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integral of 1/ln(x) in Maple...

nm 11483 Maple 2024
August 11 2024
1 0

How to get Li(x) to display as result of int(1/ln(x),x) in Maple instead of -Ei(1,-ln(x))? 

I'd like to match result of Maple with another software I use and it is also simpler to look at

int(1/ln(x),x)

Now gives

             -Ei(1,-ln(x))

How to make it show  Li(x) instead?

The Maple help page for Li is this

And the other software Li help page is this

I tried simplify in Maple but it does not do anything. How to get Li(x) in Maple for int(1/ln(x),x);  instead of -Ei(1, -ln(y)) ?

Note that 

diff(Li(x),x)

Gives 1/ln(x) so Li(x) is the correct antiderivative.

Here is also the wiki page

I know that Maple's result is correct, I am just asking about the form it is shown. Since Maple has Li(x) function, why not use it for this result?

 

Maple 2024.1

strange new warning from dsolve Warning,...

nm 11483 Maple 2024
ode dsolve differential-equations
August 09 2024
0 4

I do not think I ever saw this warning messages from dsolve. This is _Clairaut first order ode. When adding the option singsol=all in the dsolve call, Maple replies with 

I do not have earlier version of Maple to try as my C: drive died and lost all my Maple's installed versions. I need to to try to install older version of Maple sometime and check.

Is this new warning and why does it show? Is this suppose to happen? 


 

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1782 and is the same as the version installed in this computer, created 2024, August 8, 16:5 hours Pacific Time.`

> 

restart;
> 

ode:=a*(1 + diff(y(x), x)^3)^(1/3) + x*diff(y(x), x) - y(x) = 0;

a*(1+(diff(y(x), x))^3)^(1/3)+x*(diff(y(x), x))-y(x) = 0

> 

dsolve(ode,y(x),singsol=all)

Warning, only 1 systems are considered

Warning, only 1 systems are considered

y(x) = a*(c__1^3+1)^(1/3)+x*c__1

> 

 


 

Download strange_warning_message_from_dsolve.mw

I also noticed these warning messages show up only the first time dsolve is called on this ode.

Calling it again right after, using the same command, the warning messages no longer show up, which is  even more strange.

 

DEplot losses slope line when changing t...

nm 11483 Maple 2024
ode differential-equations deplot
August 08 2024
1 1

I am plotting phase plot of two first order ode's.

I noticed when added +t to one ode, the plot generated losses all the slope fields. Any one knows why and if this is just limitation of DEplot or if there is a way to workaround it. 

THis worksheet has first example showing expected output, then second example where +t was added first ode. Now same code generates plot will all the slope field gone.


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

sys:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t), 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)];
DEtools:-DEplot(sys,[x(t), y(t)],
        t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,
        [[x(0)=1, y(0)=2]],
        labels = [x(t), y(t)],
        linecolor =red,arrowsize = 1.5,axes = boxed,
        color = 'magnitude[legacy]')

[diff(x(t), t)+diff(y(t), t) = x(t)+y(t), 2*(diff(x(t), t))+diff(y(t), t) = 2*x(t)+3*y(t)]

> 

#added +t to the RHS of one ode. Everything else the same.
sys_2:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t)+t, 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)];
DEtools:-DEplot(sys_2,[x(t), y(t)],
        t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,
        [[x(0)=1, y(0)=2]],
        labels = [x(t), y(t)],
        linecolor =red,arrowsize = 1.5,axes = boxed,
        color = 'magnitude[legacy]')

[diff(x(t), t)+diff(y(t), t) = x(t)+y(t)+t, 2*(diff(x(t), t))+diff(y(t), t) = 2*x(t)+3*y(t)]

> 

dsolve([op(sys),x(0)=1, y(0)=2]);

{x(t) = 3*exp(t)-2*exp(-t), y(t) = 2*exp(-t)}

> 

dsolve([op(sys_2),x(0)=1, y(0)=2]);

{x(t) = 4*exp(t)-4*exp(-t)+1-3*t, y(t) = 4*exp(-t)-2+2*t}

> 

 


 

Download strange_DEplot.mw

update

if someone is interested, I found Maple has builtin function to check if system of ode's is autonomous or not. So changed my code to check first. Here is how to check:


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

restart;
> 

sys:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t), 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)];
if DEtools:-autonomous(sys,[x(t),y(t)],t) then
    DEtools:-DEplot(sys,[x(t), y(t)],
        t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,
        [[x(0)=1, y(0)=2]],
        labels = [x(t), y(t)],
        linecolor =red,arrowsize = 1.5,axes = boxed,
        color = 'magnitude[legacy]');
else
  print("WARNING, non-autonomous system. Will not do phase plot");
fi;

[diff(x(t), t)+diff(y(t), t) = x(t)+y(t), 2*(diff(x(t), t))+diff(y(t), t) = 2*x(t)+3*y(t)]

