This is my first problem with Maple but i am pretty confused as to why it would struggle with these steps.

Just using a standard worksheet, here is what i have:

> f:=(4^x)+1

>g:=x^4

> solve(g=f,x)

now, i would just expect this to come back with 3 answers, but instead i get 

Warning, solutions may have been lost
                     RootOf(-4^_Z - 1 + _Z^4)

if I do:

>fsolve(g=f,x)

It comes back with only one of the answers(2.094012853), instead of all three.

What am I doing wrong?

I mean, for example,

solve({4*x1+7*x2+6*x3 = 186, floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18, 
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21});
Warning, solutions may have been lost

A finite number of the solutions can be found by DirectSearch

DirectSearch:-SolveEquations([floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18, 
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21, 4*x1+7*x2+6*x3 = 186], 
{x1 >= -100, x2 >= -100, x3 >= -100, x1 <= 100, x2 <= 100, x3 <= 100}, 
AllSolutions, solutions = 3, number = 1000);

Matrix(3, 4, [[0., Vector[column](3, [0., 0., 0.]),
 [x1 = 74.18778903830886, x2 = 58.93905207777524, x3 = -87.22075344961036], 185], 
[0., Vector[column](3, [0., 0., 0.]),
 [x1 = 71.22714241634635, x2 = 56.43467122661542, x3 = -82.32521137528222], 164],
 [0., Vector[column](3, [0., 0., 0.]), 
[x1 = 73.6407870507502, x2 = 58.33738250527096, x3 = -86.15413762331626], 165]])

I don't see a way to obtain the MMA answer (in Maple notation)

(155/2 < x1 and x1 < 78 and 744/7-4*x1*(1/7) < x2 and x2 < 62 or 72 <= x1 and x1 <= 73 and
 102-4*x1*(1/7) < x2 and x2 < 62 or 73 < x1 and x1 <= 147/2 and 102-4*x1*(1/7) < x2 and
 x2 <= 726/7-4*x1*(1/7) or 147/2 < x1 and x1 < 74 and 60 <= x2 and x2 <= 726/7-4*x1*(1/7) or
 74 <= x1 and x1 < 75 and 726/7-4*x1*(1/7) < x2 and x2 < 62 or 153/2 < x1 and x1 < 78 and
 726/7-4*x1*(1/7) < x2 and x2 < 60 or x1 = 72 and 58 <= x2 and x2 < 60 or 72 < x1 and x1 < 74 and
 58 <= x2 and x2 <= 708/7-4*x1*(1/7) or 75 <= x1 and x1 < 76 and 102-4*x1*(1/7) < x2 and x2 < 60 or
 x1 = 74 and 442/7 < x2 and x2 < 64 or 74 < x1 and x1 < 75 and 738/7-4*x1*(1/7) < x2 and 
x2 <= 744/7-4*x1*(1/7) or 74 <= x1 and x1 < 75 and 708/7-4*x1*(1/7) < x2 and x2 <= 102-4*x1*(1/7) or 
151/2 < x1 and x1 < 76 and 708/7-4*x1*(1/7) < x2 and x2 < 58 or 157/2 < x1 and x1 < 80 and
 762/7-4*x1*(1/7) < x2 and x2 < 64 or 68 <= x1 and x1 < 137/2 and 56 <= x2 and x2 <= 666/7-4*x1*(1/7) or
 x1 = 137/2 and x2 = 56 or x1 = 70 and 56 < x2 and x2 < 58 or 70 < x1 and x1 <= 71 and 56 <= x2 and
 x2 < 58 or 71 < x1 and x1 < 72 and 56 <= x2 and x2 <= 690/7-4*x1*(1/7) or 70 <= x1 and x1 <= 281/4 and
 54 <= x2 and x2 < 55 or 281/4 < x1 and x1 < 72 and 54 <= x2 and x2 <= 666/7-4*x1*(1/7)) and
 x3 = 31-2*x1*(1/3)-7*x2*(1/6)

PS. MMA_solution.pdf MMA_solution.mw

I get this message everytime I am trying to open my worksheet: "Recover Corrupt File and Save As"

2.G_anden_aflevering.mw

I've tried alot, but nothing seems to work. The problem occurres whenever im trying to use multiple SI Units in caculations that require division. Example:

Download Maple_prob1.mw

Here I put two functions defined by piece-wise command and then using int(...,numeric) to take their integration but Maple computes only one while for the other one just gives the expression back. The integration domain is bounded, the function is bounded too so I don't think the reason is being divergent in the one that Maple is not computing it.

