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Maple 2023 Questions and Posts

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Change in text area component triggers action thre...

Asked by: Anthrazit 895
embedded-components textarea
May 15 2023
1  7

Why is a change in the text area component triggering an action three times in a row?

Download ThePostmanKnocksThreeTimes.mw

setoptions3d stopped working in Maple 2023...

Asked by: Rouben Rostamian 8531
font setoptions3d
May 13 2023
3  3

This code fails in Maple 2023.  It used to work in earlier versions.  Did I miss something in the release notes?

> 

restart;
> 

kernelopts(version);

`Maple 2023.0, X86 64 LINUX, Mar 06 2023, Build ID 1689885`

> 

with(plots):
> 

setoptions3d(font=[Times,roman,12]);
> 

arrow(<1,1,1>);

Error, (in plottools:-rotate) invalid arguments for 3-D transformation

 

Maple 2023 Strange error...

Asked by: Reza23 40
vector indexing physics
May 13 2023
2  2

How do I force consistency in solve output?...

Asked by: Carlos36r 25
solve realrange relations
May 13 2023
0  3

The following program:

with(RealDomain):
sol1 := solve(x-1 > 0, x);
sol2 := solve(1/x^2 > 0, x);
sol3 := solve(1/(x^2-1) > 0, x);
sol4 := solve(x^2+1 > 0, x);
sol5 := solve(x^2+1 < 0, x);

Gives the following output:

sol1 := RealRange(Open(1),infinity)
sol2 := {x <> 0}
sol3 := RealRange(-infinity,Open(-1)), RealRange(Open(1),infinity)
sol4 := x
sol5 := NULL

I would like to force some consistency in the output of solve because I need to feed the output to a third-party program. For example, what's the deal with sol2 and sol3? Why are they formatted differently?

Ideally, I would like the previous output to be:

sol1 := RealRange(Open(1),infinity)
sol2 := RealRange(-infinity,Open(0)), RealRange(Open(0),infinity)
sol3 := RealRange(-infinity,Open(-1)), RealRange(Open(1),infinity)
sol4 := RealRange(-infinity,infinity)
sol5 := NULL

How do I achieve this?

The LaTeX commands seem to be too stable....

Asked by: lcz 1039
graphtheory export latex
May 13 2023
1  0

I find that no matter how I modify the style in the Maple command, the LaTeX output seems to be always fixed. This is a bit frustrating. 

G:=Graph(6,{{1,2},{1,4},{4,5},{2,5},{2,3},{3,6},{5,6}});
DrawGraph(G);
vp:=[[0,0],[0.5,0],[1,0],[0,0.5],[0.5,0.5],[1,0.5]]:
SetVertexPositions(G,vp):
DrawGraph(G);


Latex(G, terminal, 100, 100)

\documentclass{amsart}
\begin{document}
\begin{picture}(100,100)
\qbezier(12.40,87.60)(12.40,50.00)(12.40,12.40)
\qbezier(12.40,87.60)(31.20,50.00)(50.00,12.40)
\qbezier(12.40,12.40)(31.20,50.00)(50.00,87.60)
\qbezier(12.40,12.40)(50.00,50.00)(87.60,87.60)
\qbezier(50.00,87.60)(68.80,50.00)(87.60,12.40)
\qbezier(50.00,12.40)(68.80,50.00)(87.60,87.60)
\qbezier(87.60,87.60)(87.60,50.00)(87.60,12.40)
\put(12.400000,87.600000){\circle*{6}}
\put(10.194,96.943){\makebox(0,0){1}}
\put(12.400000,12.400000){\circle*{6}}
\put(8.726,3.531){\makebox(0,0){2}}
\put(50.000000,87.600000){\circle*{6}}
\put(50.000,97.200){\makebox(0,0){3}}
\put(50.000000,12.400000){\circle*{6}}
\put(50.000,2.800){\makebox(0,0){4}}
\put(87.600000,87.600000){\circle*{6}}
\put(91.274,96.469){\makebox(0,0){5}}
\put(87.600000,12.400000){\circle*{6}}
\put(89.806,3.057){\makebox(0,0){6}}
\end{picture}
\end{document}
 

DrawGraph(G,
stylesheet=[vertexborder=false,vertexpadding=20,edgecolor = "Blue",
vertexcolor="Gold",edgethickness=3], font=["Courier",10],size=[180,180])

Even when I change their colors (any other thing), they always go their own way. I don't know if there is a setting that can make the LaTeX output more flexible and in line with our expectations after adjustment.

How can we find a shortest closed walk passing thr...

Asked by: lcz 1039
May 12 2023
1  2

A Hamiltonian walk on a connected graph is a closed walk of minimal length which visits every vertex of a graph (and may visit vertices and edges multiple times). (See https://mathworld.wolfram.com/HamiltonianWalk.html)

 

Please note that there is a distinction between a Hamiltonian walk and a Hamiltonian cycle. Any graph can have a Hamiltonian walk, but not necessarily a Hamiltonian cycle.  The Hamiltonian number h(n) of a connected G is the length of a Hamiltonian walk. 

