Maple gives solution to equation as RootOf when there is no explicit solution

restart;
eq:=x*sin(x*y)+y+1=0;
sol:=solve(eq,y)

The _Z above, is the variable we wanted to solve for, which is y in this example. My question is, why did not Maple give the solution as

sol2:=RootOf(x*sin(_Z*x)+_Z+1)

Which is a little simpler looking. Is the above not the same as what Maple gives?  I just replace y by _Z 

Digits:=100;
plot(evalf(sol-sol2),x=0..Pi)

The uploaded worksheet contains the general definition of a pedal curve related to the curve [f(t),g(t)], and includes several example pedal curves.

Is there a comparable general definition of a pedal surface? If so, in your answer please include the Maple code for one or two simple examples e.g. relating to a sphere, to an ellipsoid.

To everyone in the Maple Forum community, Happy Holidays and a fulfilling New Year!

Pedal_curves.mw 

sometimes Maple's solution for an ode is not valid for all x. When I run odetest on the solution, it is not zero.

For the case when the output of odetest contains one csgn(), I am trying to determine if odetest result will become zero, when csgn is +1  or -1. If so, then next look into the argument of csgn and solve for x under this condition and hence find the range of x when the solution is valid.

I wrote the following to do this and check the idea.

I'd like to ask if the Maple experts here can suggest improvement or if there a better way to do this.

The code below works if there is only instance of csgn() in the output of odetest. Which covers almost all the cases I saw so far.

The code first checks if csgn is present in the output of odetest. If so, it then uses indents to pick up the function csgn out. Then uses op to pick its argument. Then uses solve with inquality to find when the argument is either positive or negative. This results in the range of x needed to make odetest zero.

This is just a quick prototype to test the idea. This not the final code I will be using as that will include more checks and be more robust. 

restart;
ode :=diff(y(x),x)=2*(x*sqrt(y(x))-1)*y(x):
ic  :=y(0)=1:
sol :=dsolve([ode,ic]):
res :=odetest(sol,ode);

So we see odetest did not give zero.  The issue is that I can't just do 

solve(res=0,x)

It does not work.  So that is why I had to look inside as follows:

The goal is to check if when csgn is either +1 or -1, if it will then become zero.

And if so, then also find the range of x which will caused this.  In the above, we see that when 1/(x+1) is +1, then odetest result  will become zero. This means x has to be larger than -1.

Note that this is all done in code, without being able to look at the screen and then decide what to do

if res<>0 then
    if has(res,csgn) then
        if simplify( subsindets(res,csgn(anything),f->1)) = 0 then      
            print("the odetest becomes zero when csgn is POSITIVE");
            Z:=indets(res,specfunc(csgn));
            the_args:=map(x->op(x),Z);
            print("Now solve ",the_args," for x, when the expression is POSTIVE");
            for tmp in the_args do
                result:=solve(tmp>0,x);
                print("the solution is valid for x>", op([1,1],result));
            od;
        else
            if simplify( subsindets(res,csgn(anything),f->-1)) = 0 then      
                print("the odetest becomes zero when csgn is POSITIVE");
                indets(res,specfunc(csgn));
                the_args:=map(x->op(x),Z);
                print("Now solve ",the_args," for x, when the expression is negative");
                for tmp in the_args do
                    result:=solve(tmp<0,x);
                    print("the solution is valid for x<", op([1,1],result));
                od;
            else
                print("give up. Tried when csgn is positive or negative");
            fi;
        fi;
    fi;
fi;

If there is more than one csgn function in the odetest result, it will become much more complicated, since one have to check all combinations to find under which combination odetest will become zero. So for now, I am just doing this only for one case of csgn present.

I have a function defined by this integral: f(x):=int((sin(t)^2)^(exp(t)),t=x..infinity). The question is how to plot this function from x=-5 to x=+5 in Maple 2020? I do as follow, but it does not work for Maple 2020 (15 days trial version).

f := int((sin(t)^2)^exp(t), t = x .. infinity)
plot(f, x = -5 .. 5)

Maple version: Maple 2020.2, Maple Build ID 1502365.

Thank you very much. 

