Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

According to this help page

the transitive reduction of graph G, is the graph with the fewest edges that still shares the same reachability as G (but might contain new edges not present in G). 

However, in Maple 2023, things become strange; different branches return distinct numbers of edges: 
(33 arcs or 40 arcs?)

restart;

with(GraphTheory):

showstat(TransitiveReduction, 4)


GraphTheory:-TransitiveReduction := proc(G::GRAPHLN, $)
local D, V, T, i, j, k, A, M, n, flags, B;
       ...
   4   if _EnvDisableExt <> true then
           ...
       elif D <> (':-directed') then
           ...
       else
           ...
       end if;
       ...
end proc
 

 

G__0 := Digraph({[2, 8], [3, 1], [4, 9], [5, 10], [6, 19], [7, 12], [8, 13], [9, 3], [10, 4], [10, 14], [11, 5], [11, 15], [12, 6], [12, 16], [13, 7], [13, 17], [14, 9], [15, 10], [15, 18], [16, 19], [17, 12], [17, 20], [18, 14], [19, 11], [19, 21], [20, 22], [21, 18], [22, 16], [22, 23], [23, 19]})

G__0 := `Graph 1: a directed graph with 23 vertices and 30 arc(s)`

(1)

G__1 := TransitiveReduction(G__0)

G__1 := `Graph 2: a directed graph with 23 vertices and 33 arc(s)`

(2)

_EnvDisableExt := trueG__2 := TransitiveReduction(G__0)

G__2 := `Graph 3: a directed graph with 23 vertices and 40 arc(s)`

(3)

IsIsomorphic(G__1, G__2)

false

(4)

 


 

Download TransReduction.mw

Any bugs? 

G__0 := GraphTheory:-Digraph({[3, 1], [9, 3], [4, 9], [14, 9], [10, 4], [5, 10], [15, 10], [11, 5], [19, 11], [12, 6], [7, 12], [17, 12], [13, 7], [8, 13], [2, 8], [10, 14], [18, 14], [11, 15], [6, 19], [16, 19], [23, 19], [13, 17], [15, 18], [21, 18], [12, 16], [22, 16], [22, 23], [20, 22], [19, 21], [17, 20]}):

How to find the similarity matrix that applies A in N, B in P, C in C and B in M;
 

restart;  
with(geometry):  
with(plots):  
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':
#Vdot := proc(U, V) local i; add(U[i]*V[i], i = 1 .. 2); end proc
;

with(LinearAlgebra):
point(A, 0, 1);
point(B, 1, 1);
point(C, 1, 0);
point(E, 0, 0);
square(Sq, [A, B, C, E]);
Phi := (1 + sqrt(5))/2;
point(N, (2 - Phi)/(Phi - 1), 1);
line(BE, [B, E]);
MakeSquare(s1, [N, C, 'diagonal']);
point(M, (3 - sqrt(5))/(2*sqrt(5) - 2), (3 - sqrt(5))/(2*sqrt(5) - 2));
point(P, (1 + sqrt(5))/(2*sqrt(5) - 2), (3*sqrt(5) - 5)/(2*sqrt(5) - 2));
                               A

                               B

                               C

                               E

                               Sq

                             1   1  (1/2)
                      Phi := - + - 5     
                             2   2       

                               N

                               BE

                               s1

                               M

                               P

 display(draw([
A(color = black, symbol = solidcircle, symbolsize = 12),   
B(color = black, symbol = solidcircle, symbolsize = 12),   
C(color = black, symbol = solidcircle, symbolsize = 12),    
E(color = black, symbol = solidcircle, symbolsize = 12), 
N(color = black, symbol = solidcircle, symbolsize = 12 ),  
Sq(color=red),BE(color=green),  
s1(color = blue)]),   
textplot([[coordinates(A)[], "A"],   
[coordinates(B)[], "B"], 
[coordinates(E)[], "E"], 
[coordinates(N)[], "N"],
[coordinates(P)[], "P"],
[coordinates(M)[], "M"],   
[coordinates(C)[], "C"]], align = [above, right]), axes = none); Thank you.