For example, let's consider the graph FriendshipGraph(2).

g:=GraphTheory[SpecialGraphs]:-FriendshipGraph(2);
DrawGraph(g)

Then its Hamiltonian number is 6.  A Hamiltonian walk is as shown in the following picture.

 

 

 

PS: After being reminded by others, I learned that a method in the following post seems to work, but I don't understand why it works for now. 

it's possible to formulate this as a Travelling Salesman Problem by augmenting the sparse graph into a complete graph by adding edges. These new edges represent shortest paths between any two vertices in the original graph and have weight equal to the path length.

 

It seems that the correctness of this transformation requires rigorous proof.

 

How can I collect(,diff) in the Physics package?...

Asked by: Hullzie16 343
collect physics
May 11 2023
1  2

I would like to collect in derivatives of a function(s) in a worksheet where I have the Physics package loaded but It does not want to do it. When I bring the expression to a blank worksheet it does everything just fine. Am I missing something small? Or is there additional commands/options I need to input? 

Thoughts?

CollectDiff.mw

How to evaluate a one-dimensional improper integra...

Asked by: sursumCorda 1254
integration numeric shill
May 11 2023
1  2

The highly oscillatory integrand is: 

(sin(x + sqrt(x)) + x*BesselJ(0, x^2))/(1 + x): # int(%, x = 0 .. infinity, numeric); # Note that the upper limit of `x` is NOT finite.

Unfortunately, Maple still cannot return a result in a few minutes. For instance, 

> 

restart;
infolevel[`evalf/int`] := 1:
> 

smartplot((sin(x+sqrt(x))+x*BesselJ(0, x^2))/(1+x))

 
> 

timelimit(0.1e3, evalf(Int((sin(x+sqrt(x))+x*BesselJ(0, x^2))/(1+x), x = 0 .. infinity)))

Control: Entering NAGInt

trying d01amc (nag_1d_quad_inf)
Control: d01amc failed
evalf/int/control: NAG failed result = result
evalf/int/improper: integrating on interval 0 .. infinity
evalf/int/improper: applying transformation x = 1/x
evalf/int/improper: interval is 0 .. 1 for the integrand:

                        /     (1/2)\            /    2\
                     sin\x + x     / + x BesselJ\0, x /
                     ----------------------------------
                                   1 + x               

and interval is 0 .. 1 for the integrand:

                                                /   1 \
                                         BesselJ|0, --|
                        /       (1/2)\          |    2|
                        |1   /1\     |          \   x /
                     sin|- + |-|     | + --------------
                        \x   \x/     /         x       
                     ----------------------------------
                                 /    1\  2            
                                 |1 + -| x             
                                 \    x/               

Control: Entering NAGInt
Control: trying d01ajc (nag_1d_quad_gen)
Control: d01ajc failed
evalf/int/control: NAG failed result = result

evalf/int/control: singularity at left end-point
evalf/int/transform: series contains {x^(1/2), x^(3/2), x^(5/2), x^(7/2), x^(9/2), x^(11/2), x^(13/2), x^(15/2), x^(17/2), x^(19/2), x^(21/2), x^(23/2), x^(25/2)}

evalf/int/singleft: applying transformation x = x^2
evalf/int/singleft: interval is 0 .. 1. for the integrand:

                  /   / 2            \    2        /    4\\  
                2 \sin\x  + csgn(x) x/ + x  BesselJ\0, x // x
                ---------------------------------------------
                                        2                    
                                   1 + x                     

evalf/int/control: Applying simplify/ln, integrand is 2*(sin(x^2+x)+x^2*BesselJ(0,x^4))/(1+x^2)*x
evalf/int/CreateProc: Trying easyproc
evalf/int/CreateProc: Trying makeproc
evalf/int/ccquad: n = 2 integral estimate = .7758263476953
                    n = 6 integral estimate = .8097413335347
evalf/int/ccquad: n = 18 integral estimate = .8097470386638
                                  error = .8097470386638e-11
From ccquad, result = .8097470386638 integrand evals = 19 error = .8097470386638e-11
Control: Entering NAGInt
Control: trying d01ajc (nag_1d_quad_gen)
Control: d01ajc failed
evalf/int/control: NAG failed result = result

evalf/int/control: singularity at left end-point

evalf/int/transform: series contains {1/x^(3/2), x^(1/2), cos(1/x^2+1/4*Pi), sin((x+x^(1/2))/x^(3/2)), sin(1/4*(4+Pi*x^2)/x^2)}
evalf/int/singleft: applying transformation x = x^2
evalf/int/singleft: interval is 0 .. 1. for the integrand:

