Hello!

I want to use abstract linear operators between Lie algebras. I have the problem shown in the following short code:

with(LinearAlgebra): with(DifferentialGeometry): with(LieAlgebras):
LAr:=LieAlgebraData([ [e1,e2]=e3],[e1,e2,e3],LA);
DGsetup(LAr);
define(lin,linear);
lin(-e3);
lin(-LieBracket(e1,e2));
lin(LieBracket(e2,e1));

As you see, the minus "-" does not come out of the argument of lin() in the last line. What is going wrong?

Thanks!

-------------------------------------

Later on, I realized that the linear operator has nothing to do with the issue. The problem lies in the fact that the output of "LieBracket(e2,e1)" is "_DG([["vector", LA, []], [[[3], -1]]])" , where the latter "-1" refers to the coeffiecient. For some reason, this coefficient is not handled in the way I would expect. For example, the following two lines:

LieBracket(e2,e1)+LieBracket(e1,e2);
_DG([["vector", LA, []], [[[3], 1]]])+_DG([["vector", LA, []], [[[3], -1]]]);

give both as an output "e3+-e3" instead of "0", while both the lines

LieBracket(e2,e1) + LieBracket(e2,e1);
_DG([["vector", LA, []], [[[3], -1]]])+_DG([["vector", LA, []], [[[3], -1]]]);

give the output "2-e3" (which I interpret as "2(-e3)" ).

I don't understand what I am doing wrong.

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

It's a bug, design or  something else ?

Goodday sirs, 

            How can I get over these error message123.mw
 

Anyone with useful informations please.

Thanking you in anticipation for a favurabke response

Download 123.mw

pde := [diff(u(x, y), x, x)+diff(u(x, y), y, y) = 2*Pi*(2*Pi*y^2-2*Pi*y-1)*exp(Pi*y*(1-y))*sin(Pi*x), u(0, y) = sin(Pi*y), u(1, y) = exp(Pi)*sin(Pi*y), u(x, 2) = exp(-2*Pi)*sin(Pi*x), u(x, 0) = u(x, 1)]pdsolve(pde)

pdsolve(pde)

it does not return any solution and answer, kindly help.

Hi, 

I have a vector field that has positive constants. I don't want to set perminant values for the constants becuase future calculations will be wrong. 

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Here's the same issue (unanswered) way back in 2015 https://www.mapleprimes.com/questions/203811-DocumentTools-Retrieve-Function-Returns

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See example in attachment

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Hi all

I wnat to produce following matrix P_{2r+1, 2r+1} in maple.

can any one help me please?

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
moadele_asli2.mw

solve does not show result!!

dtm.mw

can i have step by step procedure of the solution of the follwoing problem

sys[1] := [-(diff(u(x, t), t, t))-(diff(u(x, t), x, x))+u(x, t) = 2*exp(-t)*(x-(1/2)*x^2+(1/2)*t-1), u(x, 0) = x^2-2*x, u(x, 1) = u(x, 1/2)+((1/2)*x^2-x)*exp(-1)-((3/4)*x^2-(3/2)*x)*exp(-1/2), u(0, t) = 0, eval(diff(u(x, t), x), x = 1) = 0]

I am attempting to use the Gram-Schmidt process with Maple to show that the first six orthogonal polynomials which satisfy the following orthogonality condition:

$\int_0^1 (1-x)^{3/2} \phi_n(x) \phi_m(x) dx = h_{n} \delta_{nm}$   

can be expressed in the form:

\phi_0(x) = 1, \phi_1(x) = x − 2/7 , \phi_2(x) = x^2 − (8/11)x + 8/99 , \phi_3(x) = x^3 − (6/5)x^2 + (24/65)x − 16/715 , \phi_4(x) = x^4 − (32/19)x^3 + (288/323)x^2 − (256/1615)x + 128/20995 , \phi_5(x) = x^5 − (50/23)x^4 + (800/483)x^3 − (1600/3059)x^2 + (3200/52003)x − 256/156009.

At the same time I have to find the corresponding values for h_n, so for example, h_0 = 2/5 and h_1 = 8/441.  The polynomials which I obtain have to be combined with the Gaussian quadrature method to show that

$\int_0^1 (1-x)^{3/2} \phi_n(x) \phi_m(x) dx = h_{n} \delta_{nm} \approx \sum_{k=1}^4 c_k f(x_k)$

where x_k are the four roots of \phi_4(x)=0 such that x = [0.0524512, 0.256285, 0.548299, 0.827175]

and the 4 c_k coefficients are given by c = [0.121979, 0.168886, 0.0920439, 0.0170909].

I have learned about Gram-Schmidt orthogonalisation in a basic setting in linear algebra courses where a system of N linearly independent orthogonal vectors is constructed from a system of N linearly independent vectors, but unsure how to apply it to polynomials.  I am also vaguely familar with the idea of appoximating integrals with sets of orthogonal polynomials (Legendre, for example) but not exactly sure how this all works.