## how to get the coefficient of x in this expression...

sol := y = -3283/4253 - (3283*x)/4253, How can I determine the value of the coefficient of x?
How can I take the value of the coefficient of x? Thank you.

## Why does this command only works in Maple and not ...

I am stuck this command works seemlessly in Maple:

ThermophysicalData:-CoolProp:-Property(D, T = 20*Unit('degC'), P = 760*Unit('mmHg'), water)

but it does not work in Maple Flow. Does anyone knows why? Thank you so much for your help in the matter.

## Why does 'simplify' not work when calculating Eige...

Why does 'simplify' not work when calculating Eigenvectors? Further, how can we express (2) in a more simplified form by using 'simplify'?simplify.mw

## How come does "residualQQplot" give me a strange ...

Hello :)

I have a math problem, where I first need to use Linear regression to find the equation based on a set of data. I did that, no problem.

However, in the next part of the problem I need to check if the residuals are under "normal distribution". Usually, I check if a dataset is normally distributed via "QQ-plot", and there will be no problems. But this time, because I need to check the residuals, I need to use the "residualQQplot(data,LinReg)" command to make it happen. But when I read the mean-value, mu, it says "-0," and nothing else? I know it should be "-3,2752*10^-15.

The standard deviation is correct.

How do I fix this, so the residualQQplot shows me the right result?

I have attached the worksheet here. worksheet_-_linear_reg_and_residuals_for_normal_distribution.mw

Thank you!

## Maple gives solutions may have been lost unless tw...

I can't understand this behavior. Any idea why it happens?

Solve is able to solve equation   f(y)=x+A for y, but can't solve   f(y)=x for y.

This is unexpected for me. I do not see why it can solve it when RHS is x+A but not when RHS is just x.

 > interface(version);

 > Physics:-Version();

 > restart;

 > sol:=int(1/sqrt(sin(y)),y); solve(sol=x,y)

Warning, solutions may have been lost

 > sol:=int(1/sqrt(sin(y)),y); solve(sol=x+b,y): {%}; #to eliminate duplicates

 >

I can trick it to solve  f(y)=x for y  by asking it to solve f(y)=x+A for y and then set A=0 in the solution. But one should not have to do this. Is this a bug or Am I missing something?

## How do I modify the following maple code in a simp...

Dear Colleague.

I am trying to improve the results of abs(res[i] - exy) in the following codes.

restart;
Digits := 30:

# Define the function
f := proc(n)
-0.5*y[n] + 0.5*sin(x[n] - Pi)
end proc:

# Define equations
e1 := y[n+2] = 2*h*delta[n] + y[n] - h^2*(-2*sin(u)*f(n)*u^2 - 2*sin(u)*f(n+2)*u^2 + 2*sin(2*u)*f(n+1)*u^2 + 2*cos(u)*f(n)*u - 2*cos(u)*f(n+2)*u + 2*cos(2*u)*f(n+1)*u - 2*cos(2*u)*f(n)*u - 2*sin(u)*f(n) + 2*sin(u)*f(n+2) + sin(2*u)*f(n) - sin(2*u)*f(n+2) - 2*f(n+1)*u + 2*f(n+2)*u)/((2*sin(u) - sin(2*u))*u^2):
e2 := y[n+1] = h*delta[n] + y[n] - (1/2)*h^2*(-sin(u)*f(n)*u^2 - sin(u)*f(n+2)*u^2 + sin(2*u)*f(n+1)*u^2 + 2*cos(u)*f(n)*u - 2*cos(u)*f(n+2)*u + 2*cos(2*u)*f(n+1)*u - 2*cos(2*u)*f(n)*u + 4*sin(u)*f(n+1) - 4*sin(u)*f(n) - 2*sin(2*u)*f(n+1) + 2*sin(2*u)*f(n) - 2*f(n+1)*u + 2*f(n+2)*u)/((2*sin(u) - sin(2*u))*u^2):
e3 := h*delta[n+2] = h*delta[n] + h^2*(2*sin(u)*f(n)*u + 2*sin(u)*f(n+2)*u - 2*sin(2*u)*f(n+1)*u - 2*cos(2*u)*f(n+1) + cos(2*u)*f(n) + cos(2*u)*f(n+2) + 2*f(n+1) - f(n) - f(n+2))/(u*(2*sin(u) - sin(2*u))):

