mskalsi

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9 years, 144 days

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These are questions asked by mskalsi

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

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


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

"Delta[]=((∂)^3)/(∂y ∂x^2)+((∂)^(2))/(∂y ∂x^)+((∂)^3)/(∂y ∂z^2)+((∂)^(2))/( ∂x^2)+((∂)^3)/(∂z ∂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

Dear All

I have downloaded second version of DGApplications to work with abstract Lie algebra. The file is actually .mla file and it is executale(as when we open it, a prompt ask, "do you want to execute this file"), but when I press ok for execution, a file open with command like as

"march('open',"C:\\Users\\Manjit\\Downloads\\DGApplications.mla");",

what should I do after this, is it a some sort installation procedure. I keep all my Maple file in E drive with following path:

E:\Maple work\General Maple Workout

Please guide me in simple way, as I failed to install Maple package many times.

Regards

Please check why Maple is not returning location of Minima in following case:

 

-0.6159648936e-1*sin(.9960622471*x)+0.1077739351e-1*sin(1.992124494*x)-0.6872829504e-3*sin(2.988186741*x)+0.3984248988e-4*sin(3.984248988*x)

-0.6159648936e-1*sin(.9960622471*x)+0.1077739351e-1*sin(1.992124494*x)-0.6872829504e-3*sin(2.988186741*x)+0.3984248988e-4*sin(3.984248988*x)

(1)

plot(-0.6159648936e-1*sin(.9960622471*x)+0.1077739351e-1*sin(1.992124494*x)-0.6872829504e-3*sin(2.988186741*x)+0.3984248988e-4*sin(3.984248988*x), x = -3.2 .. 3.2)

 

readlib(extrema):

{-0.6447467154e-1, 0.6447467152e-1}

(2)

Minima := op(1, {-0.6447467154e-1, 0.6447467152e-1}); 1; Maxima := op(2, {-0.6447467154e-1, 0.6447467152e-1})

-0.6447467154e-1

 

0.6447467152e-1

(3)

minimize(-0.6159648936e-1*sin(.9960622471*x)+0.1077739351e-1*sin(1.992124494*x)-0.6872829504e-3*sin(2.988186741*x)+0.3984248988e-4*sin(3.984248988*x), x = 0 .. 3.5, location)

minimize(-0.6159648936e-1*sin(.9960622471*x)+0.1077739351e-1*sin(1.992124494*x)-0.6872829504e-3*sin(2.988186741*x)+0.3984248988e-4*sin(3.984248988*x), x = 0 .. 3.5, location), {}

(4)

Why Maple is not returning location of minima?

 

Download Location_for_Max_Min.mw

Regards

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