                   /   /        /1\  \                    \
                   |   |1 + csgn|-| x|                    |
                   |   |        \x/  |  2          /   1 \|
                 2 |sin|-------------| x  + BesselJ|0, --||
                   |   |      2      |             |    4||
                   \   \     x       /             \   x //
                 ------------------------------------------
                                 3 /     2\                
                                x  \1 + x /                

evalf/int/control: Applying simplify/ln, integrand is 2*(sin((1+x)/x^2)*x^2+BesselJ(0,1/x^4))/x^3/(1+x^2)
evalf/int/control: Applying simplify/trig, integrand is (2*sin((1+x)/x^2)*x^2+2*BesselJ(0,1/x^4))/(x^3+x^5)
evalf/int/control: singularity at left end-point

evalf/int/transform: series contains {cos(1/x^4+1/4*Pi), sin((1+x)/x^2), sin(1/4*(4+Pi*x^4)/x^4)}
evalf/int/transform: no transform found
evalf/int/series: integrating on 0 .. .2493468135214 the series:

       2 (%2)     2 (%2) x   /2 (%2)      \  3   /  2 (%2)      \  5   
      --------- - -------- + |------- - %3| x  + |- ------- + %3| x    
        (1/2)       (1/2)    |  (1/2)     |      |    (1/2)     |      
      Pi      x   Pi         \Pi          /      \  Pi          /      
                                                                       
           /       2 (%2)      \  7   /     2 (%2)      \  9           
         + |- %3 + ------- - %4| x  + |%3 - ------- + %4| x            
           |         (1/2)     |      |       (1/2)     |              
           \       Pi          /      \     Pi          /              
                                                                       
                                                                       
           /2 (%2)           \  11   /          2 (%2) \  13           
         + |------- - %4 - %5| x   + |%4 + %5 - -------| x             
           |  (1/2)          |       |            (1/2)|               
           \Pi               /       \          Pi     /               
                                                                       
           /       2 (%2)      \  15   /     2 (%2)      \  17    / 19\
         + |- %5 + ------- + %6| x   + |%5 - ------- - %6| x   + O\x  /
           |         (1/2)     |       |       (1/2)     |             
           \       Pi          /       \     Pi          /             
                                                                       
                                                                       
                      /        4\                                      
             (1/2)    |4 + Pi x |                                      
      %1 := 2      sin|---------|                                      
                      |     4   |                                      
                      \  4 x    /                                      
                    /1 + x\   (1/2)                                    
      %2 := %1 + sin|-----| Pi                                         
                    |  2  |                                            
                    \ x   /                                            
             (1/2)    /1    1   \                                      
            2      cos|-- + - Pi|                                      
                      | 4   4   |                                      
                      \x        /                                      
      %3 := ---------------------                                      
                      (1/2)                                            
                  4 Pi                                                 
                        /        4\                                    
               (1/2)    |4 + Pi x |                                    
            9 2      sin|---------|                                    
                        |     4   |                                    
                        \  4 x    /                                    
      %4 := -----------------------                                    
                       (1/2)                                           
                  64 Pi                                                
                (1/2)    /1    1   \                                   
            53 2      cos|-- + - Pi|                                   
                         | 4   4   |                                   
                         \x        /                                   
      %5 := ------------------------                                   
                        (1/2)                                          
                  512 Pi                                               
                           /        4\                                 
                  (1/2)    |4 + Pi x |                                 
            1371 2      sin|---------|                                 
                           |     4   |                                 
                           \  4 x    /                                 
      %6 := --------------------------                                 
                          (1/2)                                        
                  16384 Pi                                             

evalf/int/CreateProc: Trying easyproc
evalf/int/CreateProc: Trying makeproc

evalf/int/CreateProc: Trying procmake
evalf/int/control: applying double-exponential method
evalhf mode unsuccessful -- retry in software floats
evalf/int/quadexp: applying double-exponential method

Error, (in tools/sign) time expired

  
> 

time() =

3999.500

 (1)

 =

%?

Download oscillatoryInt.mws

I tried to specify another method (as described in evalf/int), but it seems that this doesn't work. Any ideas?

Isolate variable...

Asked by: Andre Luis Alves Neves 20
isolate
May 10 2023
2  3

Hello,

How do I isolate the variable ng in the following expression:

rho := `&rho;g`*ng + `&rho;p`*np + `&rho;w`*nw;
B := np/Kp + nw/Kw + ng/Kg;

C := (B/rho)^(1/2);

As you can see, I am running the isolate command, but it is not including the variable C, or it returns the wrong result.

isolate(((np/Kp + nw/Kw + ng/Kg)/(`&rho;g`*ng + `&rho;p`*np + `&rho;w`*nw))^(1/2), ng);
                               ( Kp nw + Kw np) Kg
                   ng = -     -----------------

                                          Kw Kp       

 

isolate(C=((np/Kp + nw/Kw + ng/Kg)/(`&rho;g`*ng + `&rho;p`*np + `&rho;w`*nw))^(1/2), ng);
                             0 = 0

Thanks.                

How to solve some polynomial equation over the dom...

