Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

How I can simplify result? For factor or using rule.

Thanks

 

Hello,

I am trying to work with the Physics package to calculate Christoffel symbols. I have just started using Maple today and am coming up against a few hurdles.

I want to change the signature of the metric from (+---) to (-+++). I am typing the following in math mode:

Setup( signature = '-+++')

However, this is returning the following error:

"Error, invalid sum/difference" with my command rewritten within a red box together with the last '+" within another red box. Can you please help me out with this?

Thank you.

 

Hello,

How can write a code for determination of Laplacian in a new form is introduced in maple code (First line).

Thank you.

FOR2
 

``

"L:=(∑)`e__i`/(`h__i`)*(∂)/(∂ `xi__i`).((∑)(∑)`e__k`/(`h__k`)((∂)/(∂ `xi__k`)`U__j`*`e__j`+`U__j`(∂)/( `xi__k`)`U__j`)):"

restart; with(VectorCalculus); with(LinearAlgebra); h__1 := VectorCalculus:-`*`(a, 1/cosh(r)); h__2 := VectorCalculus:-`*`(a, 1/cosh(r)); h__3 := VectorCalculus:-`*`(sinh(r), 1/cos(theta)); U__1 := u__r; U__2 := `u__θ`; U__3 := `u__φ`

"for i from 1 to 3 do  for j from 1 to 3 do  for k  from 1 to 3 do     if i=1 then   `h__i`:=a/(cosh(r)-cos(theta)); `U__i`:=`u__r`;`e__i`:=`e__r`:`xi__i`:=r:     else  if i=2 then  `h__i`:=a/(cosh(r)-cos(theta));`U__i`:=`u__theta`;`e__i`:=`e__theta`:`xi__i`:=theta:  else ;   `h__i`:=a/(cosh(r)-cos(theta));`U__i`:=`u__phi`;`e__i`:=`e__phi`:`xi__i`:=phi:  end if;          if  j=1 then ;  `h__j`:=a/(cosh(r)-cos(theta)); `U__j`:=`u__r`;`e__j`:=`e__r`:`xi__j`:=r:   else if  j=2 then;  `h__j`:=a/(cosh(r)-cos(theta));`U__j`:=`u__theta`;`e__j`:=`e__theta`:`xi__j`:=theta:  else ;   `h__j`:=a/(cosh(r)-cos(theta));`U__j`:=`u__phi`;`e__j`:=`e__phi`:`xi__j`:=phi:  end if;       if k=1 then   `h__k`:=a/(cosh(r)-cos(theta)); `U__k`:=`u__r`;`e__k`:=`e__r`:`xi__k`:=r:   else if i=2 then  `h__k`:=a/(cosh(r)-cos(theta));`U__k`:=`u__theta`;`e__k`:=`e__theta`:`xi__k`:=theta:  else     `h__k`:=a/(cosh(r)-cos(theta));`U__k`:=`u__phi`;`e__k`:=`e__phi`:`xi__k`:=phi:  end if;                   end ;  end ;         end ;               "

Error, unterminated loop

"for i from 1 to 3 do  for j from 1 to 3 do  for k  from 1 to 3 do    if i=1 then `h__i`:=a/(cosh(r)-cos(theta)); `U__i`:=`u__r`;`e__i`:=`e__r`:xi__i:=r:     else  if i=2 then  `h__i`:=a/(cosh(r)-cos(theta));`U__i`:=`u__theta`;`e__i`:=`e__theta`:xi__i:=theta:  else ;   `h__i`:=a/(cosh(r)-cos(theta));`U__i`:=`u__phi`;`e__i`:=`e__phi`:xi__i:=phi:  end if;       if j=1 then ;  `h__j`:=a/(cosh(r)-cos(theta)); `U__j`:=`u__r`;`e__j`:=`e__r`:xi__j:=r:   else if j=2 then;  `h__j`:=a/(cosh(r)-cos(theta));`U__j`:=`u__theta`;`e__j`:=`e__theta`:xi__j:=theta:  else ;   `h__j`:=a/(cosh(r)-cos(theta));`U__j`:=`u__phi`;`e__j`:=`e__phi`:xi__j:=phi:  end if;     if k=1 then `h__k`:=a/(cosh(r)-cos(theta)); `U__k`:=`u__r`;`e__k`:=`e__r`:xi__k:=r:   else if i=2 then  `h__k`:=a/(cosh(r)-cos(theta));`U__k`:=`u__theta`;`e__k`:=`e__theta`:xi__k:=theta:  else `h__k`:=a/(cosh(r)-cos(theta));`U__k`:=`u__phi`;`e__k`:=`e__phi`:xi__k:=phi:  end if;           end ;  end ;     end ;               "