I can derive a symbolic solution by hand for the following ODE, but cannot get Maple to do it for me.  Any tricks?

restart;

Velocity field, -infinity < x and x < infinity,  t > 0.

v := (x,t) -> piecewise(x <= -t, 0, x < t, 1 - 1/2*(1 - x/t));

v := proc (x, t) options operator, arrow; piecewise(x <= -t, 0, x < t, 1/2+(1/2)*x/t) end proc

Position x(t):

de := diff(x(t),t) = v(x(t),t);

de := diff(x(t), t) = piecewise(x(t) <= -t, 0, x(t) < t, 1/2+x(t)/(2*t))

Initial condition, assuming a > 0

ic := x(0) = -a;

x(0) = -a

Symbolic solution, calculated by hand:

x__exact := t -> piecewise(t < a, -a, t - 2*sqrt(t)*sqrt(a));

x__exact := proc (t) options operator, arrow; piecewise(t < a, -a, t-2*sqrt(t)*sqrt(a)) end proc

Verify exact solution by comparing it against the numeric solution for some a > 0:

a := 3;  # any a>0 should do
dsol := dsolve({de,ic}, numeric):
plots:-odeplot(dsol, t=0..5);   # dsolve solution
plot(x__exact(t), t=0..5);      # symbolic solution (calculated by hand)
a := 'a';

3

a

Can Maple's dsolve find the exact solution?  This one returns empty in Maple 2022:

dsolve({de, ic}) assuming a > 0, t > 0;

Download ode-piecewise.mw

 

I need your help....

I want to use the maple 2023 kernel in jupyter lab. I followed, to knowledge, the maple installation in windows10 and could not get it to work
after numerous attempts. Maybe it is a path issue that I am getting wrong.
I decided to use it with EndeavourOS distro for Linux as Sagemath interest me. Here it recognizes the kernel but gives syntax errors when
running code; it does not understand ‘:-’ for example. 
Again I used maple suggested installation to no avail.
I used the alternative following comands and it recognizes Maple2023 in the kernels menu but to repeat does not run code, simply gives errors.
sudo pacman -S python-jupyterlab
python -m venv maple2023
source maple2023/bin/activate
pip install jupyter ipykernel
python -m ipykernel install --user --name=maple2023
jupyter kernelspec list
 

If I have a pde with multiple constants (for example a and b) in them such that some are fixed constants (say k) and some terms are undetermined constants , how do I put that in a PDE such that Maple knows to solve the equation not for arbritary k (in case no solution exists), but any k such that k is not a function of the differentiating variable.

I put this command and It keep saying  plot(f(x), x = -0.667 .. 1.71, y = -5 .. 20, gridlines); Error, (in plot) unexpected options: [1.71 = -.667 .. 1.71, y = -5 .. 20] . How can I fix this

I have been try to code the 

mdl:-Fit(x, y, opts)
command in Deep learning package

But i feel new to that command I am making errors 

Can I get a small toy code how to call it and its output on train and test

so that i could learn

kind help please

Hello,
 i want to increase my value monotonically  . but i don't want to do it like sequence. how can i write code.

for example my value ..starts at 0...to some values i just want to increase.
help me plz

Please help me how to plot the following Chemotaxis System in Maple. Great Thanks

PDE 1= diff(p(x,t),t)-diff(p(x,t)*q(x,t),x)=D*diff(p(x,t),x,x)

PDE 2 = diff(q(x,t),t)-diff(p(x,t),x)=0

with the initial conditions

p(x)=0.5+1/(1+exp(2*(x-30)))

and

p(x)=0.5+1/(1+exp(-2*(x-30)))

and the boundary conditions

p(0, t) = 1.5, p(1, t) = 0.5

and

q(0, t) = 0.5, q(1, t) = 1.5

Stupid question, but how do I get the code on the math apps CaesarCipher from the help page?  I see the variable cipher but it's content is a mystery.