Asked by: sursumCorda 1254
solve multivariate shill
May 09 2023
0  7

In certain tasks, I need to find all accurate positive (not just nonnegative) roots that exist of some multivariate polynomials like: 

nsd := 16*a*b*c*(9 + a^2 + b^2 + c^2)*(b*c + a*(b + c) + 3*(a + b + c)) - (3 + a + b + c)^2*(a*b + 3*c)*(3*b + a*c)*(3*a + b*c): # assume((a, b, c) >~ 0);

According to fsolve/details, for one general equation, the fsolve command only computes "a single real root", so it is inadequate to tackle this question. But if I use the solve command with floating-point values, the computation cannot finish in ten minutes instead! (Maybe a longer time will suffice, yet this is rather unacceptable.) 

> 

restart;
> 

"Digits+=Digits:"
> 

#assume((a, b, c) >~ 0);
nsd := 16*a*b*c*(a^2 + b^2 + c^2 + 9)*(a*(b + c) + 3*(a + b + c) + b*c) - (a + b + c + 3)^2*(a*b + 3*c)*(a*c + 3*b)*(b*c + 3*a):
> 

fsolve({`~`[`>`](a, b, c, ` $`, 0), nsd = 0}, fulldigits)

Error, (in fsolve) expecting an equation or set or list of equations, but received inequalities {16*a*b*c*(a^2+b^2+c^2+9)*(a*(b+c)+3*a+3*b+3*c+b*c)-(a+b+c+3)^2*(a*b+3*c)*(a*c+3*b)*(b*c+3*a) = 0, 0 < a, 0 < b, 0 < c}

  
> 

fsolve([`$`(nsd = 0, 3)], fulldigits, {`~`[`=`](a, b, c, ` $`, 0 .. infinity)}, avoid = {{a = 0}, {b = 0}, {c = 0}})eval(nsd, %)

{a = 3.0000000005817604971, b = 3.0000000004676996798, c = 3.0000000004610312655}

 (1)
> 

timelimit(0.6e3, RealDomain[solve]([`~`[`>`](a, b, c, ` $`, 0), nsd = 0.], allsolutions))

Error, (in gcd/gcdchrem1) time expired

  
> 

timelimit(0.6e3, `assuming`([solve(nsd = 0., useassumptions, allsolutions)], [`~`[`>`](a, b, c, ` $`, 0)]))

Error, (in modp1/DistDeg) time expired

  
> 

""(* However, there are (at least) five positive solutions to 'nsd = 0'. *)" map2(eval,nsd,[{a=1,b=1,c=1},{a=3,b=3,c=3},{a=3,b=3,c=9},{a=3,b=9,c=3},{a=9,b=3,c=3}])"

[0, 0, 0, 0, 0]

 (2)
> 

time()

11127.031

 (3)
> 

NULL


Download solve_numerically.mws

Is there any workaround to obtain those (finitely many) positive solutions completely?

What is wrong with my nested if statement?...

Asked by: Carlos36r 25
conditional rtfm if-then
May 07 2023
3  6

Please excuse my thickness if any.

In the following IF statement:

if 1 <> 2 then
    OuterThen;
    if 1 <> 2 then
        InnerThen;
    else
        InnerElse;
    end if;    
else
    OuterElse;
end if;

I expect the output:

OuterThen
InnerThen

but I only get:

OuterThen

Why?

Why is the performance of LinearAlgebra[MatrixPowe...

Asked by: sursumCorda 1254
performance linearalgebra shill
May 07 2023
0  9

In practice, I need calculate the (principal) squareroot of some suitable large matrix exactly (so the desired result should not involve floating-point numbers, otherwise the decomposition will be of no theoretical value as a certificate …). But I find it difficult to do so in Maple. (What about the Efficient Computations - Maple Help (maplesoft.com)?)
Below are some matrices: (They are not contrived academic examples.) 