 

i

i

(1)

j

j

(2)

``


 

Download FOR2

 

 

How can plot two  and bipolar figures as attached and extract their data.

Thank You.

with(LinearAlgebra):
assign(seq(U || i = `<,>`(x[i], y[i]), i = 1 .. 3));
U || 4 := U || 1; r := (1/6)*sqrt(3);
assign(seq(V || i = (U || i+U || (i+1))*(1/2)+(`<,>`(`<|>`(0, 1), `<|>`(-1, 0)) . (U || (i+1)-U || i))*r, i = 1 .. 3)); Norm(V || 3-V || 1, 2); is(Norm(V || 3-V || 1, 2) = Norm(V || 3-V || 2, 2)); is(Norm(V || 2-V || 1, 2) = Norm(V || 3-V || 2, 2));

Fsolve produces the correct solution.  solve followed by evalf produces a completely different solution.

What am I doing wrong?

## Ioannes Colla problem: "Divide 10 into three parts such that they
## shall be in continued proportion and that the product of the first
## two shall be 6"
eqs := [a+b+c=10, a/b=b/c, a*b=6];
fsolve(eqs); ## correct solution
evalf(solve(eqs)); ## different

Tom Dean

Would anybody be able to explain to me why I had to rewrite this one baby-procedure that has an if-statement inside my larger procedure, so that I could get a later on if-statement to work? As best I can tell, they mean exactly the same thing.


 

Information that may be pertinent:

 - The entire (overall) procedure worked without throwing any warnings prior to my adding this new if-statement.
 - The if-statement itself worked perfectly fine on another worksheet, though I hadn't tested it inside a procedure.
 - Commenting out the if-statement but retaining the interior commands led to the sheet compiling again, showing that it was in fact the presence of the if-statement causing the issue. 
 - When I commented out the offending baby-procedure that started throwing the warning, the sheet once again compiled.

The added if statement:

if eval_size > 4 then Search(max(seq(eval_cont[i], i = 4 .. eval_size)), eval_cont); evals_pairlist := evals_pairlist[[1 .. 3, %]] fi:

The error I get, and its "positioning": 

Error, invalid expression for inline function

 

Hello,

How I can remove some problems in my code.

I wrote it before in  software, but in some lines, I have some problems with it.

How I can change it in maple to run well?


 

restart

M := 2; B := 1; C := 3; K := 6; f := 2*exp(-t); q0 := 1; qd0 := -1; qd20 := 1; alpha := 1/2; beta := 1/12; gammaa := 1/4; h := .1; Tf := 2

"N:=size(M,1)  T:=0:h:Tf;  lt:=length(T);  F:=subs(f,t,T);  F:=subs(t=T,f);    qd30:=M\(F(1)-B*qd20-C*qd0-K*q0);   q:=zeros(N,lt)  qd:=zeros(N,lt)  qd2:=zeros(N,lt);  qd3:=zeros(N,lt);  q(:,1):=q0  qd(:,1):=qd0  qd2(:,1):=qd20  qd3(:,1):=qd30"

Error, invalid function arguments

"N:=size(M,1)  T:=0:h:Tf;  lt:=length(T);  F:=subs(f,t,T);  F:=subs(t=T,f);    qd30:=M\(F(1)-B*qd20-C*qd0-K*q0);  q:=zeros(N,lt)  qd:=zeros(N,lt)  qd2:=zeros(N,lt);  qd3:=zeros(N,lt);  q(:,1):=q0  qd(:,1):=qd0  qd2(:,1):=qd20  qd3(:,1):=qd30"

