Let us suppose I open Maple, write a worksheet, save it in a folder A and then quit Maple.

Now I run a new session by double clicking on some mw file located in folder B, let us say //B/test_1.mw.
Once opened I do some modifications and decide to save this worksheet into a new file, let us say test_2.mw in the same folder B test_1.mw belongs to (which means I use Save As from the menu bar)

I'm regularly fooled by the fact that the default folder is not B, but the folder A I used in the previous session.

I find this very unpleasant.
Is this a Maple (2015) issue or something related to my operating system (Mac OSX Catalina)?
In case it is a Maple issue which is still present in more recent Maple versions, Would it be possible to set the default backup folder to be the folder to which the active worksheet belongs?

Thanks in advance

It's 2024 and this is still something that doesn't exist? I'd just like to swap the Enter/Shfit+Enter behaviors since I find myself writing a lot of multi-line and custom procs and boy howdy it'd be nice if I could make Maple behave at least the littllest bit like, I dunno, every other product I own and use.

i found solution of PDE but there is some different from my solution and paper solution so there is must be a mistake becuase he solved by maple too he mentioned in the paper i try to figure out but i can't see any mistake from my solution can anyone watch where i did mistake, i change some letter in finding parameter but they are same like p=k&h=A&n=p&w=n

here is paper solution 

parameter-different.mw

I'm calcuating an endomorphism in 2d dimensions. It is contructed out of a tensor contraction, for example, in 6-dimensions, the endomorphism is

K[mu,~nu] = LeviCivita[~alpha,~beta,~gamma,~delta,~upsilon,~nu]*C[alpha,beta,gamma]*C[delta,upsilon,mu]

I appreciate that, in terms of computation, this gets big quickly: it's something like O(exp) in time to sum over repeated indices in each matrix entry. Therefore, I thought, instead of putting the above expression in Define, I could make a matrix with unsummed entries, and then do the sums in parallel using Threads[Map](SumOverRepeatedIndices,...) but looking at my CPU usage and comparing execution times, it doesn't appear that this is working.

Is there any way I can more efficiently calculate these matrix entries?

In Peter Winkler's book "Mathematical Mind-Benders" the now famous problem of dividing an ice cream cake is posed. It asks: If, when cutting the circular cake with any central angle (whether rational or irrational), neighboring piece after neighboring piece is constantly cut off, the cake segment is rotated to the previous top side, and the cut surface is considered to be healed, then after a finite number of cuts the top side is back where it was at the beginning. I also fell for it at first and assumed that according to Weyl's theorem (uniform distribution modulo 1) this is not possible and therefore the central angle must be rational. I have since found a solution according to which the cutting process must stop after a finite number of steps. Weyl's theorem is obviously not applicable here. Why - I am still puzzling over that.

Now I am interested in whether Maple can be used to animate the uniform distribution modulo 1 on the unit circle and to display the associated statistics in the sense of a sample and calculate the sample value of the uniform distribution. As a Maple beginner, I am not yet able to do this and am asking for help.

I want to calculate Hodge Star of forms on a solvable Lie algebra L, I have defined a metric tensor g on it. But when I use that g to compute the Hodge Star of an operator it tells me that the g is not a metric tensor.

with(DifferentialGeometry);
with(LieAlgebras);
A := Matrix(4, 4, [[A__11, A__12, A__13, A__14], [A__21, -A__11, A__23, A__24], [-A__24, -A__23, -A__11, A__21], [-A__14, -A__13, A__12, A__11]]);
x := [x__1, x__2, x__3, x__4, x__5, x__6];
StructureEquations := [[x[6], x[1]] = a*x[1], [x[6], x[2]] = add(A[1, i]*x[i + 1], i = 1 .. 4), [x[6], x[3]] = add(A[2, i]*x[i + 1], i = 1 .. 4), [x[6], x[4]] = add(A[3, i]*x[i + 1], i = 1 .. 4), [x[6], x[5]] = add(A[4, i]*x[i + 1], i = 1 .. 4)];
L := LieAlgebraData(StructureEquations, [x[1], x[2], x[3], x[4], x[5], x[6]], Alg1);
DGsetup(L);
with(Tensor);
e := [e1, e2, e3, e4, e5, e6];
theta := [theta1, theta2, theta3, theta4, theta5, theta6];
omega := evalDG(add(theta[i] &wedge theta[7 - i], i = 1 .. 3));
g := evalDG(add(theta[i] &t theta[7 - i], i = 1 .. 3));
HodgeStar(g, theta1)