M__4 := <1,0,-2,0,1,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0|0,3,0,-6,0,3,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,-3,0,0,0,0,0,0,0,0,6,0,0,0,0,-3,0|-2,0,7,0,-8,0,3,0,0,0,0,0,0,0,0,1,0,-7,0,2,0,0,0,0,0,0,4,0,3,0,0,0,0,-3,0,0|0,-6,0,13,0,-8,0,1,0,0,0,0,0,0,0,0,6,0,-4,0,4,0,0,0,0,0,0,-1,0,-11,0,0,0,0,6,0|1,0,-8,0,13,0,-6,0,0,0,0,0,0,0,0,4,0,8,0,-1,0,0,0,0,0,0,-11,0,-6,0,0,0,0,6,0,0|0,3,0,-8,0,7,0,-2,0,0,0,0,0,0,0,0,-3,0,-1,0,1,0,0,0,0,0,0,2,0,4,0,0,0,0,-3,0|0,0,3,0,-6,0,3,0,0,0,0,0,0,0,0,-3,0,-3,0,0,0,0,0,0,0,0,6,0,3,0,0,0,0,-3,0,0|0,0,0,1,0,-2,0,1,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0|0,0,0,0,0,0,0,0,3,0,0,0,3,0,-3,0,0,0,0,0,0,-6,0,-3,0,6,0,0,0,0,3,0,-3,0,0,0|0,0,0,0,0,0,0,0,0,4,0,0,0,-2,0,0,0,0,0,0,0,0,-6,0,6,0,0,0,0,0,0,-2,0,0,0,0|0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,-2,0,-1,0,0,0,0,2,0,2,0,0,-1|0,0,0,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,0,0,-6,0,-6,0,0,0,0,0,0,6,0,0,0,0|0,0,0,0,0,0,0,0,3,0,0,0,3,0,-3,0,0,0,0,0,0,-6,0,-3,0,6,0,0,0,0,3,0,-3,0,0,0|0,0,0,0,0,0,0,0,0,-2,0,-6,0,4,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,-2,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,0,0,-3,0,3,0,0,0,0,0,0,6,0,3,0,-6,0,0,0,0,-3,0,3,0,0,0|-2,0,1,0,4,0,-3,0,0,0,0,0,0,0,0,7,0,-1,0,2,0,0,0,0,0,0,-8,0,-3,0,0,0,0,3,0,0|0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,0,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0|2,0,-7,0,8,0,-3,0,0,0,0,0,0,0,0,-1,0,7,0,-2,0,0,0,0,0,0,-4,0,-3,0,0,0,0,3,0,0|0,3,0,-4,0,-1,0,2,0,0,0,0,0,0,0,0,-3,0,7,0,-7,0,0,0,0,0,0,-2,0,8,0,0,0,0,-3,0|-1,0,2,0,-1,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0|0,-3,0,4,0,1,0,-2,0,0,0,0,0,0,0,0,3,0,-7,0,7,0,0,0,0,0,0,2,0,-8,0,0,0,0,3,0|0,0,0,0,0,0,0,0,-6,0,-1,0,-6,0,6,0,0,0,0,0,0,13,0,8,0,-11,0,0,0,0,-8,0,4,0,0,1|0,0,0,0,0,0,0,0,0,-6,0,-6,0,6,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,-2,0,-3,0,3,0,0,0,0,0,0,8,0,7,0,-4,0,0,0,0,-7,0,-1,0,0,2|0,0,0,0,0,0,0,0,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,-6,0,12,0,0,0,0,0,0,-6,0,0,0,0|0,0,0,0,0,0,0,0,6,0,-1,0,6,0,-6,0,0,0,0,0,0,-11,0,-4,0,13,0,0,0,0,4,0,-8,0,0,1|1,0,4,0,-11,0,6,0,0,0,0,0,0,0,0,-8,0,-4,0,-1,0,0,0,0,0,0,13,0,6,0,0,0,0,-6,0,0|0,0,0,-1,0,2,0,-1,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0|0,0,3,0,-6,0,3,0,0,0,0,0,0,0,0,-3,0,-3,0,0,0,0,0,0,0,0,6,0,3,0,0,0,0,-3,0,0|0,6,0,-11,0,4,0,1,0,0,0,0,0,0,0,0,-6,0,8,0,-8,0,0,0,0,0,0,-1,0,13,0,0,0,0,-6,0|0,0,0,0,0,0,0,0,3,0,2,0,3,0,-3,0,0,0,0,0,0,-8,0,-7,0,4,0,0,0,0,7,0,1,0,0,-2|0,0,0,0,0,0,0,0,0,-2,0,6,0,-2,0,0,0,0,0,0,0,0,0,0,-6,0,0,0,0,0,0,4,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,2,0,-3,0,3,0,0,0,0,0,0,4,0,-1,0,-8,0,0,0,0,1,0,7,0,0,-2|0,0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,3,0,3,0,0,0,0,0,0,0,0,-6,0,-3,0,0,0,0,3,0,0|0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,0,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0|0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,2,0,1,0,0,0,0,-2,0,-2,0,0,1>:
M__3 := 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Unexpectedly, LinearAlgebra[MatrixPower] does not work well. For instance: 
 

> 

restart;
> 

interface(version)

