I was wondering whether the rendering of bars

looks also dot like on other computers

Looks like Newtonian notation

When the Fourier transform to the heat equation for example it is useful to represent the Fourier transform of a derivative as the derivative of the transform.  Thus

        FT{d(U(x, t)/dt}  = d(FT{U(t))} / dt,

Where FT => Fourier transform wrt the variable x.

How do I get Maple to obtain the above.

Joe Salacuse

 can be simplified :l *h*t/m

How can I ask Maple to do this.

Given

expr:=  (x^(-(44 + 12*sqrt(69))^(1/3)/6 + 10/(3*(44 + 12*sqrt(69))^(1/3)) + 2/3)) - (x^(sqrt(69)*2^(1/3)*((11 + 3*sqrt(69))^2)^(1/3)/100 - (11*(44 + 12*sqrt(69))^(2/3))/600 - (44 + 12*sqrt(69))^(1/3)/6 + 2/3))

could someone come with a trick to show this is zero using simplification and other methods? I know I can use is and coulditbe but I do not trust these too much due to false positives I've seen from them in some places.

Here is my attempts

restart;


expr:=  (x^(-(44 + 12*sqrt(69))^(1/3)/6 + 10/(3*(44 + 12*sqrt(69))^(1/3)) + 2/3)) - (x^(sqrt(69)*2^(1/3)*((11 + 3*sqrt(69))^2)^(1/3)/100 - (11*(44 + 12*sqrt(69))^(2/3))/600 - (44 + 12*sqrt(69))^(1/3)/6 + 2/3));
simplify(expr);
simplify(expr,size);
simplify(expr,symbolic);
simplify(normal(expr));
simplify(normal(expr),symbolic);
simplify(expr) assuming real;
simplify(expr) assuming positive;
is(expr=0);
coulditbe(expr=0);
evalb(expr=0);

Gives

This is for reference, the Mathematica attempt

long time ago I asked about automatic spacing to improve latex for sqrt. A nice solution was provided in https://www.mapleprimes.com/questions/231062-Adding-Space-After-Sqrt-To-Improve-The-Latex

The above is activatived using spaceaftersqrt = true option for latex:-Settings

There is a similar issue for inert integration where a space is typically added before the final dx This is done similar to the above fix using \, See for example this Latex web site giving many examples.

But there is no option I could see to tell Maple to do this automatically for integration.

So all my inert integrals now look not too good as the dx is too close to the integrand. Here are 2 examples with the settings I am using

restart;

latex:-Settings(useimaginaryunit=i,
      usecolor = false,
      powersoftrigonometricfunctions= mixed, ## computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false,
      spaceaftersqrt = true,
      usetypesettingcurrentsettings=true,
      linelength=10000      
);

sol:=sqrt(4*y^3-a*y-b)*a;
Intat( subs(y=a,1/sol),a=y(x));
latex(%);

Int(sol,y);
latex(%);

I copied the latex and compiled it, and this is the result

\documentclass[12pt]{book}
\usepackage{amsmath}
\begin{document}

\[
\int_{}^{y \left(x \right)}\frac{1}{\sqrt{4 a^{3}-a^{2}-b}\, a}d a
\]

\[
\int \sqrt{4 y^{3}-a y -b}\, a d y
\]

\end{document}

Which gives

Compare the output when adding \, by hand to the latex

\documentclass[12pt]{book}
\usepackage{amsmath}
\begin{document}

\[
\int_{}^{y \left(x \right)}\frac{1}{\sqrt{4 a^{3}-a^{2}-b}\, a}\, d a
\]

\[
\int \sqrt{4 y^{3}-a y -b}\, a \, d y
\]

\end{document}

Which now gives much better result

Actually, what would be nice if the "d" in "dx" was mathrm which becomes

\documentclass[12pt]{book}
\usepackage{amsmath}
\begin{document}

\[
\int_{}^{y \left(x \right)}\frac{1}{\sqrt{4 a^{3}-a^{2}-b}\, a}\, \mathrm{d} a
\]

\[
\int \sqrt{4 y^{3}-a y -b}\, a \, \mathrm{d} y
\]

\end{document}

But may be I am asking for too much here. But having an option to add \, only for inert integration will be good to have.