It is showing the following error,

Error, (in DifferentialGeometry:-Tensor:-HodgeStar) expected 1st argument to be a metric tensor. Received: _DG([["tensor", Alg1, [["cov_bas", "cov_bas"], []]], [`...`]])

How can I correct this? If not is there an alternative of doing what I am trying to do?

Is there any function that returns a boolean value that tells me if a point is within a polygon or not?

I need assistance with building the homotopy analysis method to solve the system of odes. here is the attempt to do it. I'm still new to maple restart; # Declare functions for the system PDEtools[declare]([f(x), g(x)], prime = x): # Order of expansion N := 4; # Define series for each function f1(x) := sum(p^i*f[i](x), i = 0..N): f2(x) := sum(p^i*g[i](x), i = 0..N): # Define the system of ODEs using Homotopy HPMEq1 := (1-p)*(diff(f1(x), x$3)) + p*(diff(f1(x), x) + f2(x)): HPMEq2 := (1-p)*(diff(f2(x), x$3)) + p*(diff(f2(x), x) - f1(x)): # Extract coefficients for the system for i from 0 to N do equl[1][i] := coeff(HPMEq1, p, i) = 0: equl[2][i] := coeff(HPMEq2, p, i) = 0: end do: # Define boundary conditions for the system cond= 0, D(f1[0])(5) = 1]: cond = 0, D(f2[0])(0) 1]: for j from 1 to N do cond = 0, D(f1[j])(0) = 0, D(f1[j])(5) , D(f2[j])(0) = 0, D(f2[j])(5) = 0]: end do: # Solve the system iteratively for each order for k from 0 to N do dsolve([equl[1][k], cond[1][k]], f1[k](x)): dsolve([equl[2][k], cond[2][k]], f2[k](x)): end do:

i try to get same result by substituation but i don't know what is mistake after i take second derivative is wronge i don't know how get same result as in paper did can anyone help  to calculate this part is not hard but is complicated ,How calculated second derivative and put in our ode to get the parameters?

>  >  >  >  >  >  (1) >  >  >  (2) >  >  (3) >  (4) >  (5) >  (6) >  >  (7) >  (8)

Download complex-issue.mw

The maple worksheet shows an incorrect evaluation of the integral in (1) which is a standard integral representation of a Bessel function.  Equations (2)-(5) along with the graph show the incorrectness of the evaluation.  What is going on?

Bessel.mw

Found this old procedure code and revived it
Trying to include an Exploreplot as well
a0,a1,a2,b1,b2 are coeifficents in a ode to construct 
How about odetype when constructing a ode is this correct in code?

