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Do I really get all values from this Roo...

C_R 2822 Maple
rootof allvalues
July 06 2024
1 4

I was about to verify two solutions of dsolve from here but could not find an agreement for negative values. This makes me wonder if all values are computed.

There is also a different behaviour that I do not understand when allvalues is given a RootOf expression or an equation containing a RootOf expression.
 

dsolve without method

> 

ode:=diff(y(x), x) = (3*x - y(x) + 1)/(3*y(x) - x + 5);
ic:=y(0)=0;
dsolve({ode,ic});
plot(rhs(%),x=-10..10,numpoints=10);
evalf(subs(x=3,%%));
evalf(subs(x=-3,%%%));

diff(y(x), x) = (3*x-y(x)+1)/(3*y(x)-x+5)

  

y(0) = 0

  

y(x) = -(-(1/36)*(x+1)^2*((-324+12*(96*x^3+288*x^2+288*x+825)^(1/2))^(2/3)-24*x-24)^2/(-324+12*(96*x^3+288*x^2+288*x+825)^(1/2))^(2/3)-x^3-x^2+x+1)/(x+1)^2

  

 

y(3) = 2.135964164

  

y(-3) = -2.302775638+0.4883358175e-9*I

 (1)

dsolve with a particular method

> 

sol:=dsolve([ode,ic],[dAlembert]);
odetest(sol,[ode,ic]);

y(x) = RootOf(-6*((x+_Z+3)/(5+3*_Z-x))^(2/3)*(-4*(-x+_Z+1)/(5+3*_Z-x))^(1/3)*_Z+2*((x+_Z+3)/(5+3*_Z-x))^(2/3)*(-4*(-x+_Z+1)/(5+3*_Z-x))^(1/3)*x+2*(-4)^(1/3)*3^(2/3)-10*((x+_Z+3)/(5+3*_Z-x))^(2/3)*(-4*(-x+_Z+1)/(5+3*_Z-x))^(1/3))

  

[0, 0]

 (2)

Since allvalues fails on this expression for real valued x, rational and integer values are tried for punctual comaprision

> 

subs(x=3,sol);
allvalues(%);
evalf(%)

y(3) = RootOf(-6*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)*_Z-4*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)+2*(-4)^(1/3)*3^(2/3))

  

y(3) = (6873/256)*(-(4/6873)*(20994724+82476*6873^(1/2))^(1/3)-(128/3)/(20994724+82476*6873^(1/2))^(1/3)+1/3-((1/2)*I)*3^(1/2)*((8/6873)*(20994724+82476*6873^(1/2))^(1/3)-(256/3)/(20994724+82476*6873^(1/2))^(1/3)))^2+(1/96)*(20994724+82476*6873^(1/2))^(1/3)+(2291/3)/(20994724+82476*6873^(1/2))^(1/3)-8947/768+((2291/256)*I)*3^(1/2)*((8/6873)*(20994724+82476*6873^(1/2))^(1/3)-(256/3)/(20994724+82476*6873^(1/2))^(1/3)), y(3) = (6873/256)*((8/6873)*(20994724+82476*6873^(1/2))^(1/3)+(256/3)/(20994724+82476*6873^(1/2))^(1/3)+1/3)^2-(1/48)*(20994724+82476*6873^(1/2))^(1/3)-(4582/3)/(20994724+82476*6873^(1/2))^(1/3)-8947/768, y(3) = (6873/256)*((8/6873)*(20994724+82476*6873^(1/2))^(1/3)+(256/3)/(20994724+82476*6873^(1/2))^(1/3)+1/3)^2-(1/48)*(20994724+82476*6873^(1/2))^(1/3)-(4582/3)/(20994724+82476*6873^(1/2))^(1/3)-8947/768

  

y(3) = -6.067982077+1.049560864*I, y(3) = 2.13596417, y(3) = 2.13596417

 (3)

Two roots match the dsolve solution without method. However doing the same only on the right hand side produces different output. For some reason allvalues produces 3 RootOf expressions with a numerical root selector.