Is there any prepared command or package for Maple which computes the integrals like this or is better than just int(...,numeric)? Or I have to write an algorithm an force Maple to compute my integral using an algorithm given by myself?
--
The codes in plain text:
 

int(piecewise(0 < -k5*x1*x2+k1*x1 < 1, 1, -k5*x1*x2+k1*x1 <= 0 and 1 <= -k5*x1*x2+k1*x1, 0)*piecewise(0 < -k5*x1*x2+k2*x2 < 1, 1, -k5*x1*x2+k2*x2 <= 0 and 1 <= -k5*x1*x2+k2*x2, 0), k1 = 0 .. 1, k2 = 0 .. 1, k5 = 0 .. 1, x1 = 0 .. 1, x2 = 0 .. 1, numeric);

int(piecewise(0 < x+y < 1, 1, x+y <= 0 and 1 <= x+y, 0)*piecewise(0 < y*x^2 < 1, 1, y*x^2 <= 0 and 1 <= y*x^2, 0), x = 0 .. 1, y = 0 .. 1, numeric);

I want to solve system of nonlinear ordinary differential equations numerically using the variational finite
element method (FEM). is it possible to solve on Maple? If anybody have a idea please share with me. I attach the image of my problem which I am tryimng to solve.

Hi,

Let a in ] 0, 1[  and  x real

Let  f := sin(x) / ( ( sin(a*x) )^a * ( sin((1-a)*x) )^(1-a) );

How can I find the limit of f as x goes to 0 ?
(limit, series, taylor don't work, wether I set or not assumptions on "a" [assume/assuming])

PS 1:  the limit is found once a numeric value is given to alpha

PS 2:  By simple calculations:
           sin(x) ~x  ;  sin(a*x) ~ ax  ; sin((1-a)*x) ~(1-a)x and thus
          ==>  f(x->0) ~ x / ( -a*x)^a * ((1-a)*x)^(1-a) )
                              = x / ( -a^a * (1-a)^(1-a) * x^(a+1-a)
                              = 1 /  ( -a^a * (1-a)^(1-a)  )

Hi,

Is it possible to write the title of a plot on two different lines with different fonts for each line?
For instance:

MyTitle := typeset("Identity function", "\n(illustration));
plot(x, x=0..1, title=MyTitle);

with the upper line  [times, bold, 14]
and the lower one   [times, roman, 12]

Hi,

I use the first example in the HeatMap help page.

restart:
with(Statistics):
RM := LinearAlgebra:-RandomMatrix(10):
HeatMap(RM);

I want to replace each tickmarks k (k=1..10) by cat(`A`, k).
So I do

NewTickMarks := [seq(k+1/2=cat(`A`, k), k=1..10)]:
HeatMap( RM, tickmarks=[NewTickMarks , NewTickMarks ] );

The horizontal tickmarks are displayed as expected: why the vertical tickmarks do not appear?

PS : HeatMap( RM, tickmarks=[NewTickMarks , default] ) changes the horizontal tickmarks without removing the vertical ones.

Thnks for the help
 

Hello!

Is there any chance to bring the expression x²+xy+y² to the form like x²+y²+xy (i.e. to set/define exact order of monomials) with Maple? What syntax (i.e. commands, packages, etc.) should I use? Many thaks in advance for any useful advice

When dsolve throws an error, is it always due to invalid user input, such as parsing error of some sort related to the input given to it, or could it throw an error not related to the parsing part? And if so, how would one know, in code, the difference between an error thrown due to parsing error, vs. something else?

For example, this will throw an error due to parsing

ode:=diff(y(x),x)+y;
try
   dsolve(ode,y(x));
catch:    
    print(StringTools:-FormatMessage( lastexception[2..-1] )); 
end try;

   "y(x) and y cannot both appear in the given ODE."