> 

#added +t to the RHS of one ode. Everything else the same.
sys_2:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t)+t, 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)];
if DEtools:-autonomous(sys_2,[x(t),y(t)],t) then
   DEtools:-DEplot(sys_2,[x(t), y(t)],
        t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,
        [[x(0)=1, y(0)=2]],
        labels = [x(t), y(t)],
        linecolor =red,arrowsize = 1.5,axes = boxed,
        color = 'magnitude[legacy]');
else
  print("WARNING, non-autonomous system. Will not do phase plot");
fi;

[diff(x(t), t)+diff(y(t), t) = x(t)+y(t)+t, 2*(diff(x(t), t))+diff(y(t), t) = 2*x(t)+3*y(t)]

"WARNING, non-autonomous system. Will not do phase plot"

> 

 


 

Download strange_DEplot_V2.mw

 

 

 

why DynamicSystems uses GLOBAL user vari...

nm 11483 Maple 2024
dynamicsystems global
August 08 2024
1 0

I found that  DynamicSystems package uses global variable called s

THis makes zero design sense. Why would a package use a global variable that could have been used by a user? 

What is the correct way to prevent this warning message from showing up, as I have no control over what variable can be used in global space.  I also tried to declare s as local to the function that is using the package, but that did not help. Only way was to remove variable from global space before.

Any suggestions?  And why DynamicSystems is even using global symbols in first place?


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

restart;

z

> 

foo:=proc()
 local sv;

 DynamicSystems:-SystemOptions('statevariable'=sv);

end proc;
 

proc () local sv; DynamicSystems:-SystemOptions('statevariable' = sv) end proc

> 

s:="test";
foo();

"test"

Warning, the global variable(s) {s} used by DynamicSystems are assigned values.  They must be unassigned to load DynamicSystems.  DynamicSystems:-SystemOptions may be used to reassign the options that use these variable(s):
  complexfreqvar = s

x

> 

restart;
> 

foo:=proc()
 local sv;
 local s;

 DynamicSystems:-SystemOptions('statevariable'=sv);

end proc;

proc () local sv, s; DynamicSystems:-SystemOptions('statevariable' = sv) end proc

> 

s:="test";
foo();

"test"

Warning, the global variable(s) {s} used by DynamicSystems are assigned values.  They must be unassigned to load DynamicSystems.  DynamicSystems:-SystemOptions may be used to reassign the options that use these variable(s):
  complexfreqvar = s

x

> 

restart;
> 

#warnign goes away when there is no global used  s before the call is made
foo:=proc()
 local sv;
 local s;

 DynamicSystems:-SystemOptions('statevariable'=sv);

end proc;

proc () local sv, s; DynamicSystems:-SystemOptions('statevariable' = sv) end proc

> 

foo();

x

> 

 


 

Download dynamic_systems_uses_gloabl_s.mw

 

labels for plots do not use Typesetting....

nm 11483 Maple 2024
typesetting label deplot
August 07 2024
2 0

For display of plot axes labels, I prefer to use the Typesseting in place so that diff(y(x),x) display as y'(x) (takes less space and looks better also).

It does that in the worksheet. But when using diff(y(x),x) as the Y axis label, the plot still shows diff(y(x),x) and not y'(x).

Is there a way to make plot and DEtools:-DEplot  use the Typesetting in place?   What is the point of using Typesetting if plots generated do not use it?
 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1781 and is the same as the version installed in this computer, created 2024, August 4, 11:27 hours Pacific Time.`

> 

restart;
> 

interface(typesetting = extended)

extended

> 

Typesetting:-Settings(prime=x,'typesetprime'=true); #this says to use y'(x) instead of dy/dx    
#Typesetting:-Suppress(y(x)); # this says to use y' and not y'(x)

x, false

> 

#phase plot for second order ode. Y axis is y'(x) and X axis is y(x)
#uses DynamicsSystems for conversion.
ode := diff(y(x),x$2) = -y(x)-1/2*diff(y(x),x);   
DynamicSystems:-SystemOptions('statevariable'=sv):
DynamicSystems:-SystemOptions('discretefreqvar'=ssv):            
DynamicSystems:-SystemOptions('outputvariable'=sssv):
DynamicSystems:-SystemOptions('continuoustimevar'=ssssv):  

DynamicSystems:-SystemOptions('continuoustimevar'=x):            
sys:=DynamicSystems:-DiffEquation(ode,'outputvariable'=[y(x)]):

sys0:=DynamicSystems:-StateSpace(sys):
eq1:=diff(X1(x),x)=sys0:-a[1,..].Vector([X1(x),X2(x)]):
eq2:=diff(X2(x),x)=sys0:-a[2,..].Vector([X1(x),X2(x)]):

DEtools:-DEplot([eq1,eq2],[X1(x),X2(x)],x=0..100,
            X2=-4..4,X1=-4..4,
            axes=boxed,
            linecolor = red,        
            labels=[y(x),diff(y(x),x)]);
 

diff(diff(y(x), x), x) = -y(x)-(1/2)*(diff(y(x), x))

> 

 


 

Download labels_for_plot_do_not_use_typesetting_maple_2024.mw

 

Notice the label on Y axis above. I'd like that to display as y'(x) as it is in the worksheet.

 

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