Please see the question posed in the opening text of the uploaded worksheet.

Oloid.mw

I have a function:

T(t) := (t+459.47) * 5/9  ,  convert degrees F to Kelvins.

I want to produce a table of values over a range of 100F to 250F with two colums,

Degrees F and Kelvins.

I have no problem doing this in Mathcad Prime, but I'm lost as to how

to accomplish this in Maple.

I am evaluating the Maple trial as a potential replacement for Mathcad Prime,

but at this point it may not work for me.

I am an electrical engineer and have been using Matlab for years.  I am switching over to Maple and am converting my extensive library of Matlab scripts to Maple.  

Among other things, I plan on using Maple, as I have Matlab, to determine component values based on design criteria (e.g. input voltage range, output voltage range, etc.) and to analyze the resulting circuit uncertainties.

I have generally released the uncertainty results to my clients and like to use the appropriate mathematical symbols to convey the information.  

I would eventually like to generate a report for my client that shows the calculated component values and the resulting uncertainties (e.g. "R1 = 2.56kΩ ± 0.01%", "Total uncalibrated uncertainty (maximum) = ±(0.23452% of reading + 0.198°C)")

I see that outside of a code edit region, I can freely use the symbols from the "common symbols" palette to generate text as shown above.

Should I avoid trying to automate this (i.e. using printf() statements)?

I found small problem in Latex(). When putting solution of ODE inside a Vector, Latex() fails to convert and returns empty vector.

restart;
sol:=[dsolve(diff(diff(y(x),x),x)*y(x) = 1,y(x))];
sol:=convert(sol,Vector);

And now

Latex(sol)


               \left[\begin{array}{c} \\ \end{array}\right]

Empty array. But if not in a Vector, it works

restart;
sol:=[dsolve(diff(diff(y(x),x),x)*y(x) = 1,y(x))];
Latex(sol)

# no problem here ====>

\left[
{\textcolor{gray}{\int}}_{}^{y \! \left(x \right)}\frac{1}{\sqrt{2 \ln \! \left(\mathit{\_a} \right)-2 \mathit{\_C1}}}\textcolor{gray}{d}\mathit{\_a} -x -\mathit{\_C2}
 = 0, 
{\textcolor{gray}{\int}}_{}^{y \! \left(x \right)}-\frac{1}{\sqrt{2 \ln \! \left(\mathit{\_a} \right)-2 \mathit{\_C1}}}\textcolor{gray}{d}\mathit{\_a} -x -\mathit{\_C2}
 = 0\right]

This seems to happen on some solutions (may be those with Int because in this other example, it works with Vector):

restart;
sol:=[dsolve(diff(diff(y(x),x),x)*y(x)^2 = 0)];
sol:=convert(sol,Vector);

And now

Latex(sol)

#now it works ===>

\left[\begin{array}{c}y \! \left(x \right)=0 \\y \! \left(x \right)=\mathit{\_C1} x +\mathit{\_C2}  \end{array}\right]

I am using Maple 2020.2 with Physics 897

Edit 1/2/2021

I found another strange problem with Latex conversion related to Vector. If the first entry is y(x)=0 in the vector, then it keeps this, but throws away the rest of the entries in the Vector.

This might be related to the same bug. Not sure. Here is an example

restart;
ode:=(2*cot(x)*diff(y(x),x)*y(x)+diff(y(x),x)^2-y(x)^2 = 0,singsol=all);
sol:=convert([dsolve(ode)],Vector)

Now watch what happens when converting sol to Latex

Latex(sol)

    \left[\begin{array}{c}y \! \left(x \right)=0 \\ \\ \end{array}\right]

Only reason I use Vector() is to display in Latex many solutions on top of each others, so easier to see instead of as a list() where they are all on one line, which might not fit the page.

I need to find an alternative to using Vector to do this. 

For some reason every := on my work sheet has turned to "d" how to if fix this.