with(LinearAlgebra):
epsilon := 10^(-10):
inx := 0:
ind := 1:
iny := 0:
h := 0.01:
n := 0:
omega := 1:
u := omega * h:
tol := 1e-4:
N := solve(h * p = 8 * Pi, p):

err := Vector(round(N)):
exy_lst := Vector(round(N)):

c := 1:
for j from 0 to 2 do
t[j] := inx + j * h:
end do:

vars := y[n+1], y[n+2], delta[n+2]:

step := [seq(eval(x, x = c * h), c = 1 .. N)]:
printf("%6s%15s%15s%16s%15s%15s%15s\n", "h", "Num.y", "Num.z", "Ex.y", "Ex.z", "Error y", "Error z");

st := time():
for k from 1 to N / 2 do
par1 := x[0] = t[0], x[1] = t[1], x[2] = t[2]:
par2 := y[n] = iny, delta[n] = ind:

res := eval(<vars>, fsolve(eval({e1, e2, e3}, [par1, par2]), {vars}));

for i from 1 to 2 do
exy := eval(sin(c * h)):
exz := eval(cos(c * h)):
printf("%6.5f%17.9f%15.9f%15.9f%15.9f%13.5g%15.5g\n", h * c, res[i], res[i+1], exy, exz, abs(res[i] - exy), abs(res[i+1] - exz));

err[c] := abs(evalf(res[i] - exy));
if Norm(err) <= tol then
h := 0.1 * h * (c + 1) * (tol/Norm(err))^(0.2);
else
break
end if;
exy_lst[c] := exy;
numerical_y1[c] := res[i];
c := c + 1;
end do;
iny := res[2];
ind := res[3];
inx := t[2];
for j from 0 to 2 do
t[j] := inx + j * h;
end do;
end do:
v := time() - st;
v / 4;
printf("Maximum error is %.13g\n", max(err));
NFE = evalf((N / 4 * 3) + 1);

# Get array of numerical and exact solutions for y1
numerical_array_y1 := [seq(numerical_y1[i], i = 1 .. N)]:
exact_array_y1 := [seq(exy_lst[i], i = 1 .. N)]:

# Get array of time steps
time_t := [seq(step[i], i = 1 .. N)]:

# Display graphs for y1
with(plots):
numerical_plot_y1 := plot(time_t, numerical_array_y1, style = point, symbol = asterisk, color = blue, symbolsize = 20, legend = ["TFIBF"]);
exact_plot_y1 := plot(time_t, exact_array_y1, style = point, symbol = box, color = red, symbolsize = 20, legend = ["EXACT"]);

display({numerical_plot_y1, exact_plot_y1});
Error_plot_y1 := plot(time_t, err, style = line, symbol = box, tickmarks = [piticks, decimalticks], color = navy, labels = [`h=Pi/8`, typeset(`Absolute Errors`)]);

I am suspecting that I didnt update the new h properly (I may be wrong, though). Please kindly help modify the code to allow the values of abs(res[i] - exy) to about 10^(-11). Thank you and best regards.

## Help pages. ...

Is there a way to change the font on the help pages?

## warning (`rtable_alias`)...

Hi,

I'm trying out the 2024 version of Maple and I'm getting the following warning message:

Warning, not a built-in function (`rtable_alias`)

which I didn´t get for the 2023 version. I have no clue where it is coming from since it happens even when I start a new worksheet:

I've also attached print outs of the same worksheets (from Maple help examples and from Maple Portal), one using Maple 2023 version and the other one using Maple 2024 version so youcould see the warning and some other problems.

I really appreciate if someone would have an idea of what is going on here. Thanks very much in advance.

interpolation_2023.pdf

interpolation_2024.pdf

optimization_2023.pdf

optimization_2024.pdf

## Multiplaction "dot" is way too small - causes erro...

Multiplaction "dot" in Maple 2022 is way too small - causes errors.

e.g. two variables multiplied s*m ends up being sm a new variable as I cannot really see that there is a missing multiplication operator between the variables. This causes huge unnecessary errors.