 

"A:=M+alpha*h*B+gammaa*(h^2)*C+beta*(h^3)*K;  for n:=1:lt-1 do      D:=F(n+1)-B*(qd2(:,n)+(1-alpha)*h*qd3(:,n))-...          C*(qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n))-...          K*(q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n));      qd3(:,n+1):=A\D;      qd2(:,n+1):=qd2(:,n)+(1-alpha)*h*qd3(:,n)+alpha*h*qd3(:,n+1);      qd(:,n+1):=qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n)+gammaa*(h^2)*qd3(:,n+1);      q(:,n+1):=q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)+...          beta*(h^3)*qd3(:,n+1);  end do"

Error, invalid function arguments

"A:=M+alpha*h*B+gammaa*(h^2)*C+beta*(h^3)*K;  for n:=1:lt-1 do      D:=F(n+1)-B*(qd2(:,n)+(1-alpha)*h*qd3(:,n))-...          C*(qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n))-...          K*(q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n));      qd3(:,n+1):=A\D;      qd2(:,n+1):=qd2(:,n)+(1-alpha)*h*qd3(:,n)+alpha*h*qd3(:,n+1);      qd(:,n+1):=qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n)+gammaa*(h^2)*qd3(:,n+1);      q(:,n+1):=q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)+...          beta*(h^3)*qd3(:,n+1);  end do"

 

plot(T, q, 'r-o', 'linewidth', 1.5)

Error, (in plot) unexpected options: [r-o, , 1.5]

 

``


 

Download

 

Hi freind,

Anybody knows what happen to this coding?

why this error happens? how can i fix it?

thank you!

Please help me for removing an error in my code.

Thank you


 

"   restart:     NL:=960:    LL:=4:      BB:=0.6 :  T:=16:    MM:=NL*(LL+1):          for  NC  from 0 by 1 to MM-1  do       S:=BB+(2*Pi*NC/T)*I;          powerFactor := 0.05 * (sqrt(2.0) - 1.202081528);     powerTerm := sqrt(S)*sqrt(49*S^(2)+280*S+800)/sqrt(S+4);       preFactor := 1/((exp(sqrt(2.0)*powerTerm/10.0)-1.0)*S);       XS(NC+1):= preFactor * ((-exp(-powerFactor*powerTerm) + exp(powerFactor*powerTerm)) * exp(sqrt(2.0)*powerTerm/20.0));    end  do;    for  timeCounter from 0 by 1 to  NL-1  do     totalTerm:=0;     for KK from 0 to NL-1 do        for L from 0 to LL do           Term1:=Re(XS(KK+L*NL+1))+I*(Im(XS(KK+L*NL+1)));           Term2:=exp((timeCounter*KK*2*Pi/NL)*I);           totalTerm:=totalTerm+Term1*Term2;        end do     end do     XT(timeCounter+1):=((2.0/T)*exp(BB*timeCounter*T/NL)*(-0.5*Re(XS(1))+Re(totalTerm)));     TT(timeCounter+1):=(timeCounter*T)/NL;         end do    "

Error, invalid loop statement termination

"   restart:    NL:=960:  LL:=4:  BB:=0.6 :  T:=16:    MM:=NL*(LL+1):       for NC  from 0 by 1 to MM-1  do     S:=BB+(2*Pi*NC/T)*I;    powerFactor := 0.05 * (sqrt(2.0) - 1.202081528);   powerTerm := sqrt(S)*sqrt(49*S^2+280*S+800)/sqrt(S+4);    preFactor := 1/((exp(sqrt(2.0)*powerTerm/10.0)-1.0)*S);     XS(NC+1):= preFactor * ((-exp(-powerFactor*powerTerm) + exp(powerFactor*powerTerm)) * exp(sqrt(2.0)*powerTerm/20.0));    end  do;    for timeCounter from 0 by 1 to NL-1  do  totalTerm:=0;     for KK from 0 to NL-1 do        for L from 0 to LL do  Term1:=Re(XS(KK+L*NL+1))+I*(Im(XS(KK+L*NL+1)));  Term2:=exp((timeCounter*KK*2*Pi/NL)*I);  totalTerm:=totalTerm+Term1*Term2;        end do     end do   XT(timeCounter+1):=((2.0/T)*exp(BB*timeCounter*T/NL)*(-0.5*Re(XS(1))+Re(totalTerm)));   TT(timeCounter+1):=(timeCounter*T)/NL;      end do    "