> 

subs(x=3,rhs(sol));
allvalues(%);
evalf(%)

RootOf(-6*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)*_Z-4*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)+2*(-4)^(1/3)*3^(2/3))

  

RootOf((3*I)*3^(1/6)*2^(2/3)+2^(2/3)*3^(2/3)-6*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)*_Z-4*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3), -6.067982082+1.049560860*I), RootOf((3*I)*3^(1/6)*2^(2/3)+2^(2/3)*3^(2/3)-6*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)*_Z-4*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3), 2.135964164), RootOf((3*I)*3^(1/6)*2^(2/3)+2^(2/3)*3^(2/3)-6*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)*_Z-4*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3), 2.135964164-0.*I)

  

-6.067982082+1.049560860*I, 2.135964164, -6.067982082+1.049560860*I

 (4)

Why this change?
Now the same with a negative value. Now the root does not match the solution of the dsolve call without method.

> 

subs(x=-3,sol);
allvalues(%);
evalf(%)

y(-3) = RootOf(-6*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)*_Z-16*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)+2*(-4)^(1/3)*3^(2/3))

  

y(-3) = -1/2+(1/2)*13^(1/2)

  

y(-3) = 1.302775638

 (5)
> 

subs(x = -3, rhs(sol));
allvalues(%);
evalf(%);

RootOf(-6*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)*_Z-16*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)+2*(-4)^(1/3)*3^(2/3))

  

RootOf((3*I)*3^(1/6)*2^(2/3)-6*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)*_Z+2^(2/3)*3^(2/3)-16*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3), 1.302775638+0.*I)

  

1.302775638

 (6)
> 

NULL

 

NULL


 

Download allvalues.mw

Why does the interface command performs ...

C_R 2822 Maple 2024
interface typesetting
June 28 2024
0 3

Maple formats output depending on typesetting options "extened" and "standard" for the GUI (or interface). An example taken from

restart;
ts_standard:=proc(k::anything)
     interface(typesetting=standard):
     print(k);
     interface(typesetting=extended): 
     NULL;
end proc:
k:=3/8*ln(55/52)+sin(x)+3/4*exp(x);
                    3   /55\            3       
               k := - ln|--| + sin(x) + - exp(x)
                    8   \52/            4       

ts_standard(k);

Why is the input two times returned and why one time as a list?
Somehow the first interface statement is responsible for that.

I am only interested in the reformated input inside the list.
Is it possible to fix the code?

Other observation with typesetting=standard:

restart;
interface(typesetting=standard);
expr:=cos(x)^2;
((x->x)=combine[trig])(expr);
                      

((x->x)=combine[trig])(expr);#subsequent call
                          2   1            1
                    cos(x)  = - cos(2 x) + -
                              2            2

(with Maple 2024.1 this only accurs in Math-1D)
but

restart;
expr:=cos(x)^2;
interface(typesetting=standard);
((x->x)=combine[trig])(expr);
                                      2
                        expr := cos(x) 

                            extended

                          2   1            1
                    cos(x)  = - cos(2 x) + -
                              2            2

Interrupting an operation: What does it ...

C_R 2822 Maple
interrupt gui
June 25 2024
0 3

GUI state after interupting with :

After switching to untitled 17 and back to test_timeout:

Sometimes it is necessary to switch back and forth twice.

Does this mean that the kernel did not receive the interupt?

Browse Matrix: Why is the legend formate...

C_R 2822 Maple
matrix legend
June 22 2024
0 6

For the legend in the image below I would have expected a black image and not a white

 

 

How to test a Maple process for thread s...

C_R 2822 Maple
parallel multithreading
June 18 2024
1 2

I was wondering if Maple could be setup in a way that no parallel processing is performed (as on a single core)?

I know, it's a poor way to test an algorithim/method for thread safety (i.e. deterministic behaviour). But it is better than nothing.

Are there other ways to test for thread safety?

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