Maple 9.x e.g had nice clear and big operators and this kind of error was avoided.

How can I undo this unfortunate regression in Maple 2022 to increase the size of multiplication operator and other operators, so that they actually becom visible and not just a little dot almost a pixel in size.

If I was a falcon (20x20)^infinity then this would have been ok, but I am not, I am human.

So how do I change this unfortunate regression so that these errors can be avoided.?

## Can I convert InlinePlot(P3) back to a regular plo...

See attached worksheet in Maple 2023.

This example is taken from the Maple help page. I want to 'zoom in' on a plot3d object. The only way I have found was from responses [1] on the maple primes forum. It uses InlinePlot and the scale option to perform the 'zoom in'. Since InlinePlot generates the plot in terms of XML there is no graphic out, only a text based output. In order to reconstitute the InlinePlot as a plot object I can view visually I need to use some additional commands from the DocumentTool package. This is all great but the output, which in our case is P3, is not a plot object and therefore cannot be exported as a png. Is there a way to convert the InlinePlot with the scaling applied back to a typical plot object so I can export it as a .png, using Export("output_plot.png",P3,base=worksheetdir)?

can_I_convert_InlinePlot(P3)_back_to_a_regular_plot_object_so_I_can_export_it_as_a_png.mw

## Why it's not allowed to contract the tensor with c...

When I try to contract the tensor with connection, maple encounters such promble:

Error, (in DifferentialGeometry:-Tensor:-ContractIndices) expected 2nd argument to be a tensor. Received: _DG([["connection", O, [["con_bas", "cov_bas", "cov_bas"], []]], [`...`]])

The expression is Cacd Hab

## Maple solve hangs depending on what letters are us...

Could someone help me understand why Maple hangs solving these two equations when the names of unknowns is c__1,c__2   or the old _C1, _C2?

This worksheets shows this. I had to put timelimit of 90 seconds, else it hangs may be forever.

This example came from looking at why Maple seems to hang randomly when I run the same problem. I still do not know why, but is seems to have something to do with the use of  lower case c__1 or _C1.

 > interface(version);

 > Physics:-Version();

 > restart;
 > dsolve(diff(y(x),x\$9)=1,arbitraryconstants=subscripted);

 > eqs:=[-1/2*arctanh(1/2*sqrt(1 + 2*c__1)*sqrt(2)/sqrt(c__1))*sqrt(2)/sqrt(c__1) = c__2, 1 = (-exp(2*c__2*sqrt(c__1)*sqrt(2)) + 1)*sqrt(c__1)*sqrt(2)/(exp(2*c__2*sqrt(c__1)*sqrt(2)) + 1)]; unknowns:=[c__1,c__2]; time(); C_sol:=[timelimit(90,solve(eqs,unknowns))]; time()

Error, (in evalf/hypergeom) time expired

 > restart; #try again but do not do the arbitraryconstants=subscripted now.
 > eqs:=[-1/2*arctanh(1/2*sqrt(1 + 2*c__1)*sqrt(2)/sqrt(c__1))*sqrt(2)/sqrt(c__1) = c__2, 1 = (-exp(2*c__2*sqrt(c__1)*sqrt(2)) + 1)*sqrt(c__1)*sqrt(2)/(exp(2*c__2*sqrt(c__1)*sqrt(2)) + 1)]; unknowns:=[c__1,c__2]; time(); C_sol:=[timelimit(90,solve(eqs,unknowns))]; time()

 > #see? it finisghed instantly now.

The same thing happens If I use the old _C1 and _C2 instead of c__1 and c__2. It also hangs.

The following worksheet shows this.  If I change _C1 and _C2 to other symbols, say C1 and C2, then it does not hang.

Why the names of the unknowns makes difference to solve?