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

 (1)
> 

M__4 := <1,0,-2,0,1,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0|0,3,0,-6,0,3,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,-3,0,0,0,0,0,0,0,0,6,0,0,0,0,-3,0|-2,0,7,0,-8,0,3,0,0,0,0,0,0,0,0,1,0,-7,0,2,0,0,0,0,0,0,4,0,3,0,0,0,0,-3,0,0|0,-6,0,13,0,-8,0,1,0,0,0,0,0,0,0,0,6,0,-4,0,4,0,0,0,0,0,0,-1,0,-11,0,0,0,0,6,0|1,0,-8,0,13,0,-6,0,0,0,0,0,0,0,0,4,0,8,0,-1,0,0,0,0,0,0,-11,0,-6,0,0,0,0,6,0,0|0,3,0,-8,0,7,0,-2,0,0,0,0,0,0,0,0,-3,0,-1,0,1,0,0,0,0,0,0,2,0,4,0,0,0,0,-3,0|0,0,3,0,-6,0,3,0,0,0,0,0,0,0,0,-3,0,-3,0,0,0,0,0,0,0,0,6,0,3,0,0,0,0,-3,0,0|0,0,0,1,0,-2,0,1,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0|0,0,0,0,0,0,0,0,3,0,0,0,3,0,-3,0,0,0,0,0,0,-6,0,-3,0,6,0,0,0,0,3,0,-3,0,0,0|0,0,0,0,0,0,0,0,0,4,0,0,0,-2,0,0,0,0,0,0,0,0,-6,0,6,0,0,0,0,0,0,-2,0,0,0,0|0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,-2,0,-1,0,0,0,0,2,0,2,0,0,-1|0,0,0,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,0,0,-6,0,-6,0,0,0,0,0,0,6,0,0,0,0|0,0,0,0,0,0,0,0,3,0,0,0,3,0,-3,0,0,0,0,0,0,-6,0,-3,0,6,0,0,0,0,3,0,-3,0,0,0|0,0,0,0,0,0,0,0,0,-2,0,-6,0,4,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,-2,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,0,0,-3,0,3,0,0,0,0,0,0,6,0,3,0,-6,0,0,0,0,-3,0,3,0,0,0|-2,0,1,0,4,0,-3,0,0,0,0,0,0,0,0,7,0,-1,0,2,0,0,0,0,0,0,-8,0,-3,0,0,0,0,3,0,0|0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,0,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0|2,0,-7,0,8,0,-3,0,0,0,0,0,0,0,0,-1,0,7,0,-2,0,0,0,0,0,0,-4,0,-3,0,0,0,0,3,0,0|0,3,0,-4,0,-1,0,2,0,0,0,0,0,0,0,0,-3,0,7,0,-7,0,0,0,0,0,0,-2,0,8,0,0,0,0,-3,0|-1,0,2,0,-1,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0|0,-3,0,4,0,1,0,-2,0,0,0,0,0,0,0,0,3,0,-7,0,7,0,0,0,0,0,0,2,0,-8,0,0,0,0,3,0|0,0,0,0,0,0,0,0,-6,0,-1,0,-6,0,6,0,0,0,0,0,0,13,0,8,0,-11,0,0,0,0,-8,0,4,0,0,1|0,0,0,0,0,0,0,0,0,-6,0,-6,0,6,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,-2,0,-3,0,3,0,0,0,0,0,0,8,0,7,0,-4,0,0,0,0,-7,0,-1,0,0,2|0,0,0,0,0,0,0,0,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,-6,0,12,0,0,0,0,0,0,-6,0,0,0,0|0,0,0,0,0,0,0,0,6,0,-1,0,6,0,-6,0,0,0,0,0,0,-11,0,-4,0,13,0,0,0,0,4,0,-8,0,0,1|1,0,4,0,-11,0,6,0,0,0,0,0,0,0,0,-8,0,-4,0,-1,0,0,0,0,0,0,13,0,6,0,0,0,0,-6,0,0|0,0,0,-1,0,2,0,-1,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0|0,0,3,0,-6,0,3,0,0,0,0,0,0,0,0,-3,0,-3,0,0,0,0,0,0,0,0,6,0,3,0,0,0,0,-3,0,0|0,6,0,-11,0,4,0,1,0,0,0,0,0,0,0,0,-6,0,8,0,-8,0,0,0,0,0,0,-1,0,13,0,0,0,0,-6,0|0,0,0,0,0,0,0,0,3,0,2,0,3,0,-3,0,0,0,0,0,0,-8,0,-7,0,4,0,0,0,0,7,0,1,0,0,-2|0,0,0,0,0,0,0,0,0,-2,0,6,0,-2,0,0,0,0,0,0,0,0,0,0,-6,0,0,0,0,0,0,4,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,2,0,-3,0,3,0,0,0,0,0,0,4,0,-1,0,-8,0,0,0,0,1,0,7,0,0,-2|0,0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,3,0,3,0,0,0,0,0,0,0,0,-6,0,-3,0,0,0,0,3,0,0|0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,0,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0|0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,2,0,1,0,0,0,0,-2,0,-2,0,0,1>:
> 

M__3 := 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> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(M__4, 1/2)))

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 10 x 10 matrix

  

IntegerCharacteristicPolynomial: Used total of  2  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 10 x 10 matrix

  

IntegerCharacteristicPolynomial: Used total of  2  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 10 x 10 matrix

  

IntegerCharacteristicPolynomial: Used total of  2  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 6 x 6 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

Error, (in simplify/sqrt/fraction) time expired

  
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(M__3, 1/2)))

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 13 x 13 matrix

  

