Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Can one hope that next version of Maple will be able to solve the standard convection-diffusion pde in 1D?

pde:=diff(u(x,t),t)=d*diff(u(x,t),x$2)+c*diff(u(x,t),x);

in 1D. Even the most simple form with zero boundary conditions can't be solved.

pde:=diff(u(x,t),t)=d*diff(u(x,t),x$2)+c*diff(u(x,t),x);
bc:=u(0,t)=0,u(L,t)=0;
ic:=u(x,0)=f(x);
sol:=pdsolve([pde,ic,bc],u(x,t)) assuming d>0,c>0,L>0

              sol := NULL

I tried some HINT's also but not all of them.

FYI, Mathematica 12.1 is now able to solve the above PDE

ClearAll["Global`*"];
pde=D[u[x,t],t]==d*D[u[x,t],{x,2}]+c*D[u[x,t],x];
bc={u[0,t]==0,u[L,t]==0};
ic=u[x,0]==f[x];
DSolve[{pde,bc,ic},u[x,t],{x,t},Assumptions->{d>0,c>0,L>0}]

Gives

Is it possible I am overlooking some other option or a trick to obtain solution for the above using pdsolve? Only reason I am asking is that Maple can solve much more complicated PDE's and the above is one of the basic diffusion based PDE's. So I am surprised why Maple still can't solve this as it is just a seperation of variables method.

Maple 2020 on windows 10. Physics version 631

Why is my figure not smooth? How can I make it smooth?
 

with(plots, implicitplot); with(plots)

pp1 := implicitplot(mu*x-ln(1+x) = 0, mu = -10 .. 5, x = -5 .. 5, color = black)

 

``


 

Download mm.mw

 I have a problem about extremal function.

The function is shown below with restricted condition of x and a:  x>=2 and -1 < a <0.

(x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)

I guess that  it's minimum value is greater than 0.  In other words,  I want prove that  (x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)>0

when I use Minimize function,

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<a, a<0})

I 'm not seeing but Error, (in Optimization:-NLPSolve) strict inequalities are not valid constraints. I cannot but add the condition of equality of a : -1<=a, a<=0.

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<=a, a<=0})

A result is returned with a warning:
Warning, no iterations performed as initial point satisfies first-order conditions
[0.000000, [a = -2.225074*10^(-308), x = 2.000000]]

 

Local or Global ?

When I read recent question post 

https://www.mapleprimes.com/questions/229132-Maximize-Function-Does-Not-Work?ref=Feed:MaplePrimes:New%20Questions

 I'm worrying  that Maple only returns local  extremun. So I use the freely  maple package DirectSearch. We can get it from  https://www.maplesoft.com/applications/view.aspx?SID=101333.

DirectSearch:-GlobalOptima(-((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)),{x>=2, -1<a, a<0},maximize);

 Note: I add a  minus sign to find maximize value .

It returns: [0.002264, [a = -0.000203, x = 1.019590*10^13], 605]

But I substitute the value of a and x  into the function,it returns strange result:   4078.360000 not  -0.002264.

I’m confused.. 

I try to use  Mathematica, 

NMinimize[{(x - 3/2)^a - (x - 1)^
    a + (1 - 2^(a - 1))*((x - 3/2)^a - (x - 1/2)^a) - 
   x*((x - 3/2)^a + x^a - (x - 1/2)^a - (x - 1)^a), 
  x >= 2 && a > -1 && a <= 0}, {x, a}]

It retruns {0., {x -> 13.256, a -> 0.}}  May be well.

 

mimimize.mw

 

i need to create a table with information from plots like how many times x become 0

this is the way to make an null oscillation 

please help!