I want to check programmatically, if and when an error thrown by dsolve, if it is due to input itself being invalid, such as parsing error, or invalid initial conditions, and such bad input from the user, vs. other possible error that could be generated internally for other reasons when the input is valid.

I looked at help and there is no mention of what type of exceptions dsolve can throw, or how would would determine the type of exception, as Maple exceptions seem to be just strings and there is no actual identifier or type associated with them to use to check on.

I also looked at https://www.maplesoft.com/support/help/Maple/view.aspx?path=ErrorMessageGuideOverview  and seen nothing there that helps. It just says
 

There are three circumstances that would generate an error in Maple:

1. 	User Errors - the user has supplied incorrect input
2. 	No Solution - in some cases, a Maple routine will issue an error, indicating that the given problem has no solution
3. 	Maple Errors - Maple generates an error during internal computation in response to a problem with its own code

Great., But it does not say how a would a user know which is which when an error is thrown? (using code, not by looking at the screen and then using google).

In Mathematica for example, error messages have actual names, and one could check for the actual message tag itself in the code, to find what the error actually is, instead of using just a plain string of the error message. 

Does Maple have such a thing to use to help find what class of error was thrown out the above three classes shown in the above web page?

In this procedure I roll x dies and request a sum of the dies, n.
I then specify the third argument, o, to be exactly, minimum or maximum, so that it generates random rolls until the sum matches the conditions of my third argument.
It then returns the roll in a list and the number of rolls needed to match the conditions.

optional_argument.mw
Can I somehow make the third argument optional, with exactly being the default, so that I can enter only sim(3,12) to get a roll that is exactly 12?
I've written through this maplesoft document, but don't quite seem to understand how to make an optional argument in  this regard: https://fr.maplesoft.com/support/help/maple/view.aspx?path=parameter_classes

Any help in understanding this is appreciatet :)

Hello,

1 .

If A and B are non-commuting operators and I want to calculate

(A+B)^n for some integer n, how can I tell maple to not commute them?

2.

And if I have this operator construct A^3. How can I replace it with some defined function f, so A^3 becomes (f@@3)(...)

A := (a^6)^(1/3)*(-b^3)^(1/3)/a^3

I Can't get this to simplify to -b/a. 

I am developing an algorythm which returns some differential equation, which I want to simplify. Here is an example:

eqq:= k[t]*(`ℓ`^2)*(diff(q[3](tau), tau, tau)+(5*alpha-sigma+2*theta+1)*q[3](tau)+(-4*alpha+sigma-theta)*q[2](tau)+q[1](tau)*alpha) = -(sqrt(m*(1/k[t]))*`ℓ`*k[t]*`Δθ`*(q[3](tau)-q[2](tau))*sin(sqrt(Lambda*k[t]*(1/m))*sqrt(m*(1/k[t]))*tau)+2*xi*sqrt(lambda*k[t]*m)*(diff(q[3](tau), tau)))*`ℓ`*(1/sqrt(m*(1/k[t])))

I want the parameters to be associated to the the variables, , ,  and their derivattives. So, I have used "collect" command, as below:

vars:= {q[1](tau),q[2](tau),q[3](tau),diff(q[1](tau),tau),diff(q[2](tau),tau),diff(q[3](tau),tau),diff(q[1](tau),tau$2),diff(q[2](tau),tau$2),diff(q[3](tau),tau$2)}:
collect(eqq,vars);

The problem is that the equations remain with non-simplified terms, such as the terms inside the "sine" functions and the term "k[t]*ell^2". The command "simplify" does not have any effect. Ideally, I would like to have something like this:

(diff(q[3](tau), tau, tau))+alpha*q[1](tau)+(-4*alpha+sigma-theta)*q[2](tau)+(5*alpha-sigma+2*theta+1)*q[3](tau)+2*xi*sqrt(lambda)/`ℓ`*(diff(q[3](tau), tau))-`Δθ`*sin(sqrt(Lambda)*tau)*q[2](tau)+`Δθ`*q[3](tau)*sin(sqrt(Lambda)*tau) = 0;

Does anyone know how to solve that?