Given two sets of lie algebra data, How to check, using maple software, that these lie algebras are isomorphic?

for example : 

The two sets of lie algebras are given as : L1 := [[e1, e4] = e1, [e2, e3] = e1, [e2, e4] = e2]

and

L2 := [[e1, e2] = e1].

Hi there,

Could you help me with Harley's norm computation algorithm that is based on the Fast Extended Euclidean Algorithm that was suggested by Harley in an email to NMBRTHRY list in 2002 and that described in Vercauteren's thesis pp 87-90:

https://pdfs.semanticscholar.org/c945/c98267db064b272c87a885fc5eeb764b0b2d.pdf

My implementation working correctly and fast for low degree polynomials without modulo and for high degree polynomials with modulo M, where M is a prime number greater than 2^N. But all I need - it's a resultant modulo 2^N (or 2^(Nc) due to Vercauteren's Remark 3.10.3) of two large polynomials. So I should include in routine mod 2^N (or mod 2^(Nc)...) instructions to avoid exponential coefficients' growing. But since the 2^N is not prime it's a problem - polynomials contain even coefficients and this leads to some even denominators - and for example multiplicative inverse 1/2 mod 2^N doesn't exist. Please tell me how to solve this problem?

How to adapt XGCD routine for correct mod 2^N calculation of resultant (norm)?

Thank you.

mod prime version of XGCD:

XGCD.mw

Hi everyone. I'm using Maple 2020. I encountered an error as "Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation". I saw this first time. Can you help me? I added source file.

Space_Fractional.mw

 

Hi,
I want to plot an equation, but I couldn't. Who can guide me?

Ra.mw

Suppose that a function f  has derivatives of all orders at a.  The the series

∑=(f(k)(a)/(k!))*(x−a)^k (limits are infinity and k=0, i donot how to insert that)

is called the Taylor series for f  about  a, where  f(n) is the n th order derivative of  f.

Suppose that the Taylor series for e2 x sin(5 x) about 0 is

a0+a1x+a2x2+⋯+a8x8+⋯

Enter the exact values of a0 and a8  in the boxes below.

      a0=      

     a8=      

Use Maple to find the solution of the initial value problem

y*(d^(2)*y/d*x^2)+(dy/dx)^2=0 0 with initial conditions y(0)=5and y'(0)=8.

Using Maple syntax, type in your answer in the box below, or copy (Ctrl-C) from your Maple worksheet and paste (Ctrl-V) in the answer box the solution. Do NOT enter the y(x)= part of the Maple output.

Why is pdsolve's 'generalsolution' option giving the particular solution u(x, y) = 0 instead of the general solution u(x, y) = A sin(x) sin(2 y) + B sin(2 x) sin(y) for the attached problem?

Problem.mw

Is there a way to convert a Fourier series (from the OrthogonalExpansions package) automatically into the sum of odd/even terms if the even/odd terms are 0 respectively?

Download FourierSeries.mw

what is the most elegant way to get coefficients of a series that contains negative powers.

for example in this:

tt := a*N__s^3 + N__s + CSxSx__0 + CSxSx__1/N__s + CSxSx__2/N__s^2 + CSxSx__3/N__s^3;

i would like

fancy_coeff(tt, 1/N__s, 3)

to give me `CSxSx__3`

while

fancy_coeff(tt, 1/N__s, -3)

give me `a`

(the standard coeff call doesn't work with this, as would be known to people here)

thanks!

Hi,

The black circle below is vanishing at the peak. How do I make the entire  circle visible?

Transparency=0.5 is not a good solution.

A1 := -12; A1 = log*sigma[matrix];
print(`output redirected...`); # input placeholder
                              -12
                    -12 = log sigma[matrix]
sigma[matrix] := 0.1e-11;
print(`output redirected...`); # input placeholder
                                -12
                            1 10   
A1 := 6; A1 = log*sigma[CNT];
print(`output redirected...`); # input placeholder
                               6
                       6 = log sigma[CNT]
a := phi;
print(`output redirected...`); # input placeholder
                              phi
sigma[CNT] = 0.1e7;
print(`output redirected...`); # input placeholder
                                        6
                       sigma[CNT] = 1 10 
eq := log10(sigma[CNT]*a+(1-a)*sigma[matrix]);
print(`output redirected...`); # input placeholder
             /                     -12       -12    \
           ln\phi sigma[CNT] + 1 10    - 1 10    phi/
           ------------------------------------------
                             ln(10)                  
plot(eq, phi = 0.15e-1 .. 0.21e-1);
%;
Warning, expecting only range variable phi in expression ln(phi*sigma[CNT]+.1e-11-.1e-11*phi)/ln(10) to be plotted but found name sigma[CNT]

How can i solve that please ?

How to find the values of unknown parameters for these equations with initial and  boundary conditions

where Pr=6.2,M=2,nu=0.3,phi=0.05 and lambda=Sc=Ks=1

Could some one help me out to find the exact way to find the values of unknown parameters

Hello everyone,

I'm trying to generate plots in Maple so that I can export the image and be easily read in a document. I usually use the plots [display] command as I often reuse "subplots". The main problem appears when entering a legend, as it disrupts the proportions and I have to rescale everything manually. In doing so I sometimes get small, hard-to-read images or captions. Is there any way to resize the image and caption other than manually? Even better, is there a way to scale both to a certain image size and to make the caption legible at that size (e.g. image 7 cm wide and font equivalent to 10 pt in Word)?

Thank you so much in advance

A is a 2 x 2 matrix with eigenvalue, eigenvector pairs:

5,<4,1> and 1,<3,4>.

1. Find an invertible matrix M and a diagonal matrix D such that A=MDM^(-1).

M=                                          D=      

2. For any integer n, find the matrix A^n   as a single matrix (i.e. explicitly entry-by-entry). Use Maple notation for a matrix.

   An=       

(Hint: compose your answer in Maple to make sure your syntax is correct and your answer is what you think it should be.)

Something goes wrong with the DE   : de  
Error, unexpected single forward quote

I solved this by converting this : de  to a 2 D Math input 
Something must be chanced
in the configuration settings ? 

Ch05Sec03Prob19.mw