What is the letter O doing inside this pde solution by Maple 2020.2 and what does it mean? There is no O in the PDE itself and it is not a name of a mathematical special function 

restart;
interface(version);
pde :=  diff(w(x,y),x)+ (a*x^2*y+b*y^3)*diff(w(x,y),y) = 0;
sol:=pdsolve(pde,w(x,y));

lprint(sol)

w(x,y) = _F1(1/9*(2*2^(2/3)*3^(5/6)*b*x*O*y^2-3*2^(2/3)*3^(1/3)*b*x*GAMMA(1/3,-\
2/3*x^3*a)*GAMMA(2/3)*y^2+9*O*GAMMA(2/3)*exp(2/3*x^3*a))/O/GAMMA(2/3)/y^2)

Please see this example. This Latex generated gives Latex compile error.

restart;
Latex:-Settings(UseImaginaryUnit=i,
      UseColor = false,
      powersoftrigonometricfunctions= mixed, ## computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false,
      spaceaftersqrt = true  
);

L:=3;
c:=4;
h:=1/10;
b:=Pi*c/L;
f:=piecewise(0<x and x<L/3,3*h/L*x,L/3<x and x<L,h);
pde := diff(u(x,t),t$2) + b*diff(u(x,t),t) = c^2*diff(u(x,t),x$2);
bc  := u(0,t)=0,D[1](u)(L,t)=0;
ic  := D[2](u)(x,0)=0,u(x,0)=f;
sol:=pdsolve([pde,bc,ic],u(x,t));

The Latex generated does not compile:

Latex(sol)


u \left(x , t\right) = 
\Mapleoverset{\infty}{\Mapleunderset{n =0}{\sum}}\left\{\begin{array}{44}\frac{4 \,{\mathrm e}^{-\frac{2 t \pi}{3}} \left(t \pi +\frac{3}{2}\right) \sin \left(\frac{\pi  x}{6}\right)}{5 \pi^{2}} & n =0 \\\frac{3 \sin \left(\frac{\left(1+2 n \right) \pi  x}{6}\right) \left(\sqrt{3}\, \sin \left(\frac{\pi  n}{3}\right)+\cos \left(\frac{\pi  n}{3}\right)\right) \left(\left(2 \sqrt{n}\, \sqrt{n +1}+i\right) {\mathrm e}^{\frac{2 i \pi  \left(-2 \sqrt{n}\, \sqrt{n +1}+i\right) t}{3}}-{\mathrm e}^{\frac{2 i \pi  \left(2 \sqrt{n}\, \sqrt{n +1}+i\right) t}{3}} \left(-2 \sqrt{n}\, \sqrt{n +1}+i\right)\right)}{10 \sqrt{n}\, \sqrt{n +1}\, \pi^{2} \left(1+2 n \right)^{2}} & \mathit{otherwise}  \end{array}\right.

Gives

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{maplestd2e}  

\begin{document}
\[
u \left(x , t\right) = 
\Mapleoverset{\infty}{\Mapleunderset{n =0}{\sum}}\left\{\begin{array}{44}\frac{4 \,{\mathrm e}^{-\frac{2 t \pi}{3}} 
   \left(t \pi +\frac{3}{2}\right) \sin \left(\frac{\pi  x}{6}\right)}{5 \pi^{2}} 
    & n =0 \\\frac{3 \sin \left(\frac{\left(1+2 n \right) \pi  x}{6}\right) 
    \left(\sqrt{3}\, \sin \left(\frac{\pi  n}{3}\right)+\cos \left(\frac{\pi  n}{3}\right)\right) 
    \left(\left(2 \sqrt{n}\, \sqrt{n +1}+i\right) {\mathrm e}^{\frac{2 i \pi  \left(-2 \sqrt{n}\, 
    \sqrt{n +1}+i\right) t}{3}}-{\mathrm e}^{\frac{2 i \pi  \left(2 \sqrt{n}\, \sqrt{n +1}+i\right) t}{3}} 
    \left(-2 \sqrt{n}\, \sqrt{n +1}+i\right)\right)}{10 \sqrt{n}\, \sqrt{n +1}\, \pi^{2} \left(1+2 n \right)^{2}} 
    & \mathit{otherwise}  \end{array}\right.
\]

\end{document}

This, using latest TeXLive on Linux, gives  Illegal character in array arg.

