14) = 1.00000000000000000000000000000000000000000070, (10, 15) = 376.295638946336949362327994692547262453058894, (11, 1) = 0, (11, 2) = -.771395089635626888037058585282289072153672569, (11, 3) = .251315638632409886572894533969222074089643996, (11, 4) = -.494467079738422222368894560870844350373447897, (11, 5) = .311917252680552965184041884461266972741091408, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (12, 1) = 6, (12, 2) = -.888607277416217966051928947403779522572804242, (12, 3) = -.106822611437208274601612056689973427508887756, (12, 4) = .227628951666705815052303897780904267397418654, (12, 5) = .383602784885339918445575993340862111408067307, (12, 6) = -33.2619224164850716022540679651061384838837392, (12, 7) = -70.5221377558306752001316338827006032187340768, (12, 8) = -520.235208378859672763343647578296600919428272, (12, 9) = .403127155352863813666160452061241985268802920, (12, 10) = .229875128453580499649930605383626391667210087, (12, 11) = .249025243344440313757976839460134436215711022, (12, 12) = .850077849442508503270095108095866473994329709, (12, 13) = .999999999999999999999999999999999999999999990, (12, 14) = 1.00000000000000000000000000000000000000001494, (12, 15) = 526.046005054204528169704406776278260629227147, (13, 1) = 0, (13, 2) = -.888607277416217966051928947403779522572804242, (13, 3) = .106822611437208274601612056689973427508887756, (13, 4) = -.227628951666705815052303897780904267397418654, (13, 5) = .383602784885339918445575993340862111408067307, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (14, 1) = 7, (14, 2) = -1.37465842397864539997343521056744950913464373, (14, 3) = -.4720070715*I, (14, 4) = 1.04887251334709968989772260444378754238846281*I, (14, 5) = .658208509656740520048240372814155977066034431, (14, 6) = -139.935858043713569770172241394940432701557933, (14, 7) = 1009.16689416507143999697715965318783801532828, (14, 8) = -35.05063705*I, (14, 9) = -1.081758215*I, (14, 10) = .805172606177376737844957657938233921696306905, (14, 11) = -1.28822588438750284892199202326992770781607054, (14, 12) = .370982506039653923963789326359229665746676298*I, (14, 13) = 1.00000000000000000000000000000000000000004448, (14, 14) = 1.00000000000000000000000000000000000002308483, (14, 15) = 1018.21968036744599747318369866423941656487034, (15, 1) = 0, (15, 2) = -1.37465842397864539997343521056744950913464373, (15, 3) = .472007071498869469711464480852290076392886818*I, (15, 4) = -1.048872513*I, (15, 5) = .658208509656740520048240372814155977066034431, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (16, 1) = 8, (16, 2) = .516501806300516366332207827845271720295699875, (16, 3) = .157087667438024041386330713987768482051008262*I, (16, 4) = .113781789011852812312696505223578179747798329*I, (16, 5) = .877979905726868500805204485093148911811362591, (16, 6) = -45.5583959992909648360043286735679679113587631, (16, 7) = -49.2104104577498887775211368820566392860712299, (16, 8) = 893.506783720169698656724304667952267191687315*I, (16, 9) = -.866146675707479268632063873487527071333386044, (16, 10) = -0.3920154867e-1*I, (16, 11) = .141165764599481508540163197537118257205129796*I, (16, 12) = .520820958366521078324036803446408915170112964, (16, 13) = .999999999999999999999999999999999999997268842, (16, 14) = .999999999999999999999999999999999999974976375, (16, 15) = 890.986610791943203054869284606448158021303178*I, (17, 1) = 0, (17, 2) = .516501806300516366332207827845271720295699875, (17, 3) = -.1570876674*I, (17, 4) = -.1137817890*I, (17, 5) = .877979905726868500805204485093148911811362591, (17, 6) = 0, (17, 7) = 0, (17, 8) = 0, (17, 9) = 0, (17, 10) = 0, (17, 11) = 0, (17, 12) = 0, (17, 13) = 0, (17, 14) = 0, (17, 15) = 0})

 (6)

``

``

 

Download matrix_imaginery_elements.mw

Creating a sequence of functions ...