I am trying to calculate the following integra   
r*rr*g1^2*h1^2*f1^2*fh1^2*exp(-2*t)/t

here g1 is a kummerM functin in s, and also h1 is another kummerM function  in ss, and f1 and fh1 are the HeunB functions with complex arguments in r and rr. and t=sqrt((r-rr)^2+(s-ss)^2).I would like to integte over dr drr ds dss

restart; F := rsolve({16*s(n+1) = 2+12*s(n)-2*s(n-1), s(1) = 1, s(2) = 5/8}, s); Error, (in s) cannot determine if this expression is true or false: n
solve({sigma*E-(mu+alpha+gamma)*I = 0, gamma*E+Lambda*N*P-(mu+alpha)*R = 0, Beta__1*S*E+Beta__2*S*I/(I*M+1)-(mu+sigma)*E = 0, Lambda(1-p)*N-mu*S-Beta__1*S*E-Beta__2*S*I/(I*M+1) = 0}, {E, I, R, S}, explicit)

I'm not sure if there's something on the page I'm not seeing but even  https://www.maplesoft.com/support/help/Maple/view.aspx?path=Optimization/Minimize#examples

 

Maximize(2*x^2 + 2*y^2 + y, {2*x + y <= 6, y^2 - x <= 2})

a literal copy-paste of the posted example maple just repeats what I posted Idk whats wrong. btw is there some way to read the maple documentation pages?

 

Wis_BS2_Taak2_2019-2020_20200323-1.mw

Hello,

I have some huge troubble with making sure all formula's wont be forgotten by Maple.

For example:

f(x):=a+b;
a:=5;
b:=2;
f(x):=f(x);  --> gives me f(x):=f(x) instead of saying f(x):=7

In my document the naming is a bit more complex.

I have a variable named "M_Inwendig2[y]" in the uploaded document. When i name it "M_Inwendig2(y)" (notice [-->( )
maple refuses to use the previous filled/calculated variables.

Due to this error i have copy and pasted the answer to a new formula to continue my work, therefor it becomes quite messy... Now i am trying to fix this.

Ideal all names will be M[inwendig2](y). So the first letter will tell the kind of variable (Moment) the subscript will tell the part (inside) and the depending variable will be between ().

In the document i have marked all error's and copy's RED.

Anyone can advice me? i have named variables the same way in the past, but now it doesnt work.

Regards,


 

I am interested in how easy it is to work with formulae in the Maple language.  For example, you can easily add two equations together with '+'.

 

e1:=x^2+1=2*x;

x^2+1 = 2*x

(1)

e2:=x^3+x=5;

x^3+x = 5

(2)

e1+e2;

x^3+x^2+x+1 = 2*x+5

(3)

 

I was pleased when the following example added (x+1) to both sides of an equation,

 

e3:=x+1;

x+1

(4)

e1+e3;

x^2+x+2 = 3*x+1

(5)

Some other algebraic operations work.

e1-e3;

x^2-x = x-1

(6)

e1*e3;

(x+1)*(x^2+1) = 2*(x+1)*x

(7)

e1/e3;

(x^2+1)/(x+1) = 2*x/(x+1)

(8)

e1^(1/2);

(x^2+1)^(1/2) = 2^(1/2)*x^(1/2)

(9)

 

Build-in functions do not work, though, but there is a simple solution.

exp(e1);

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received x^2+1 = 2*x

 

exp(rhs(e1))=exp(lhs(e1));

exp(2*x) = exp(x^2+1)

(10)

map(exp,e1);

exp(x^2+1) = exp(2*x)

(11)

 

The methods also apply to inequality formulae.  I'm not as pleased about how it does '*' and '/' for inequalities.  You can get more control using rhs and lhs functions.  Here are some examples:  

e4:=x^3<5*(x+1);

x^3 < 5*x+5

(12)

e4+e3;

x^3+x < 6*x+5

(13)

e4-e3;

x^3-x < 4*x+5

(14)

e4*e3;

(x^3 < 5*x+5)*(x+1)

(15)

e4/e3;

(x^3 < 5*x+5)*(1/(x+1))

(16)

eval(%,x=4);

64/5 < 5

(17)

evalb(%);

false

(18)

(16)/x^2;

((x^3 < 5*x+5)*(1/(x+1)))/x^2

(19)

simplify(%);

((x^3 < 5*x+5)*(1/(x+1)))/x^2

(20)

lhs(e4)/e3/x^2 < rhs(e4)/e3/x^2;

x/(x+1) < (5*x+5)/((x+1)*x^2)

(21)

simplify(%);

x/(x+1) < 5/x^2

(22)

 


 

Download equations.mw

Any  idea is good for me !