 

``

``


 

Download

 

Hello,

How I can write a code for the determination of Laplacian in a new form that is introduced in the maple code (First line).

Thank you.

FOR

Maple Worksheet - Error

Failed to load the worksheet //convert/FOR
 

Download FOR

 

 

How to do the partition of integer?
If I input:
>Partition(10,2)
then output is:
>[[1, 9], [2, 8], [3, 7], [4, 6],[5,5]]
-------------------------------------------------
"10" is the number that I want to part,and "2" means that there are "two" number's sum = 10
Sorry my Engilsh is not good,but I really need help.
no other restriction!!

Hi everyone

 

Im new to MaplePrimes aswell as to Maple.

I have a task where i shoud plot the following shape (with a hole in the centre) using the plot3d function:

 

 

 

 

 

 

 

All i have accomplished in the last hours is the following file A1.0.mw:

As you can see i havent been able to get rid off the surface in the centre nor the spikes on the edge...
 

  • In order to fix the issue regarding the centre I assume I have to exclude the range -2..2 from x, but havent been able to do so.
  • Regarding the spikes on the edge Im honestly pretty much clueless why they appear in the first place.

 

After several hours of trying on my own, I really need your help please!

A1.0.mw
 

f := (x, y) -> ((((((x^2)+(y^2))^(1/2))-4))/(((((x^2)+(y^2))^(1/2))-2)*((((x^2)+(y^2))^(1/2))-6)))+15;
plot3d(f, -6..6, -sqrt(-x^2+36) .. sqrt(-x^2+36), grid=[400,400], view=0..30);

proc (x, y) options operator, arrow; ((y^2+x^2)^(1/2)-4)/(((y^2+x^2)^(1/2)-2)*((y^2+x^2)^(1/2)-6))+15 end proc

 

 

 


 

Download A1.0.mw
 

 

 

Please check this code and fix the error. And help me with the below two questions.

1- In the above image, I'm getting the error when I'm to plot my solutions.

2- How to get information from this system?

      The values of x_1 and corresponding y_1 and so on and errors etc

This is a downloadable link to my worksheet [Practice.mw]

Thanks!


>restart;
> ODEtools[declare]((S, L, B)(t), prime = t);
         ODEtools[declare](S(t), L(t), B(t), prime = t)
> DE1 := diff(S(t), t) = -L*S*beta-`&mu;S`+mu;
                    d                               
            DE1 := --- S(t) = -L S beta - &mu;S + mu
                    dt                              
> DE2 := diff(L(t), t) = L*S*beta-(gamma+mu)*S;
                  d                                  
          DE2 := --- L(t) = beta S L - (gamma + mu) S
                  dt                                 
> DE3 := diff(B(t), t) = L*gamma-gamma*mu;
                      d                           
              DE3 := --- B(t) = L gamma - gamma mu
                      dt                          
> init_conds := S(0) >= 0, L(0) >= 0, B(0) >= 0;
         init_conds := 0 <= S(0), 0 <= L(0), 0 <= B(0)
> sys := {init_conds, diff(B(t), t) = L*gamma-gamma*mu, diff(L(t), t) = L*S*beta-(gamma+mu)*S, diff(S(t), t) = -L*S*beta-`&mu;S`+mu};

> sol := dsolve(sys, numeric, parameters = [mu, beta, gamma, S(t), L(t), B(t)], method = rkf45);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations


> sol(parameters = [mu = .234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123]);
           sol(parameters = [mu = 0.234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123])

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