IntegerCharacteristicPolynomial: Used total of  4  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

memory used=2.84GiB, alloc change=8.00MiB, cpu time=3.05m, real time=3.01m, gc time=5.84s

  

_rtable[36893490642867319380]

 (2)
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(M__2, 1/2)))

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 6 x 6 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 6 x 6 matrix

  

IntegerCharacteristicPolynomial: Used total of  1  prime(s)

  

memory used=2.40GiB, alloc change=0 bytes, cpu time=2.85m, real time=2.82m, gc time=4.08s

  

_rtable[36893490642428505372]

 (3)
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(M__1, 1/2)))

CharacteristicPolynomial: working on determinant of minor 2

  

CharacteristicPolynomial: working on determinant of minor 3

  

CharacteristicPolynomial: working on determinant of minor 4

  

CharacteristicPolynomial: working on determinant of minor 5

  

CharacteristicPolynomial: working on determinant of minor 6

  

CharacteristicPolynomial: working on determinant of minor 2

  

CharacteristicPolynomial: working on determinant of minor 3

  

CharacteristicPolynomial: working on determinant of minor 4

  

CharacteristicPolynomial: working on determinant of minor 5

  

CharacteristicPolynomial: working on determinant of minor 6

  

CharacteristicPolynomial: working on determinant of minor 2

  

CharacteristicPolynomial: working on determinant of minor 3

  

CharacteristicPolynomial: working on determinant of minor 4

  

CharacteristicPolynomial: working on determinant of minor 5

  

CharacteristicPolynomial: working on determinant of minor 6

  

CharacteristicPolynomial: working on determinant of minor 2

  

CharacteristicPolynomial: working on determinant of minor 3

  

CharacteristicPolynomial: working on determinant of minor 4

  

CharacteristicPolynomial: working on determinant of minor 5

  

CharacteristicPolynomial: working on determinant of minor 6

  

CharacteristicPolynomial: working on determinant of minor 2

  

CharacteristicPolynomial: working on determinant of minor 3

  

CharacteristicPolynomial: working on determinant of minor 4

  

CharacteristicPolynomial: working on determinant of minor 5

  

CharacteristicPolynomial: working on determinant of minor 6

  

Error, (in LinearAlgebra:-MatrixFunction) time expired

  
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(evalhf[hfloat](M__4), 1/2)))

Eigenvalues: calling external function

  

Eigenvalues: CLAPACK hw_dgeevx_

  

memory used=468.66MiB, alloc change=0 bytes, cpu time=18.48s, real time=19.71s, gc time=1.09s

  

_rtable[36893490642747474396]

 (4)
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(evalhf[hfloat](M__3), 1/2)))

Eigenvalues: calling external function

  

Eigenvalues: CLAPACK hw_dgeevx_

  

Multiply: copying first Matrix to enable external call

  

Multiply: calling external function

  

Multiply: NAG hw_f06yaf

  

unknown: NAG hw_f06yaf

  

unknown: NAG hw_f06yaf

  

unknown: NAG hw_f06yaf

  

memory used=13.43GiB, alloc change=0 bytes, cpu time=8.66m, real time=8.46m, gc time=26.41s

  

_rtable[36893490642773280876]

 (5)
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(evalhf[hfloat](M__2), 1/2)))

Eigenvalues: calling external function

  

Eigenvalues: CLAPACK hw_dgeevx_

  

Multiply: copying first Matrix to enable external call

  

Multiply: calling external function

  

Multiply: NAG hw_f06yaf

  

unknown: NAG hw_f06yaf

  

memory used=13.45GiB, alloc change=0 bytes, cpu time=8.39m, real time=8.23m, gc time=26.12s

  

_rtable[36893490642902286332]

 (6)
> 

timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(evalhf[hfloat](M__1), 1/2)))

Eigenvalues: calling external function

  

Eigenvalues: CLAPACK hw_dgeevx_

  

Multiply: copying first Matrix to enable external call

  

Multiply: calling external function

  

Multiply: NAG hw_f06yaf

  

unknown: NAG hw_f06yaf

  

Error, (in LinearAlgebra:-MatrixFunction) time expired

  
> 

"Digits+=5:"timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(evalf(M__4), 1/2)))

Eigenvalues: calling external function

  

Eigenvalues: copying first Matrix, to enable external call

  

Eigenvalues: CLAPACK hw_dgeevx_

  

memory used=418.17MiB, alloc change=0 bytes, cpu time=16.33s, real time=16.16s, gc time=796.88ms

  

_rtable[36893490642540182332]

 (7)
> 

"Digits+=5:"timelimit(0.1e4, CodeTools:-Usage(LinearAlgebra:-MatrixPower(evalf(M__1), 1/2)))

Eigenvalues: calling external function

  

Eigenvalues: copying first Matrix, to enable external call

  

Eigenvalues: CLAPACK sw_dgeevx_

  

Multiply: copying first Matrix to enable external call

  