>  restart; Odegenerator := proc(V, x, y, df, const_values)     local input_args, xi, F, result, a0, a1, a2, b0, b1, sol, Fsol, rows, numrows, eq, count, odeplot_cmd, ode_type, row_number, values;     uses plots, PDEtools;        if nargs = 1 and V = "help" then         printf("Use this procedure as follows:\n");         printf("Define an ODE template:\n");         printf("Odegenerator(V, x, y, df, const_values)\n");         printf("V: A set of values for iteration over constants (if df > 0)\n");         printf("x: The independent variable\n");         printf("y: The function\n");         printf("df: The row number in the DataFrame or 0 for manual input\n");         printf("const_values: A list of values for the constants (used if df = 0)\n");         return;     end if;     if nargs < 4 or nargs > 5 then         error "Incorrect number of arguments. Expected: V, x, y, df, [const_values (optional)]";     end if;     # Determine the ODE type using odeadvisor for the global eq_template     ode_type := odeadvisor(eq_template);     # Display the ODE and its type     print(eq_template, ode_type);     rows := [];     count := 0;     ###################### BOF manuele invoer ###################     if df = 0 then     # If df = 0, use const_values for substitution     if nargs < 5 or not type(const_values, list) then         error "When df = 0, a list of constant values must be provided as the fifth argument.";     end if;     # Assign constant values     if nops(const_values) <> 5 then         error "The list of constant values must contain exactly 5 elements.";     end if;     # Find the corresponding row number by unique identification     count := 1;     for a0 in V do         for a1 in V do             for a2 in V do                 for b0 in V do                     for b1 in V do                         if [a0, a1, a2, b0, b1] = const_values then                             row_number := sprintf("%d", count);  # Convert to string                         end if;                         count := count + 1;                     end do;                 end do;             end do;         end do;     end do;     if not assigned(row_number) then         row_number := "Unique (outside iterative rows)";  # Mark as unique     end if;     # Substitute the given values     eq := subs({'a__0' = const_values[1], 'a__1' = const_values[2], 'a__2' = const_values[3], 'b__0' = const_values[4], 'b__1' = const_values[5]}, eq_template);     # Solve the equation     sol := dsolve(eq, y(x));     if type(sol, `=`) then         Fsol := rhs(sol);     else         Fsol := "No explicit solution";     end if;     # Display the solution and its row number     odeplot_cmd := DEtools[DEplot](eq, y(x), x = 0 .. 2, y = -10 .. 10, [[y(0) = 1]]);     print(plots:-display(odeplot_cmd, size = [550, 550]));     printf("The found function is:\n");     print(Fsol);     printf("The corresponding row number is: %s\n", row_number);     # -- Start of Additional Functionality --     # Optionally display the simplified ODE     printf("The simplified ODE using the given coefficients is:\n");     print(eq, ode_type);     # -- End of Additional Functionality --     return Fsol;      ################# EOF manuele berekening ##################      ############## BOF iterative berekening##############     else         # Iterative approach for DataFrame generation         for a0 in V do             for a1 in V do                 for a2 in V do                     for b0 in V do                         for b1 in V do                             xi := x;                             F := y;                             # Substitute constant values into the ODE                             eq := subs({'a__0' = a0, 'a__1' = a1, 'a__2' = a2, 'b__0' = b0, 'b__1' = b1}, eq_template);                             sol := dsolve(eq, F(xi));                             if type(sol, `=`) then                                 Fsol := rhs(sol);                             else                                 Fsol := "No explicit solution";                             end if;                             rows := [op(rows), [a0, a1, a2, b0, b1, Fsol]];                         end do;                     end do;                 end do;             end do;         end do;         numrows := nops(rows);         result := DataFrame(Matrix(numrows, 6, rows), columns = ['a__0', 'a__1', 'a__2', 'b__0', 'b__1', y(x)]);         interface(rtablesize = numrows + 10);         if df > 0 and df <= numrows then             a0 := result[df, 'a__0'];             a1 := result[df, 'a__1'];             a2 := result[df, 'a__2'];             b0 := result[df, 'b__0'];             b1 := result[df, 'b__1'];             eq := subs({'a__0' = a0, 'a__1' = a1, 'a__2' = a2, 'b__0' = b0, 'b__1' = b1}, eq_template);             # Display the additional parameters             print(eq, ode_type, [df], [a0, a1, a2, b0, b1]);             # Retrieve the solution             Fsol := result[df, y(x)];             # Display the solution in DEplot             odeplot_cmd := DEtools[DEplot](eq, y(x), x = 0 .. 2, y = -10 .. 10, [[y(0) = 1]]);             print(plots:-display(odeplot_cmd, size = [550, 550]));             printf("The found function for row number %d is:\n", df);             print(Fsol);         else             printf("The specified row (%d) is out of bounds for the DataFrame.\n", df);         end if;         return result;      ########## EOF iteratief bwrekening ########################     end if; end proc: >  # Test cases V := {0, 1}; eq_template := diff(y(t), t) = 'a__0'*sin(t) + 'a__1'*y(t) + 'a__2'*y(t)^2 + 'b__0'*exp(-t);   (1)     >  # Iterative test result := Odegenerator(V, t, y, 25); The found function for row number 25 is:   (2)   >  # Manual input test Odegenerator(V, t, y, 0, [1, 1, 0, 0, 0]); #0 after y is rownumber = 0 and [1, 1, 0, 0, 0] are coeifficents The found function is:   The corresponding row number is: 25 The simplified ODE using the given coefficients is:   (3)     >    Download ODEGENERATORFUNCTIE_opgepakt-uitgebreid_naar_MprimesDEF_14-1-2025.mw

