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

Any idea why

if 2+89^(1/2)>0 then
   print("yes");
else
   print("no");
fi;

gives

Since 

evalf(2+89^(1/2))

is 11.4339.

I tried in Mathematica, and it works there

If[2 + 89^(1/2) > 0, Print["Yes"], Print["No"]]

What is the correct way to do this in Maple? i.e. to check that a numerical value is >0 ?

This is done in code, where the value I am doing this check on are known to be numeric, but I do not know what form they will be, I just know they will contain no floating point numbers. Only exact numbers.

The problem is the 89^(1/2). Maple knows it is >0 

is(89^(1/2)>0)

        true

but 

if (89)^(1/2)>0 then
   print("yes");
else
   print("no");
fi;

May be because 89 is prime. Should I replace my if with is for this check? 

interface(version)
Standard Worksheet Interface, Maple 2020.1, Windows 10, July 30 

   2020 Build ID 1482634

Physics:-Version()
The "Physics Updates" version in the MapleCloud is 867 and is 

   the same as the version installed in this computer, created 

   2020, November 12, 9:14 hours Pacific Time.

The uploaded worksheet contains a copy of figure of a pencil from a geometry book, followed by a failed attempt to code Maple to produce the same figure.

The book containing the figure gives no indication of how to code for the figure. Can the figure be produced in Maple?

Respondents will have to establish their own path to DirectSearch.

Pencil.mw

I am a newbie in Maple! I tried both ThermophysicalData and its CoolProp package to find saturation pressure of vapor for given air-water mixture temperature.

I want to calculate water vapor density in air or simply Absolute humidity (kg/m3)

But i can not see any meaningful function or combination of functions/properties in CoolProp to give such output.

P_w in CoolProp, HApropSI takes this as input only that is not usefule either way inpoutput

The rationale is to work from RH and then calculate P_w as output: P_w=RH x P_g where P_g is vapor saturation pressure at the given ambient condition.

From there all world is yours!

You can use ideal gas rules to do everything. But i cant use CoolProp to calculate the ABsolute humidty for given RH and ambient condition.

Note that clearly i can calculate all these from hand calculation as well as approximation formuale of Clausius-Clapeyron equation. But i wanted to do in Maple with its packages.

Any help is appreciated!?

Regards

Sina

Dear there,

I want to create a new package. 

Goal of the package:

I have two functions psi(n,m,x) and w(n,x).

These functions are defined differently in case A, and in case B. 

In my future works,

I want to use the functions psi(n,m,x) and w(n,x) in ONE (same) worksheet by calling the package.

Case A;

 K:=2^(k-1):
with(orthopoly): 
psi:=(n,m,x)->piecewise((n-1)/K <= x and x <= n/K,
(sqrt((m+1/2)*2^k))*LegendreP(m,2^k*x-2*n+1), 0);   
w:=(n,x)->1;  
 

Case B;

K:=2^(k-1):
with(orthopoly):
unprotect(gamma):
h:=(m,epsilon,gamma)->2^(epsilon+gamma+1)*GAMMA(epsilon+m+1)*GAMMA(gamma+m+1)/((2*m+1+epsilon+gamma)*m!*GAMMA(epsilon+gamma+1));


psi:=(n,m,x)->piecewise((n-1)/K <= x and x <= n/K,  2^(k/2) *h(m,epsilon,gamma)*simplify(JacobiP(m,epsilon,gamma,2^(k)*x-2*n+1)), 0); 
  

w:=(n,x)->(1-x)^(epsilon)*(1+x)^gamma; 

How can we achieve this in the simplest way?

MY TRY: (Please click to download the code.mw)

test:=module()
export functionA,functionB;
 option package;


######################################################
functionA:=proc(k,M) local K,h,psi,w; 
K:=2^(k-1):
with(orthopoly): 
psi:=(n,m,x)->piecewise((n-1)/K <= x and x <= n/K,
(sqrt((m+1/2)*2^k))*LegendreP(m,2^k*x-2*n+1), 0);   
w:=(n,x)->1;   
return psi(n,m,x) ,w:
end proc:
######################################################


functionB:=proc(k,M,epsilon,gamma) local K,h,psi,w; 
K:=2^(k-1):
with(orthopoly):
unprotect(gamma):
h:=(m,epsilon,gamma)->2^(epsilon+gamma+1)*GAMMA(epsilon+m+1)*GAMMA(gamma+m+1)/((2*m+1+epsilon+gamma)*m!*GAMMA(epsilon+gamma+1));


psi:=(n,m,x)->piecewise((n-1)/K <= x and x <= n/K,  2^(k/2) *h(m,epsilon,gamma)*simplify(JacobiP(m,epsilon,gamma,2^(k)*x-2*n+1)), 0); 
  

w:=(n,x)->(1-x)^(epsilon)*(1+x)^gamma;   
return psi(n,m,x),w(n,x):
end proc:
######################################################

end module;


savelib(test):


# FOR EXAMPLE
restart:
with(test);

#For k=2,M=3 in FunctionA, let's calculate values of "Psi(2)" and "w(2,x)"
k:=2:
M:=3:
K:=2^(k-1):
N:=K*M:
(psi,w):=functionA(2,3):
psi:=(n,m,x)->psi; 
w:=(n,x)->w;
unprotect(Psi):
Psi:=x->Array([seq(seq(psi(i,j,x),j=0..M-1),i=1..K)] )^+:
Psi(2);
w(2,x);