lualatex foo5.tex
This is LuaHBTeX, Version 1.12.0 (TeX Live 2020)
 restricted system commands enabled.
(./foo5.tex
LaTeX2e <2020-10-01> patch level 2


 L3 programming layer <2020-12-07> xparse <2020-03-03> (/usr/local/texlive/2020/texmf-dist/tex/latex/base/article.cls
Document Class: article 2020/04/10 v1.4m Standard LaTeX document class
(/usr/local/texlive/2020/texmf-dist/tex/latex/base/size11.clo)) (/usr/local/texlive/2020/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/local/texlive/2020/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/local/texlive/2020/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/mnt/g/public_html/styles/maplestd2e.sty
Package: maple2e 2005/03/17 v1.16
Defining Maple Utility Macros
(/mnt/g/public_html/styles/mapleenv.def)
Defining Maple Plot Environemnts
 ...Defaults to "dvips" Driver
(/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/epsfig.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/graphicx.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/graphics.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/trig.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics-cfg/graphics.cfg) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics-def/dvips.def))))
Defining Automatic Style Generation Macros
Defining Maple Spreadsheet Environments
Maple Spreadsheet and Table Support
) (/usr/local/texlive/2020/texmf-dist/tex/latex/l3backend/l3backend-luatex.def) (./foo5.aux) (/usr/local/texlive/2020/texmf-dist/tex/latex/base/ts1cmr.fd)

! LaTeX Error: Illegal character in array arg.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...haracter\or Missing @-exp\or Missing p-arg\fi \space in array arg.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help\@err@

l.8 \Mapleoverset{\infty}{\Mapleunderset{n =0}{\sum}}\left\{\begin{array}{44}
                                                                           \frac{4 \,{\mathrm e}^{-\frac{2 t \pi}{3}}
?

fyi. No errors are generated from the old latex() command.

The following is another example, with the same Latex error. 

restart;
Latex:-Settings(UseImaginaryUnit=i,
      UseColor = false,
      powersoftrigonometricfunctions= mixed, ## computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false,
      spaceaftersqrt = true  
);

c:=3;
f:=piecewise(4<x and x<5,1,true,0);
pde := diff(u(x, t), t$2) = c^2*(diff(u(x, t), x$2));
bc  := eval( diff(u(x,t),x),x=0)=0;
ic  := u(x,0)=f(x),eval(diff(u(x,t),t),t=0)=0;
sol:=pdsolve([pde, bc,ic],u(x,t)) assuming x>0,t>0;

Latex(sol);  #gives Latex that do not compile

Maple 2020.2, with Physics 897

colect(expr,y)  and collect(expr,y,factor) do not work on these.  The expression can be anything. No necessarily a polynomial in y.

I have as input an expression, which has y  in it, and I want to find if I can write it  as   y*(....)  of y^2*(...) or y^3*(...), etc...

Basically, I want to see if y can be taken out as common term. Just like we do by hand. 

So, given expression as  y^2+y^3*sin(x)+3*x*y^5 then I want to see if it can be written as y^2*(1+y*sin(x)+3*x*y^3)

In the above y^2 was extracted as common term. I found that simplify sometimes work, but I can't depend on simplify, since it is not guranteed to work all the time. Here is an example where it worked

expr:=y^2+y^3*sin(x);
simplify(expr)

but if expression is this, then it did not extract out y^2

expr:=y^2+y^3*sin(x)+3*x*y^5;
simplify(expr)

I am doing this  all in code, without looking at the expression and decide what to do. 

I just know  y is the name of the variable, and the expression will be a function of y  and I just want to know if I can extract a common y^n  term out, so the result is y^n*g(y)

For example, for expr:=y^2+y^3*sin(x)+3*x; it will fail, since  I can't extract y from all terms. In this case the result will be  y^2*(1+y*sin(x))+3*x  and this is not type(`*`). So it is ok for the method to fail, if it can not do it. I can always check the result to see if it failed or not.

Does Maple have build in method to do this? Or one has to program this? I wanted to ask first before if there is some hidden Maple function that can do this I did not see.

