Hello

I'm using the package DifferentialGeometry with Maple 2019. I have 2 questions whose answer I've not found in the Help section:

a) If I have a 2-form omega with d(omega)=0, how can I obtain the 1-form alpha such that d(alpha) = omega?

b) if alpha is a 1-form and X a vector field, how can I calculate alpha(X)?

Thanks Nicola

  Hello: 
    As a first step to my question, let  G be  a graph and  I'd like to know  whether it contains a C₄ (cycle of 4) as its subgraph.
     For example: .   It contains C₄. So  program may be return true.  
    I'm most concerned about the following thing ( it is important problem for me, since in graph theory, we usually consider some class graphs contain no sepecific graph ) :
   1 Further , I want to  get all connected graphs of order less than 6  which  contains no C₄ .
   2 More generally, I want  to konw  a graph  whether contains some graph as its subgraph.For example : does it contain K4CompleteGraph(4) ，K32  CompleteGraph(3, 2)  and so on ?
    I read the  function subgaph.  But  It didn't solve my problem. Many thanks for your help or advise.
   # I  just know there is a function  IsTriangleFree which test if graph is triangle-free ( graph comtains no C₃)  in Maple 2019. I think my question and how to program may be  meaningful.

Hi, 

I found that using the packages heometry and simplex in the same worksheet (only one restart at the top of it) causes a conflict in the command simplex:-convexhull(`some set of points`, option = area).

It seems that Maple doesn't confounds  that area in the option=area  with geometry:-area
Is it possible to fix this?


 

Download geometry_vs_simplex.mw

Dear all,

I have the following metric

Is there any way to make the terms dt dphi and dphi dt not symmetric?

Denis

Calculate  where the domain Ω is bounded by the surfaces x + y + z = 1, x = 0, y = 0, z = 0.

What am I doing wrong?

Task: Calculate   where Ω is the part of a circle of radius a centered at
point O (0; 0), lying in the first quarter.

My attempt to solve:

What values need to be taken instead of infinity?

Dear all,

I need a Maple sheet or algorithm in order to solve the enclosed problem (myproblem.pdf . )

Thanks for your meaningful help.

Eric

Yo I have fit a surface to a curve using polynomial regression:

(It's only supposed to be fit for negative t domain)

Now I've attempted to cap this function off at 0, using a piecewise function of the original:

Which when I print, looks somewhat about right:

Sorry it's so hard to see but you get the idea. The problem is that this seems to set the whole function to 0, rather than just the bits that should clip:

The piecwise function seems to be evaluating the fN>0 condition to true for all input values p,t, rather than substituing the new input values into the original function fN, and then evaluating the condition for every point, not really sure what the problem is, would appreciate some help!

Calculateif 

Determine which of the limits exist and calculate 
if 

Find the intersection points of the curves and build graphics. 
P.S. Sorry for the spam questions on the forum, but I need to pass the work as soon as possible.

Determine the dimension of the system solution space: 

Implement a procedure that calculates the number of all non-zero elements of a given matrix, and apply this procedure to the matrix: 

Hi, 

Versions concerned:  [ Maple 2015 ... Maple 2018 ]

I use DocumentTools:-Tabulate to display a matrix of numbers while coloring them according to some condition.
(line DocumentTools:-Tabulate(M, color=((M,i,j)->`if`(M[i,j]>3,....) below ... please note the output is not loaded for some unknown reason).
The fact is that the matrix appears with black characters meaning 'color' doesn't work.

In a second attempt I convert matrix M into a matrix of strings and use now
DocumentTools:-Tabulate(S, color=((S,i,j)->`if`(parse(S[i,j])>3,...)
I get now the desired result with some blue and red numbers.

So converting to strings could be a workaround.
But think to matrices where elements would be algebraic expressions, for instance 
M := Matrix(2, 2, (i,j)->exp(x^i)+cos(x*j))
and that we use the coloring scheme is color=((M,i,j)->`if`(i+j>3, "Red", "Blue")
Converting M to a string matrix will display the element [2, 2] in red and the others in blue, but what you get then is a no longer a 2D pretty output but, literally, things like exp(x^2)+cos(x*2) 

The "convert to string" workaround is thus far from perfect.
Is the fact that 'color' only acts on strings a "normal and known" behaviour?
Is it possible to change the color of the font for non "string type matrices" ?
 

Download Tabulate_Color.mw

Draw the coordinate grid of the elliptical coordinate system.