I've been studying the  drawing  of graph lately .    One of the themes is  1-planar graph .

A 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point,  where it crosses a single additional edge. If a 1-planar graph, one of the most natural generalizations of planar graphs, is drawn that way, the drawing is called a 1-plane graph or 1-planar embedding of the graph.

 

 

 

 

 

I know it is NP hard to determine whether a graph is a 1-planar . My idea is to take advantage of some mathematical software to provide some roughly and  intuitive understanding before determining .

Now,  the layout of vertices or edges becomes important.  The drawing of a plane graph is a good example.

My problem is that I see that  Maple2020 has updated a lot of layouts about DrawGraph  graph theory backpack , and I don’t know which ones are working towards the least possible number of crossing of  each edges of graph . 

Some links that may be useful:

https://de.maplesoft.com/products/maple/new_features/Maple2020/graphtheory.aspx

https://de.maplesoft.com/support/help/Maple/view.aspx?path=GraphTheory/SetVertexPositions

I think the software can improve some calculations related to topological graph theory, such as crossing number of graph, etc.

 

The uploaded worksheet plots conics in polar coordinates.

A circle, parabola and hyperbola all plot correctly, but the plot command for the ellipse displays a shifted circle. What's wrong?

Conic_quandry.mw

How to find sgn on maple?

signum.mw

I am trying to generate all non-isomorphic graphs of a certain order and size that have the same degree sequence (not necessarily regular). I assume I would have to use the select option in GraphTheory[NonIsomorphicGraphs] command, however, there are no examples (that I could find) of how to use the option. Any idea how this could be done?

I have an n x n matrix. I am trying to write a procedure that will randomly choose a row (column) in the matrix, and replace another row (column) with the entries of the chosen row (column). So, the end result will be another n x n matrix that has two identical rows (columns). How could one do this?

Hello there, 

Would you please tell me how to get the 'Desired' expression from the 'Sec_Z2prim' expression?

My 'Attempt' did not work. 

 

>  restart; >  TR_turns_ratio := N = n2 / n1; (1) >  Sec_Z2prim := Z1 = Z2*n1^2/n2^2; (2) >  Attempt := subs(TR_turns_ratio, Sec_Z2prim) assuming (n1 > 0, n2 > 0); (3) >  Desired := Z1 = Z2*(1/N)^2; (4) >

 

Thank you, 
 

Download Q20201014.mw

I usually piecewise functions in my maple codes. I want to export  the my maple code to a Matlab code in order to utilize advantages of plots of Matlab.

What methods would you recommend me?

 

For example:

Suppose that I have a piecewise u function.

restart:
u:=1/(1. + exp(x))^2 + 1/(1. + exp(-5.*t))^2 - 0.2500000000 + x*(1/(1. + exp(1 - 5*t))^2 - 1./((1. + exp(-5*t))^2) + 0.1776705118 + 0.0415431679756514*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + 0.00922094377856479*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + 0.0603742508215732*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) - 0.00399645630498528*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.)) + (-0.00243051684581302*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000809061198761621*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0152377552205917*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00195593427342862*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + (-0.000433590063316381*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000146112803263678*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.00319022339097685*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.000477063086307787*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + (-0.00276114805649180*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000933166016624500*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0207984584912892*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00314360556336114*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) + (0.000172746997599710*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) + 0.0000586775450031145*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) + 0.00136190009033518*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) + 0.000211410172315387*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.);

 

 

I use the following code to transform a Matlab code, but the output is not working in Matlab.

 

with(CodeGeneration):
 	
Matlab(u,resultname="w");

 

Using solve on this example:

restart;
eq:=x^3 - 3*x^2 + 3*x - 1=0;
solve(eq,x);

gives solution x=1, with multiplicty 3

              1, 1, 1

When using PDEtools:-Solve

restart;
eq:=x^3 - 3*x^2 + 3*x - 1=0;
solve(eq,x);
PDEtools:-Solve(eq,x);

it gives

         x = 1

How can one make it show x=1, x=1, x=1 ?