Sometimes math is easier to do by hand than using the computer :)

Maple 2020.2

Thanks.

edit: I also tried factor, but it does not work on everything. An example where it did not work

expr:=y^2+y^3*sin(x)+3*x*y^(7/2);
factor(expr);

It did not factor out y^2 because of y^(7/2) is not "integer, rational. numeric, or algebraic coefficients"? according to help.

Edit:

Thanks to all the answers. I used a combination of all of them to check if it can be factored or not, and now it is working for every example I tried it on. So if one method failed, I try the next method shown in the answers. 

Dear all,

I have a long Maple code.

After running the code, suppose that we get an error in one of the lines.  I can't simply find the mouse cursor in the line which includes the error.

Question 1: How to find quickly which line has the error? What are your solution methods?

Question 2: Enlarging more or highlighting the cursor mark maybe works. Is it possible?

I have function that accept keyword argument. From this function, I need to pass this argument to another function using the same signature and using same name for the keyword. But it is not possible to do. 

Easier to explain with an example.   This is what I want to do

restart;
foo:=proc(n::integer,{ic::`=`:=[]})   
   post_process(n+1,'ic'=ic);
end proc;

post_process:=proc(n::integer,{ic::`=`:= []})
    print("in postprocess, n=",n, "ic=",ic);
end proc;

foo(3,'ic'=(y(0)=5))

Gives 

The problem is that when calling post_process(), using 'ic'=ic it does not work. Currently I have to change the keyword name as workaround, like this

restart;
foo:=proc(A::integer,{ic::`=`:=[]})
   print("in foo, A=",A, "ic=",ic);
   post_process(A,'new_ic'=ic);
end proc;

post_process:=proc(A::integer,{new_ic::`=`:= []})
    print("in postprocess, A=",A, "ic=",new_ic);
end proc;

foo(3,'ic'=(y(0)=5))

Which gives

Now it passed it. I would have liked to keep same keyword name ic in both function signatures instead of coming up with new name.

Is there a way to do that? 

This is not the only problem. The problem with this workaround, is that it does not work when the keyword argument is not passed to the first function. Because now it will use the default values of [].

Hence when calling the post_process() function, it fails due to type mismatch. This now gives an error

restart;
foo:=proc(A::integer,{ic::`=`:=[]})
   print("in foo, A=",A, "ic=",ic);
   post_process(A,'new_ic'=ic);
end proc;

post_process:=proc(A::integer,{new_ic::`=`:= []})
    print("in postprocess, A=",A, "ic=",new_ic);
end proc;

foo(3)

Error, (in foo) invalid input: post_process expects value for keyword parameter new_ic to be of type `=`, but received []

So the way I do this now, is to add an extra check each time, like this

restart;
foo:=proc(A::integer,{ic::`=`:=[]})
   if nargs = 2 then #is ic passed in?     
      post_process(A,'new_ic'=ic);
   else
      post_process(A);
   fi;
end proc;

post_process:=proc(A::integer,{new_ic::`=`:= []})
    print("in postprocess, A=",A, "ic=",new_ic);
end proc;

foo(3)# now it works

But in my actual code, I have more than one keyword argument, and I have to keep checking for correct number of arguments each time, to know which arggument to pass along. 

So far, I did not find an easy way around this.

Any suggestion how to do this better? passing keyword argument with default values? from one function to another without getting into these problems?

Maple 2020.2

This simple set of integrations works correctly and quickly in Maple 17 and other releases, but not in Maple 2020.

psi(x) := (-1)^v*(alpha*GAMMA(k-v)/v!/GAMMA(k-2*v-1)/GAMMA(k-2*v))^(1/2)*exp(-1/2*k*exp(-alpha*x))*                 (k*exp(-alpha*x))^(1/2*k-v-1/2)*LaguerreL(v,k-2*v-1,k/exp(alpha*x))/binomial(k-v-1,v);

Int(eval(%, [k=30.5, v=j, alpha=2.5])^2, x=-1..infinity) =
   seq(evalf[12](Int(eval(%, [k=30.5, v=j, alpha=2.5])^2, x=-1..infinity)), j=0..5);

Every time that I try this simple integration in Maple 2020 I receive a message "kernel connection lost".  Why???