Multiply: copying second Matrix to enable external call

  

Multiply: calling external function

  

Multiply: NAG sw_f06yaf

  

unknown: copying second Matrix to enable external call

  

unknown: calling external function

  

unknown: NAG sw_f06yaf

  

Error, (in LinearAlgebra:-MatrixFunction) time expired

  

time() = 5731.593NULL


 

Download performance_of_`sqrtm`.mw

The last six numerical experiments all fail to compute the square root. (Accordingly, here it is impossible to convert each numeric element to one of the "simplest" algebraic numbers that approximates it well.) As you can see, if I execute them directly (i.e., without converting each entry to the nearest floating-point value), the elapsed time required to run the procedure is still unacceptable! (Note that they can be evaluated symbolically in fact.) Is this a bug of Maple? And how do I get the desired results in Maple efficiently?

Unable to handle exact expressions that contain th...

Asked by: sursumCorda 1254
simplify simplification lambertw
May 06 2023
0  6

Let y＞1. It can be proved (maybe by hand) that the following four expressions are mathematically equivalent: 

assume(y > 1); # Assumption!
expr := [0, 0, 0, 0]: # Preallocation.
expr[1] := exp(y*LambertW(ln(y))):
expr[2] := (ln(y)/LambertW(ln(y)))^y:
expr[3] := eval(x^(x^x), x = exp(LambertW(ln(y)))):
expr[4] := eval(x^(x^x), x = ln(y)/LambertW(ln(y))):

But unfortunately, when I tried to simplify expri - exprj (symbolically), I just got: 

seq(seq(ifelse(j <> i, [i, j, verify(expr[j], expr[i], equal)], NULL), j = 1 .. numelems(expr)), i = 1 .. numelems(expr)); # is(expr[j] = expr[i]) does not work as well.
 = 
   [1, 2, FAIL], [1, 3, FAIL], [1, 4, FAIL], [2, 1, FAIL], 

     [2, 3, FAIL], [2, 4, FAIL], [3, 1, FAIL], [3, 2, FAIL], 

     [3, 4, true], [4, 1, FAIL], [4, 2, FAIL], [4, 3, true]

In other words, Maple can only determine that expr[3] = expr[4].
One may check that, for example, 

MmaTranslator:-Mma:-Chop([seq](seq(evalhf(subs(y = log10(rand()), expr[i] - expr[j])), j = 1 .. numelems(expr)), i = 1 .. numelems(expr)), 2^(-26));
 = 
        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

However, the desired approach is simplifying them symbolically. Is there a way to do so in Maple?

Kudos for Maple 2023!

by: rcorless 750 Maple 2023
polynomial integration rootfinding
May 05 2023
2  3

Just installing Maple 2023 on my office machine (a mac); installed it on my travel computer (a Surface Pro running Windows) yesterday.

Configured Jupyter notebooks to use the 2023 Maple Kernel and it all went smoothly.  I was *delighted* to notice that plotting Lambert W in Jupyter with the command

plot( [W(x), W(-1,x)], x=-1..4, view=[-1..4, -3.5..1.5], colour=[red,blue], scaling=constrained, labels=[x,W(x)] );

produced a *better* plot near the branch point.  This is hard to do automatically!  It turns out this is a side effect of the better/faster/more memory efficient adaptive plotting software, which I gather from "What's New" was written for efficiency not for quality.  But the quality is better, too!  Nice!

I am working my. way through the "What's New" and I'm really pleased to learn about the new univariate polynomial rootfinder, *not least because it cites the paper describing the algorithm*.  Lots of other goodies too; the new methods of integration look like serious improvements.  Well done. (One thing there: "parallel Risch" is a term of art, and may lead people to believe that Maple is doing something with parallel computing there.  I don't think so.  Could a reference be supplied?)

The new colour schemes and plotting features in 3d and contour plotting look fabulous.

Direct Python language support from a code edit region is not at all what I expected to see---I wonder if it will work in a Jupyter notebook?  I'm going to have to try it...

I'm quite impressed.  The folks at Maplesoft have been working very hard indeed.  Congratulations on a fine release!

 

Why does the figure generated from the tex code ha...

Asked by: lcz 1039
export plotting latex
May 04 2023
0  5

I followed the code on the website https://de.maplesoft.com/support/help/maple/view.aspx?path=updates/Maple18/GraphTheory to convert a graph to LaTeX code. However, after compiling with pdflatex, I found that some edges of the graph are jagged.

restart:    
with(GraphTheory):
with(SpecialGraphs):
S:=SoccerBallGraph():
Latex(S,FileTools:-JoinPath([currentdir(), "soccer.tex"]),300,300,true)

soccer.pdf

I suspect it's because of the converted LaTeX code.

PS: The PDF conversion issue from last time still remains unsolved in Maple 2023; see

https://www.mapleprimes.com/questions/236142-How-To-Remove-The-Mosaic-Of-Vertices.

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