 

According to Wikipedia  https://www.wikidata.org/wiki/Q3115604 ,

Outerplanar graph  is a graph that can be drawn without crossings in the plane (means it is planar graph) with all vertices on the outer face.  

For example 

 

Recently  in my project, I  need to judge whether a planar graph is a  outerplanar graph.

I tried to find some algorithms but failed. 

Maple  only considers how to test wheather a graph is  planar.

like following:

with(GraphTheory):
with(SpecialGraphs)
K4 := CompleteGraph(4)
IsPlanar(K4, 'F')

   Dear friends,on the left I created two Tasks named a and aa.However,I do not know how to delete these two Tasks.Then I refer to the help pages below.

The text I marked says I should enter full filename.I do not know the fullfile name of customized Tasks.So does anyone know how to delete them?

 

I am exploring the idea of porting some of my functions to Maple from Mathematica. But I just found a big problem in importing comma delimited data that contains a string within a string. This is not a problem being imported in Mathematica, but I need help to do same thing in Maple.

I tried ImportMatrix (as suggested in https://www.mapleprimes.com/questions/221509-How-To-Read-Lines-From-File-With-Quoted-Strings and also tried Import then convert and in both cases Maple does not read the full string in the field. I will show simple example

This file, called data.txt

1,2,3,"x+y, algorithm=["123"]","OK",5

It has 6 fields (since comma seperated.

But when importing it, Maple reads the 4th field above as "x+y, algorithm=[" and drops the rest 123"]"

Here is the code

#currentdir("C:\\bug"); #change as needed
data:=ImportMatrix("data.txt", source=csv);
print(data(4));
print(data(5));

This is the output

I also tried

data := Import("data.txt",format="CSV");
data := convert(data,Matrix):
print(data(4));
print(data(5));

Same output as above.

Compare the output in Mathematica. Using the same file as input. It automatically escapes the embedded strings and reads the full field OK

SetDirectory[NotebookDirectory[]];
data = First@Import["data.txt", "Table", "FieldSeparators" -> {","}, "Numeric" -> True]

               {1, 2, 3, "x+y, algorithm=[\"123\"]", "OK", 5}

data[[4]]

              "x+y, algorithm=[\"123\"]"

What would be the right way in Maple to import such files without losing part of the field?

The file has mixed strings and non strings, just like this example shows, and each file fields are seperated by comma, but I need to be able to read fields that can contain embedded strings in them automatically.

I am using Maple 2020. I think I might have to forget about import and try to do it using lower level code using scanf, or may be there is better method using Filetools package? but thought to check first if I am overlooking some option.

I depend alot on bracket matching to help me during writing code.

Maple suddenly losses bracket matching at some lines. I think it related to using strings with "\\" in them.

I make sure I have bracket matching on

 

I use worksheet mode (corrected), Maple 2020 under windows 10.

I made small video. Notice how the brackets do not match on the second line there.

Do you see how the brackets do not match on that second line there? This movie below shows what happens when I remove "\\string" from the line. Now bracket match starts to work again.

This is a serious problem for me. Any suggestions what to try to fix it and what can cause it?. Once bracket matching is lost, it is lost all the way to the rest of the code below the location where it started to lose first time.

restart;
if length(data_last(k,8))>300 then
   fprintf(file_id,"%s\n","\\footnotesize");
fi;

I think I have to find different editor to use and write the code to .mpl file since I have lots of such code and I need to have bracket matching working.

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