every thing is correct but i dont know why my PDE is not be zero, i did by another way is satidy but i change whole equation by sabstitutiin then i did ode test is satisfy by putting case in equation and solution with condition but when i want to use pdetest  test in pde is not satisfy ?

>  >  >  >  >  (1) >  (2) >  (3) >  >  >  (4) >  >  (5) >  (6) >  >  (7) >  >  (8) >  (9) >  (10) >  (11)

Download pdetest.mw

I have a system of 4 nonlinear equations in 4 lambda variables. I cannot obtain a solution using solve():

4_nonlinear_equations.mw

I can sometimes simplify similar systems by rescaling equations to reduce parameters. With only 3 parameters (sigma_v, sigma_d, sigma_d3) in this case, complexity arises from the interactions of the 4 lambdas in the 4 equations. Upon examining the equations (highlighted in yellow), I suspect hidden symmetries. Is it possible to solve the system by rewriting the equations in terms of each other to find an equivalent system? I am exploring if a smarter and simpler reformulation could lead to a solution. Thank you.

i want to factoring the (m+G'/G) in my long equation but i use some trick but still i can't get the exactly system and still G will remain in my system what should i factoring for remove this G(xi) from my system is all about factoring , my system of equation are wrong contain G(xi) How i can remove it by taking a factoring or any other technique,

not parameter is arbitrary except V and sigma''

>  >  >  >  >  >  (1) >  Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.   >  (2) >  >  (3) >  (4) >  (5) >  >  (6) >  (7) >  (8) >  (9) >  (10) >  (11) >  >  >  >  >  >  >  >  (12) >  >  # rewritting rule RR := isolate(m+diff(G(xi), xi)/(G(xi))=Phi, diff(G(xi), xi)/G(xi)); (13) >  # Apply RR and collect wrt Phi subs(RR, L): normal(%): PhiN := collect(numer(lhs(%)), phi): PhiD := denom(lhs(%%)); (14) >  with(LargeExpressions): LLE := collect(PhiN, Phi, Veil[phi] ): LLE / PhiD = 0; (15) >  # phi[i] coefficients phis := [ seq( phi[i] = simplify(Unveil[phi](phi[i]), size), i=1..LastUsed[phi] ) ]: print~( phis ): (16) >  # WATCHOUT: you have 9 coefficients and so its desirable to have the same number of unknowns unknowns := indets(rhs~(phis), {e[-1],e[0],e[1],'identical'(mu),'identical'(lambda),'identical'(a[1]),'identical'(alpha)}); COEFFS := solve(rhs~(phis), unknowns) (17) >  case1 := COEFFS[2] (18) >  >  (19) >  (20) >  (21) >  >  (22) >  (23) >  (24) >  (25) >  (26) >  (27) >  (28)

Download G-factoring.mw

I’m trying to solve a stiff system 1-D PDEs numerically in Maple but I’m getting the following error:

“Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence”

I included a picture of the PDEs and their BCs in the attached maple file. For easy reading, the attached file includes highlighted sections for parameters and variables. You can skip those to PDEs, BCs and ICs sections at the end of the document to reach the error I’m facing.

For reference, I used another software to solve the system and I was able to get the results in few seconds, so I think it is solvable. However, personally I prefer to use Maple so any inputs, insights, workarounds that I could use to handle the system in Maple would be of great help to me. Thank you.

question.mw