Asked by: abdelkarim 5
sequence
May 15 2016
1  9

i'm using maple in a research but i want to add a recursive function h_m(t) in 2 case : if m is integer positive and not, 
la formule est donnée comme suit : if (mod(m,1) = 0 and m>0) then h:=proc(m,t) local t ; h[0,t]:=t ; for i from -4 to m by 2 do h [m,t]:= h[0, t]-(GAMMA(i/(2)))/(2*GAMMA((i+1)/(2)))*cos(Pi*t)*sin(Pi*t) od: fi: end; 
  if (mod(m,1) = 0  and m>0) then  h:=proc(m,t)  local  t ;  h[0,t]:=t ;   for  i from -4 to  m  by  2 do  h [m,t]:= h[0, t]-(GAMMA(i/(2)))/(2*GAMMA((i+1)/(2)))*cos(Pi*t)*sin(Pi*t)  od:  fi:  end;
and i wanna to know how to programmate a Gaus Hypegeometric function. Thank You

 

How to assign letters as constants?...

Asked by: billyp245 10
May 14 2016
1  13

Hi all,

I seem to be quite stuck on figuring out how to leave certain letters (e.g. planck's constant h) inside the equation without having to assign it as some particular number. 

What I am trying to do is find the value of a when the following equation is at a minimum:

E = (a*(h^2)/2m) + 0.3989422804/sqrt(a)

Here h and m are what I want to set as constants without actually setting them to h := 1 because I want a in terms of h and m. I have already found the derivative dE/da:

((h^2)/2m) - 0.1994711402/a^(3/2)

But I cannot use fsolve to find the value of a at the minimum because it keeps saying that h and m are variables and unsolved for.

Any help would be greatly appreciated.

Defining custom operator for partial differentiati...

Asked by: mskalsi 290
May 11 2016
0  6


Suppose we have a function "f(x,y,z), "can we build a code such that for operator defined as

"Delta[]=((&PartialD;)^3)/(&PartialD;y &PartialD;x^2)+((&PartialD;)^(2))/(&PartialD;y &PartialD;x^)+((&PartialD;)^3)/(&PartialD;y &PartialD;z^2)+((&PartialD;)^(2))/( &PartialD;x^2)+((&PartialD;)^3)/(&PartialD;z &PartialD;x^2)"

Such that

Delta*f(x, y, z)returns f[yxx]+f[yx]+f[yzz]+f[xx]+f[zxx]

where subscripts denote partial derivatives.


Download operator.mw

Regards

Numerov algorithm in Maple

by: Amitabh Biswas 108 Maple 18
algorithm numeric
May 10 2016
0  0

Hi there, fellow primers, it's good to be back after almost 5 years! I just want to share a worksheet on Numerov's algorithm in Maple using procedures as I've recently found out that google could not find any Maple procedure that implements Numerov's algorithm to solve ODEs.   numerov.mw   Reference.pdf 

How to re-evaluate a Matrix?...

Asked by: Ronan 1022
matrix unassign
May 09 2016
1  9

How do I get the Matrix to recalculate?

restart

a := 5

5

 (1)

``

M := simplify(Matrix(2, 2, {(1, 1) = a, (1, 2) = 2*a, (2, 1) = 3*a, (2, 2) = a^2}))

M := Matrix(2, 2, {(1, 1) = 5, (1, 2) = 10, (2, 1) = 15, (2, 2) = 25})

 (2)

``

unassign('a')

a

a

 (3)

 

M

Matrix(2, 2, {(1, 1) = 5, (1, 2) = 10, (2, 1) = 15, (2, 2) = 25})

 (4)

expand(M)

Matrix(2, 2, {(1, 1) = 5, (1, 2) = 10, (2, 1) = 15, (2, 2) = 25})

 (5)

``

 

Download Re-evaluate_a_Matrix.mw

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