 > restart;

 > eqs:=[-1/2*arctanh(1/2*sqrt(1 + 2*_C1)*sqrt(2)/sqrt(_C1))*sqrt(2)/sqrt(_C1) = _C2, 1 = (-exp(2*_C2*sqrt(_C1)*sqrt(2)) + 1)*sqrt(_C1)*sqrt(2)/(exp(2*_C2*sqrt(_C1)*sqrt(2)) + 1)]; unknowns:=[_C1,_C2]; time(); C_sol:=[timelimit(90,solve(eqs,unknowns))]; time()

Error, (in evalf/cos) time expired

 > restart;

 > eqs:=[-1/2*arctanh(1/2*sqrt(1 + 2*C1)*sqrt(2)/sqrt(C1))*sqrt(2)/sqrt(C1) = C2, 1 = (-exp(2*C2*sqrt(C1)*sqrt(2)) + 1)*sqrt(C1)*sqrt(2)/(exp(2*C2*sqrt(C1)*sqrt(2)) + 1)]; unknowns:=[C1,C2]; time(); C_sol:=[timelimit(90,solve(eqs,unknowns))]; time()

Only thing I see in help related to name of symbols to solve for is this:

The solve command solves one or more equations or inequalities for the specified unknowns. The unknowns may be names, including indexed names (though for efficiency reasons, indexed names should be avoided when possible),

ps. This looks like a bug to me. So I send bug report to Maplesoft support also.

pps. I tried this in Maple 2023 and Maple 2022 and same behavior. Could someone with earlier version of Maple try to see if this behavior was there also?   It can possibly be correct that the choice of letter used makes difference for solving equations. I have to use c__1 and c__2 etc.. since these equations come from differential equations and this is what I use for constants of integrations., Otherwise I have to make lots of changes now to use different letters.

Update

did trace on solve using _C1 and _C2 and then using A,B for variables to solve for. Code flow is different. This expalins why it hangs. The flow starts the same until it gets to

TriangularDecomposition: something went wrong during backsubstitution - trying a different variable order

Then when using _C1 and _C2 the code goes into different path than when using A,B.

Here is flow when using _C1,_C2.

eqs:=[-1/2*arctanh(1/2*sqrt(1 + 2*_C1)*sqrt(2)/sqrt(_C1))*sqrt(2)/sqrt(_C1) = _C2, 1 = (-exp(2*_C2*sqrt(_C1)*sqrt(2)) + 1)*sqrt(_C1)*sqrt(2)/(exp(2*_C2*sqrt(_C1)*sqrt(2)) + 1)];
unknowns:={_C1,_C2};
time();
infolevel[solve]:=5;
C_sol:=[timelimit(60,solve(eqs,unknowns))];
time()

Main: Entering solver with 2 equations in 2 variables
Main: attempting to solve as a linear system
Recurse: recursively solving 2 equations and 2 inequations in 2 variables
Transformer:   solving for linear equation in _X000001
Recurse: recursively solving 2 equations and 2 inequations in 2 variables
Recurse: recursively solving 3 equations and 2 inequations in 3 variables
Dispatch: dispatching to Exponentials handler
Transformer:   solving for linear equation in _S000004
Recurse: recursively solving 3 equations and 3 inequations in 4 variables
Dispatch: dispatching to Rename handler
Dispatch: renaming _S000005 = arctanh(1/2*_S000002*RootOf(_Z^2-2,index = 1)/_S000001)
Recurse: recursively solving 3 equations and 3 inequations in 5 variables
Dispatch: handling polynomials of the form a*x^n-b
Dispatch: dispatching to PolynomialSystem handler
Main: polynomial system split into 1 parts under preprocessing
Main: using RegularChains based methods
SolverVariableOrder: using the variable order  _S000003 > _X000002 > _S000005 > _S000002 > _S000001
TriangularDecomposition: using deterministic algorithm for decomposition
TriangularDecomposition: decomposition successfully found 1 components
TriangularDecomposition: backsubstituting to form solutions
TriangularDecomposition: something went wrong during backsubstitution - trying a different variable order
Transformer:   solving the uncoupled linear subsystem in {_S000003, _X000002}
Linear: solving 2 linear equations
Polynomial: # of equations is: 2
Polynomial: best equation / unknown _S000005*_z1 _X000002 2*_S000001
Polynomial: # of equations is: 1
Polynomial: best equation / unknown -_z1*_S000001+1 _S000003 _z1*_S000001+1
Polynomial: backsubstitution at: 2
Polynomial: backsubstitution at: 1
Main: polynomial system split into 1 parts under preprocessing
Main: subsystem is essentially univariate
UnivariateHandler: subsystem has only one equation
UnivariateHandler: solving as if univariate in _S000002
Recurse: recursively solving 1 equations and 0 inequations in 1 variables
Dispatch: dispatching to OnlyIn handler
Transformer:   solving for linear equation in _S000006
Recurse: recursively solving 1 equations and 0 inequations in 1 variables
Transformer:   solving the uncoupled linear subsystem in _S000006
Recurse: recursively solving 1 equations and 1 inequations in 1 variables
Transformer:   solving the uncoupled linear subsystem in t
Error, (in evalf/hypergeom) time expired