(Sorry guys, I changed the title to better reflect the content of the question and it bumped back up the top)

This happened on Windows 10 clicking on *.mws documents while Maple 2023 was not running.

My observations with one document (I do not have others at hand at the moment):

No freeze when Maple is already running.

No freeze when the startup page (Start.mw) is disabled.

Older versions opened in Windows file explorer with “right click and open with” did not show this behavior.

Since there are ways to open such old documents, my intention is to document my observations and to find out if others can reproduce it. If not, my setup might differ from default or the file has an issue.

Here is a demonstration involving two decision problems (where evalf is applied to the output for better readability): 
 

interface(version);

restart;

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

(1)

RealDomain:-solve({x*y = 3*z^5+4, x^2*y^2-3*x^2*z^2 = 1., x^3+y^3+z^3 = 12})

{x = 2.948903259, y = -2.257458014, z = -1.288554964}, {x = -.7294615910, y = 2.402430460, z = -1.139060479}, {x = .6177631401, y = 2.331476708, z = -.9687540923}, {x = 2.113678892, y = 1.450731881, z = -.7917893433}

(2)

SMTLIB:-Satisfy({x*y = 3*z^5+4, x^2*y^2-3*x^2*z^2 = 1, x^3+y^3+z^3 = 12}, showsmtlib)

(declare-fun x () Real)
(declare-fun y () Real)
(declare-fun z () Real)
(assert (and (= (* x y) (+ (* (* z z z z z) 3) 4)) (= (+ (* (* x x) (* y y)) (* (* (* x x) (* z z)) (- 3))) 1) (= (+ (* x x x) (* y y y) (* z z z)) 12)))
(check-sat)
(exit)

 

Error, (in SMTLIB:-smtlib_execute) external linking: error loading external library mplsmtlib.dll: Ҳ���ָ����ģ�顣

 

RealDomain:-solve({(x^2-2*y*z)*(x^3-y+z) = 0, x^4-y*z^3 = 2., z^4+x^3-2*x*y+3*y*z = 0})

{x = -1.130532018, y = -.1818551573, z = 1.263080805}, {x = 1.123233144, y = .4467032548, z = -.9704268675}, {x = 1.250562423, y = 2.517328867, z = .5615663246}, {x = 2.489770959, y = 16.73009962, z = 1.296110460}, {x = -1.336432744, y = -.7736167557, z = -1.154352246}, {x = 1.209937072, y = 1.655230257, z = .4422187526}

(3)

SMTLIB:-Satisfy({(x^2-2*y*z)*(x^3-y+z) = 0, x^4-y*z^3 = 2, z^4+x^3-2*x*y+3*y*z = 0}, showsmtlib)

(declare-fun x () Real)
(declare-fun y () Real)
(declare-fun z () Real)
(assert (and (= (* (+ (* x x) (* (* y z) (- 2))) (+ (* x x x) (* y (- 1)) z)) 0) (= (- (* x x x x) (* y (* z z z))) 2) (= (+ (* z z z z) (* x x x) (* (* x y) (- 2)) (* (* y z) 3)) 0)))
(check-sat)
(exit)

 

Error, (in SMTLIB:-smtlib_execute) external linking: error loading external library mplsmtlib.dll: Ҳ���ָ����ģ�顣

 

?SMTLIB:-Satisfy


 

Download SMTLIB[Satisfy].mw

As you can see, the SMTLIB:-Satisfy command fails to work in Maple 2023, and I have to install the Visual Studio 2013 (VC++ 12.0) manually. But unfortunately, even if I have installed the vcredist_x64.exe beforehand, the computation still cannot be done in 1000 seconds! (Please note that I just require one real instance rather than all solutions.) Does anyone know why? 
By the way, since the default SMT solver (in Maple 2023) is Z3, will another SMT solver (like cvc5) be supported in future Maple releases?

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