Does there exist an option to do this that may be I overlooked?

Maple 2023.2

I have the function: 2*sin(x)+1/2x-1

I want the x-intercepts, but Maple only provides one answer with fsolve.

I am trying to find the integer numbers a, b, c, d, t so that the equation sqrt(a x^2 + b x + c) = d x + t have two integer solutions. My code

First I solve

solve(a*x^2 + b*x + c = (d*x + t)^2, x);

I get

(2*d*t - b + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2))/(2*(-d^2 + a)), -(-2*d*t + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2) + b)/(2*(-d^2 + a))

And then, I solve
restart;
n := 0;
for a to 10 do
for b to 10 do
for c to 10 do
for d to 10 do
for t to 10 do
mydelta := 4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2;
if 0 < mydelta and type(mydelta, integer) then
x1 := (2*d*t - b + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2))/(2*(-d^2 + a));
x2 := -(-2*d*t + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2) + b)/(2*(-d^2 + a));
if 0 < d*x1 + t and 0 < d*x2 + t and type(x1, integer) and type(x2, integer) and nops({a, b, c, d, t}) = 5 and c <> t^2 and -d^2 + a <> 0 and nops({x1, x2}) = 2 then n := n + 1; L[n] := [a, b, c, d, t]; end if; end if; end do; end do; end do; end do;
end do;
L := convert(L, list);
nops(L);

I don't get any solutions. But, when I  solve(sqrt(2*x^2 + 3*x + 5) = x + 9, x); I get two solutions 19, -4.
Where is wrong in my code?
 

S := [1, 2];
                          S := [1, 2]

T := [1, 2];
                          T := [1, 2]

is(S = T);
                              true

Sv := Vector([1, 2]);
                              

Tv := Vector([1, 2]);
                              

is(Sv = Tv);
                             false

is(convert(Sv, list) = convert(Tv, list));
                              true

how to solve tis type of pdefirst_order_pde.mw

I obtained a Plot p, then trying to find if it has Float(undefined) in it. I am basically trying to find if DEplot returns an empty plot or not. I found that it the plot structure has HFlat(undefined) then this seems to imply an empty plot. So I said, then in the code I can check for HFlat(undefined) in the plot and it is there, then I know the plot is empty.

But this check is not working.

I used has(....,Float(undefined)) and this returns false. But if I copy and paste part of the plot structure and try the check on the copy, it gives true. 

I do not understand what is the difference. First here is screen shot, and below if complete code to reproduce.

restart;
ode2:=2*y(t)+t*diff(y(t),t) = t^2-t+1;

p:=DEtools:-DEplot(ode2,y(t),t=0..3.5,y=0..3,
                        linecolor = red,                        
                        arrowsize ='magnitude',
                        numpoints = 200 ,
                        axes = boxed,color = ('magnitude[legacy]')):


p0:=Array(1 .. 3,1 .. 2,{(1, 1) = HFloat(undefined), (1, 2) = HFloat(undefined), (2
, 1) = HFloat(undefined), (2, 2) = HFloat(undefined), (3, 1) = HFloat(undefined
), (3, 2) = HFloat(undefined)},datatype = float[8],order = C_order);
whattype(p0);
has(p0,HFloat(undefined)) 

p1:=op([1,2],p);
whattype(p1);
has(p1,HFloat(undefined)) 

Worksheet attached also.

Maple 2023.2 on windows 10
 

question is: Why the above give different result? And what is the correct way to check if the output plot from DEplot is empty or not (in code)?

Download why_has_works_different.mw

The documentation says:

So “_” can be treated as an argument placeholder in a for–in loop. Nevertheless, I would like to know if there is an argument placeholder like MatLab's tilde (~) operator:

• Ignore Function Outputs
• Ignore Inputs in Function Definitions

Ordinarily, there is no need to to ignore inputs in function definitions, but as for the former, since there is a _nresults keyword in Maple (and some "built-in" routines do use it), when accessing the source code is unavailable, how do I ignore specific outputs from such a function (e.g., a procedure with option encrypted that has been loaded from a r