#Now, let's calculate values of "Psi(2)" and "w(2,x)" For  k=3,M=4, epsilon=1, gamma=2 in FunctionA 

 (psi,w):=functionB(3,4,1,2):
Psi(2);
w(2,x);

restart;
deq1 := diff(u(x, y), x) - diff(u(x, y), y$2) = exp(x+y);
                              /  2         \             
              / d         \   | d          |             
      deq1 := |--- u(x, y)| - |---- u(x, y)| = exp(x + y)
              \ dx        /   |   2        |             
                              \ dy         /             

deq2 := diff(u(x, y), x) - diff(u(x, y), y$2) = exp(1)^(x+y);
                            /  2         \                  
            / d         \   | d          |           (x + y)
    deq2 := |--- u(x, y)| - |---- u(x, y)| = (exp(1))       
            \ dx        /   |   2        |                  
                            \ dy         /                  

pdsolve(deq1, u(x,y));  ### no result
pdsolve(deq2, u(x,y));
                        /                                        
                        |                                        
PDESolStrucApplyFunction|uApplyFunction(x,y)=_F1ApplyFunction(x)
                        \                                        

                        1
  _F2ApplyFunction(y) - -
                        2

                       x+y                                                                                   
  (expApplyFunction(1))    (_C1 expApplyFunction(uminus0y)+_C2 expApplyFunction(y)+_C3 expApplyFunction(y) y)
  -----------------------------------------------------------------------------------------------------------
                                            _C3 expApplyFunction(y)                                          

  ,[{diffApplyFunction(_F1ApplyFunction(x),x)=_c[1] _F1

  ApplyFunction(x),diffApplyFunction(diffApplyFunction(_F2

                                                    \
                                                    |
  ApplyFunction(y),y),y)=_c[1] _F2ApplyFunction(y)}]|
                                                    /

No solution appears when the differential equation is expressed in standard form, but when exp(x + y) is converted to

exp(1)^(x + y) the correct solution appears.

I want to create a 2D and 3D graph of the following question. Evaluate F xy+y+z along the curve r(t)=2ti+tj+(2-2t)k, 0<=t<=1 I found the line integral to be 13/2. I am just stuck on how to graph this in 2D and 3D.

Thank you all in advance! I enjoy learning all the new tricks in Maple from you all.

Hello

I am not familiar with the use of notsero in SolveTools:-PolynomialSystem. Is there any special syntax to use it?  In the following example, the trivial solution {x=0,y=0} is to be eliminated.  

SolveTools:-PolynomialSystem({x*(x^2 - 2), y*(y^2 - 2)}, {x, y},explicit=true)

If I issue the command

SolveTools:-PolynomialSystem({x*(x^2 - 2), y*(y^2 - 2)}, {x, y},{x,y},explicit=true)

all roots with either x=0 or y=0 are eliminated.  

Can netzero be used to eliminate only the trivial solution?  

Many thanks

I'm trying to compute the numerical solution for a PDE using the numerical solution of a first-order ODE. I looked at the INTEGRATE keyword of the pdsolve function, but I'm not sure how to use it. Can someone show an example of how to use this keyword?

Hello

I have a funtion defined as 

a := diff(u*ln(m__o/(-q*t + m__o)) - g*t, t)

where m_0, q, g, and u are constants with dimensions. T is the variable and has dimensions as well. I need to print out columns of this function and other similar functions, v and h, in 4 seconds intervals of t. So what I have is this:

for i from -4 by 4 to 80 do
    if i = -4 then printf("%12s %18s %15s %15s \n", "time", "acceleration", "velocity", "altitude"); else printf("%10d %c %10.2f  %s %10.2f  %s %10.2f  %s \n", i, "s", eval(a, t = i), "ft/s^2", eval(v, t = i), "ft/s", eval(h, t = i), "mi"); end if;
end do

this works perfectly fine until I assign units to the constants and t. Then I get the error: Error, (in fprintf) number expected for floating point format. 

Then I also need to plot a v and h against t. Seems like plot doesn't work either with units.

So what do i do?

Thanks

Hi, 

Whenever I open Maple 2020 and type one single letter or number (doesn't matter) Maple 2020 will "freeze" and load forever (i have had it open for a long time, just watching that f**king blue circle spin...

I have tried reinstalling, repairing, running as admin, and changing the compatibility mode, still, nothing works:(

I run Maple 2020 as a Student with WithGym

Pc specs:

Intel i5-10300h 2.6 ghz

Geforce 1660 ti 6gb

Windows 10 x64

Hi,

I don't speak well in english but I 'll try

I can't print a matrix multiplication without maplke simplify it

i want 

A*b=x

so 

|1 2 3|     |x|        |1|

|4 5 6|  * |y|    =   |2|

|7 8 9|     |z|        |3|

but maple simplify A*x

so i have something like

|1x 2y 3z|            |1|

|4x 5y 6z|       =   |2|

|7x 8y 9z|            |3|

Thank a lot.