This is trace when using A,B

eqs:=[-1/2*arctanh(1/2*sqrt(1 + 2*A)*sqrt(2)/sqrt(A))*sqrt(2)/sqrt(A) =B, 1 = (-exp(2*B*sqrt(A)*sqrt(2)) + 1)*sqrt(A)*sqrt(2)/(exp(2*B*sqrt(A)*sqrt(2)) + 1)];
unknowns:={A,B};
time();
infolevel[solve]:=5;
C_sol:=[timelimit(90,solve(eqs,unknowns))];
time()

Main: Entering solver with 2 equations in 2 variables
Main: attempting to solve as a linear system
Recurse: recursively solving 2 equations and 2 inequations in 2 variables
Transformer:   solving for linear equation in A
Recurse: recursively solving 2 equations and 2 inequations in 2 variables
Recurse: recursively solving 3 equations and 2 inequations in 3 variables
Dispatch: dispatching to Exponentials handler
Transformer:   solving for linear equation in _S000004
Recurse: recursively solving 3 equations and 3 inequations in 4 variables
Dispatch: dispatching to Rename handler
Dispatch: renaming _S000005 = arctanh(1/2*_S000002*RootOf(_Z^2-2,index = 1)/_S000001)
Recurse: recursively solving 3 equations and 3 inequations in 5 variables
Dispatch: handling polynomials of the form a*x^n-b
Dispatch: dispatching to PolynomialSystem handler
Main: polynomial system split into 1 parts under preprocessing
Main: using RegularChains based methods
SolverVariableOrder: using the variable order  _S000003 > B > _S000005 > _S000002 > _S000001
TriangularDecomposition: using deterministic algorithm for decomposition
TriangularDecomposition: decomposition successfully found 1 components
TriangularDecomposition: backsubstituting to form solutions
TriangularDecomposition: something went wrong during backsubstitution - trying a different variable order
Main: polynomial system split into 1 parts under preprocessing
Main: applying the solver for domain=absolute, engine=traditional
PseudoResultant: 225530 [1 200002087 _S000001] 3 3 151 2 45 0
PseudoResultant: 120059 [2 200004772 _S000003] 2 2 131 0 3 0
PseudoResultant: 134507 [1 700002396 _S000002] 1 1 53 0 3 0
PseudoResultant: -10 [] 0 0 3 0 3 0
PseudoResultant: 1 solutions found, now doing backsubstitution
PseudoResultant: backsubstitution of _S000002
PseudoResultant: backsubstitution of _S000003
PseudoResultant: backsubstitution of _S000001
SolutionsLost: setting solutions lost flag
Main: solving successful - now forming solutions
Main: Exiting solver returning 0 solutions

solve: Warning: no solutions found

## Does Maple support (negative) lookahead and lookbe...

I can't achieve this using StringTools:-RegSplit. The StringTools,Regular_Expressions documentation doesn't seem to address these functionalities.

My goal is to split the string at the occurences of "." that are somewhere between "]" and "["* yet not enclosed between the two digits, and to ignore all other occurences of "."

## File open not working on Windows system...

This is new:

Maple 2024 frozen on opening recent files

Maple 2023 frozen on opening

Maple 2022 frozen on opening start page

Maple 2020 opening start page

The above system state is constant for about 30 min. Maple sessions without start page are working. I can enter code but file opeing and saving does not work. The fact that Maple 2020 is also not working makes it unlikely that the Java environement is part of the problem.

I have several times restarted the system. The rest of the system is working.

Something happened to the system and I have no clue what is was and what I can do about it.

Any ideas or suggestions what I could try? Windows 10.

## integration in if-statement...

How can I get the evaluation of integration inside if-statement?