Found that only when using PDEtools:-Solve(eq,x,numeric) it gives 

           x = 1., x = 1., x = 1.

How to make it do the same without using numeric?

Maple 2020.1.1

 

What is the reason that error accepts its arguments without being inside paranthesis? This is different from all other Maple functions I've seen. For example, both these below work the same

f := proc (x) 
     if x<0 then 
        error "invalid x: %1", x; 
     else 
        x^(1/2); 
     end if 
end proc:

And

g := proc (x) 
     if x<0 then 
        error("invalid x: %1", x); 
     else 
        x^(1/2)
     end if 
end proc:

One can't do for other Maple functions. For example sin x  gives an error. It must be sin(x)

Looked at help page for error and did not see something about this difference.

I have been having difficulty with plotting these graphs from Cartesian to Polar. I know that with double integrals there is an inclusion of r when you go from Cartesian to Polar. I think my graph of the function being integrated is correct. I am having difficulty with the command for the shaded region. I know with Cartesian, I can use inequal command to get the right shaded area. Will this command work with polar coordinates? 

I attached the Maple worksheet.

Thank you all for help in advance!

When I select "oldest first", the first post shown is the newest.  Vice-versa when selecting "newest first".  Am I misunderstanding the meaning of the term?  I suppose it doesn't matter as both options are available but it's weird.

eqell := expand((x+(1/2)*R1-(1/2)*R)^2/a^2+y^2/b^2-1); geometry:-ellipse(ell, eqell, [x, y]); detail(ell); ellipse: hint: unable to determine if 1/(1/2*R+1/2*R1)^2*(1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R^2+2/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1*R+1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1^2) is zero Error, (in geometry:-ellipse) the given polynomial/equation is not an algebraic representation of a ellipse. How to manage this error ? Thank you.

The expressions f(1), f(1,2,3), or f with any number of arguments, all match the type specfunc(f), while the expression f(g(1), 2 ,3) matches the type f(g(anything), anything, anything). However, is there a type which is matched by expressions like f(g(1), 2, 3 ...), with an arbitrary number of arguments after g(something)?

 

The command Typesetting:-Settings(prime=x,typesetprime=true):  makes diff(y(x),x) gives the latex as y'(x) which is what I wanted.

But I'd like to also be able to turn this off.  The reason is that in my program, I could have different variables in different places, and need to be able to turn this off/on as the program runs.

I know I can change the setting, by calling the above command again, with different variable. But I was looking for a way to turn it off as well. 

Similar to Typesetting:-Suppress  

Is there a way to do that? Actually the best solution would be, is to have the effect of Typesetting:-Settings(prime=x,typesetprime=true): be local to the proc. So if this command is used inside a proc, when leaving the proc, its effect will be automatically removed, as if this command was never issued.

Only when it is issued in global context, it will remain in effect until one does a restart.   Right now, the effect of Typesetting:-Settings(prime=x,typesetprime=true): is global. Even when called from inside a proc.  But this might be hard to implement. Therefore, being just able to turn it off is good for now.

Here is an example

restart;
foo:=proc(expr,x,y)
   Typesetting:-Settings(prime=x,typesetprime=true):
   print(Physics:-Latex(expr));

   #How to turn off the effect of above Typesetting command now?
   #so the following command works as the default setting?

   print(Physics:-Latex(expr));
end proc;


expr:=diff(y(x),x)=3:
foo(expr,x,y);

 

Hi

I am trying to implement a recursive algorithm for matrix inverses, its a seventh-order method

for n to 7 do
    new := (1/16*old) . (120*I + ((A . old) . (735*I + ((A . old) . (-861.*I + ((A . old) . (651*I + ((A . old) . (93*I + (A . (old(-15*I + (A . old)))))))))))));
    old := new;
    print(n);
end do

However I get a error informing me that this is a recursive statment. Which it is, but maple thinks this is a bad thing.

So it is clear that I am doing somthing wrong, Can anyone help me by explaining what I am doing wrong?

Mvh

Eric Ragnarsson