This is the context. I am doing reduction of order on an ODE. This sometimes converts the ode to form  where common factor containing only  x can be moved outside, making the ode looks like  f(x)*(y''(x)+....etc...) = 0 then now I can eliminate f(x)  and only solve (y''(x)+....etc...) = 0 which is simpler.

I found if I can call factor on the ode, it works. It does remove any common terms. The problem I am having is how to cleanly determine the factors obtained. In the above example, it will be f(x) and (y''(x)+....etc...) 

For an example, the ODE   x^2 y'' + x y' = 0 can be written (using factor) as  x ( x y'' + y') =0 and now canceling x<>0, the ode becomes simpler x y''+ y' = 0.

I am now trying to find the two factors, using using op() on the result of factor.

But it does not work for all cases. There should be a way more robust way to obtain the factors.  I give 2 examples to better explain.

Example 1

ode:=x^2*diff(y(x),x$2)-(x-3/16)*y(x)=0:
ode:=expand(algsubs( y(x)=v(x)*x^(1/4)*exp(2*sqrt(x)),ode));
ode:=factor(ode);

After factoring the original ODE, there is common term found, which is the one shown UP. I need to find this to cancel it and keep the rest.

Currently I do this, which does not work for call cases

#check it is factored OK. If the type is `*` then Maple
#found common factor.
if type(lhs(ode),`*`) then 
   #add code to extract the two parts
   LHS:=op([1..-2],lhs(ode));
   RHS:=op(-1,lhs(ode));
fi;

Even though this worked here. I can now check it is the LHS which needs to be canceled. But all what I have are the operands. I do not know how to reconstruct the LHS from the operands. They could be + or *.  If it was `*` between the oprands for LHS, then I can do LHS:=mul(LHS) and this gives 

But I got lucky here. I do not know if it will be `*` all the time for LHS operands.

example 2

ode:=x^2*diff(y(x),x$2)-x*(x+2)*diff(y(x),x)+(x+2)*y(x)=0;
ode:=algsubs( y(x)=v(x)*x,ode):
ode:=factor(ode);

For this, the code I have works, but this is only because the LHS was simple.

if type(lhs(ode),`*`) then #factored OK
   LHS:=op([1..-2],lhs(ode));
   RHS:=op(-1,lhs(ode));
fi;

My question is: I expect factor, if there is common factor, to generate 2 expressions with `*` between them. I am looking for a good way to find what these two factors are. Once I do, it is easy for me to find which is the ODE and which is not and cancel the one which is not out.

I tried collect, but this does not work in general. Since I do not know beforehand, what is the common term, if any, present.

If this needs more clarification please feel free to ask. I have many more examples. This is all done by coding. Non-interactive. So solution based on looking at the output then do something, will not work for me.

Currently to parse initial conditions of ODE entered bu user in the form y(x0)=y0 in order to determine x0 and y0 I use patmatch on lhs and rhs separatly which is not a big deal. I wanted to see if I can use an equation inside patmatch.

I could not figure how to use patmatch on both sides of equation on one call.  Help says expression to patmatch is algebraic expression. Does this means an equation can't be used as whole? Here is an example to make it more clear

restart;
ic:=y(0) = 1;
patmatch(ic,y(x0::anything)=y0::anything,'la')

Which gives false. i.e. no match found.

Is there a trick to make the above work if possible? This is just a basic example. I might want to apply this on more complicated equation where more things are on lhs and rhs of =  but patmatch does not like `=` in the middle there. 

After I just updated to Physics 871, my main worksheet which allready has for long time now:

Physics:-Latex:-UseColor := false;  
Physics:-Latex:-UseImaginaryUnit:=i;

Now I get 

The reason I use Physics:-Latex:-UseImaginaryUnit:=i; is to make the Latex use i for complex number in Latex instead of I

What is now the correct way to use these settings with the new Physics update? if I do not use them, then compelx I  will still show as I whcih I do not want. I want lower case i

I could add interface(imaginaryunit=i); in place of Physics:-Latex:-UseImaginaryUnit:=i; and that work for the latex, making the Latex generate i. But this solution now makes the User interface no longer accept I  as complex number any more and must be typed as lower case, which is not what I want.

That is why I was using Physics:-Latex:-UseImaginaryUnit:=i; This keeps the user interface complex number as Uppercase, but let the latex generated be lower case.

I feel I am doing something wrong, but do not see it. Made sure I use Physics:-Latex on everything now.

Please see below 2 worksheets. One using the 871 version and one using 865 version.
 

Download latex_871.mw
 

Download latex_865.mw

New error seems to have been introduced 

restart;
expr:=arccos(1/x);
Physics:-Latex(expr);

it seems to happen with the inverse trig functions when there is a fraction inside.

Do others have the same issue? I am currently using  869.  Maple 2020.1

Rolling back Physics version one at a time, I found the version this happened at. It was OK in version 865, but gives the error starting at version 866.

Hopefully this should make it easy to find the code change which caused it using source control diff.

As Latex improves in Maple (thanks to Physics:-Latex), I'd like to suggest not using \rm and replacing it with \mathrm.

\rm is now obsolete for long time. Reference: https://tex.stackexchange.com/questions/107186/how-to-write-norm-which-adjusts-its-size

 In addition, some Latex classes give warning or error when using it and workarounds are needed. For an example

\documentclass{scrbook}%notice the class is not article.
\usepackage{amsmath}
\begin{document}
${\rm e}^{-t}$
\end{document}

When compiled using lualatex foo4.tex gives

(base) >lualatex foo4.tex
This is LuaHBTeX, Version 1.12.0 (TeX Live 2020)
 restricted system commands enabled.
(./foo4.tex
LaTeX2e <2020-02-02> patch level 5
 L3 programming layer <2020-08-07> (/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/scrbook.cls
Document Class: scrbook 2020/07/22 v3.31 KOMA-Script document class (book)
(/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/scrkbase.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/scrbase.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/scrlfile.sty))) (/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/tocbasic.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/scrsize11pt.clo) (/usr/local/texlive/2020/texmf-dist/tex/latex/koma-script/typearea.sty)) (/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)) (/usr/local/texlive/2020/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def) (./foo4.aux) (/usr/local/texlive/2020/texmf-dist/tex/latex/base/ts1cmr.fd)

! Class scrbook Error: undefined old font command `\rm'.

See the scrbook class documentation for explanation.
Type  H <return>  for immediate help.
 ...MAClassName  Error: undefined old font command `\string \rm '.

See the \KOMAClassName  class documentation for explanation.
Type  H <return>  for immediate help\@err@
                                                                                                                                                                                                        
l.7 ${\rm
        e}^{-t}$
?

And Maple generates lots of these. For example

Physics:-Latex(exp(-t))
 
          {\rm e}^{-t}

mathrm works and give same output. Here is an example, where now I change the class to article to make it compile 

\documentclass{article}
\usepackage{amsmath}
\begin{document}

${\rm e}^{-t}$

$\mathrm{e}^{-t}$

$e^{-t}$

\end{document}

gives

The first is \rm, the second is mathrm and the last is the default with no modification.

Do others see any problem if this change could be made to Maple's Latex?

I am using Maple 2020.1 and Physics  867