nm

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13 years, 198 days

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These are questions asked by nm

This is just cosmotics, but it looks ugly for me. For some reason Maple converts exp(2*a) to (exp(a))^2 under certain operations such as expand

expr:=exp(2*a);
expand(%);
simplify(%);
expand(%)

.

This happens in worksheet under typesetting level extends or standard.

Any specific reason why Maple likes to rewrite exp(2*a) as (exp(a))^2  and is there a way to tell it not to do that?

ps. it is little more than cosmotic actually, it affects the Latex generated

 

latex(expr)
{\mathrm e}^{2 a}


latex(expand(expr))
\left({\mathrm e}^{a}\right)^{2}

 

Maple 2024 on windows 10

Is this internal error expected? Why does it happen? Reported to Maplesoft just in case.

``

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

restart;

189352

e:= RootOf(csc(_Z));
simplify(e);

RootOf(csc(_Z))

Error, (in simplify/trig/do/1) expression independent of, _Z

e:= RootOf(csc(x));
simplify(e);

RootOf(csc(_Z))

Error, (in simplify/trig/do/1) expression independent of, _Z

 

 

Download simplify_Z_error_maple_2024_march_22_2024.mw

ps. Reported to Maplesoft just in case.

I do not like this feature at all. called Scrollable Matrices:

https://mapleprimes.com/maplesoftblog/224789-Discover-Whats-New-In-Maple-2024

Is there a way to turn it off? 

In Maple 2024 when I display a wide matrix, it no longer wraps around if the worksheet window width was smaller as it did in Maple 2023. I prefer the 2023 behavior.

A:=Matrix(3,4,{(1, 1) = (y(x) = RootOf(-Intat(1/(_a^(3/2)+1),_a = _Z+x)+x+Intat(1/
(_a^(3/2)+1),_a = 0))), (1, 2) = "explicit", (1, 3) = "", (1, 4) = false, (2, 1
) = (y(x) = -1/2+1/2*I*3^(1/2)-x), (2, 2) = "explicit", (2, 3) = "", (2, 4) = 
false, (3, 1) = (x = -2/3*ln(((y(x)+x)^(3/2))^(1/3)+1)+1/3*ln(((y(x)+x)^(3/2))^
(2/3)-((y(x)+x)^(3/2))^(1/3)+1)+2/3*3^(1/2)*arctan(1/3*(2*((y(x)+x)^(3/2))^(1/3
)-1)*3^(1/2))+1/9*3^(1/2)*Pi), (3, 2) = "implicit", (3, 3) = "", (3, 4) = true}
,datatype = anything,storage = rectangular,order = Fortran_order,shape = []);

 

Screen shot on Maple 2023

 

Screen shot on Maple 2024

I looked at Tools->options->Display and Interface but see nothing there to turn it off.

Maple 2024 on windows 10.

Maple gives solutions that do not satisfy the equation. Wondering what do I need to change.  

restart;
n:=3;m:=2;
eqx:=x^(n/m)=a;
maple_sol:=[PDEtools:-Solve(eqx,x)]; #also tried solve()
F:=map(X->eval(eqx,X),maple_sol);
map(X->evalb(X),F);

 

I always verified in Mathematica

Any thought what is going on and what do I need to change in my Maple code to make it give the solution x=a^(2/3) only?  

It is also possible that Mathematica is the one who is skipping the two complex solutions, but then I need to verify these in Maple, and so far I can't. Only the first solution is verified by Maple.

Even simplification with assuming a>0 do not verify these two extra solution given with complex values. I also tried RealDomain package but this also had no effect. I tired assuming real also and tried simplify with symbolic option.

Anything else I should try?

Maple 2024 on windows 10

update

As I said, I tried RealDomain but with PDEtools:-Solve. With solve it works. Is this a bug? worksheet below

35788

restart;

35788

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1701. The version installed in this computer is 1693 created 2024, March 7, 17:27 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

restart;

35788

n:=3;m:=2;
eqx:=x^(n/m)=a;
use RealDomain in (PDEtools:-Solve(eqx,x)) end use;
F:=map(X->eval(eqx,X),[%]);
map(X->evalb(X),F);

3

2

x^(3/2) = a

x = a^(2/3), x = (1/4)*a^(2/3)*(1+I*3^(1/2))^2, x = (1/4)*a^(2/3)*(I*3^(1/2)-1)^2

[a = a, (1/16)*4^(1/2)*(a^(2/3)*(1+I*3^(1/2))^2)^(3/2) = a, (1/16)*4^(1/2)*(a^(2/3)*(I*3^(1/2)-1)^2)^(3/2) = a]

[true, false, false]

restart;

35788

n:=3;m:=2;
eqx:=x^(n/m)=a;
use RealDomain in (solve(eqx,x)) end use;
F:=map(X->eval(eqx,x=X),[%]);
map(X->evalb(X),F);

3

2

x^(3/2) = a

a^(2/3)

[a = a]

[true]

 

 

Download real_domain_solve_vs_PDEtools_Solve.mw

May be someone can come up with a way to simplify this ode solution? I used the option useInt but the solution can be written in much simpler way than Maple gives.  Below is worksheet showing Maple's 2024 solution and my hand solution.

(having trouble uploading worksheet, will try again).


 

144036

ode:=diff(y(x),x)^3=y(x)+x

(diff(y(x), x))^3 = y(x)+x

maple_sol:=dsolve(ode,useInt):
maple_sol:=Vector([maple_sol]);

Vector(3, {(1) = x-Intat(3*_a^2/(_a+1), _a = (y(x)+x)^(1/3))-_C1 = 0, (2) = x-Intat(3*_a^2/(_a+1), _a = -(1/2)*(y(x)+x)^(1/3)-((1/2)*I)*sqrt(3)*(y(x)+x)^(1/3))-_C1 = 0, (3) = x-Intat(3*_a^2/(_a+1), _a = -(1/2)*(y(x)+x)^(1/3)+((1/2)*I)*sqrt(3)*(y(x)+x)^(1/3))-_C1 = 0})

mysol1:= Intat(1/(_a^(1/3) + 1), _a = (y(x) + x))=x+_C1:
mysol2:= Intat(1/( -(-1)^(1/3)*_a^(1/3) + 1), _a = (y(x) + x))=x+_C1:
mysol3:= Intat(1/( (-1)^(2/3)*_a^(1/3) + 1), _a = (y(x) + x))=x+_C1:
mysol:=Vector([mysol1,mysol2,mysol3]);

 

Vector(3, {(1) = Intat(1/(1+_a^(1/3)), _a = y(x)+x) = x+_C1, (2) = Intat(1/(-(-1)^(1/3)*_a^(1/3)+1), _a = y(x)+x) = x+_C1, (3) = Intat(1/((-1)^(2/3)*_a^(1/3)+1), _a = y(x)+x) = x+_C1})

map(X->odetest(X,ode),mysol)

 

Vector(3, {(1) = 0, (2) = 0, (3) = 0})

 


 

Download simpler_solution.mw

I keep losing the edits I do. I post screen shot. Click submit, then find all my changes are lost. Will try one more time and give up:

This is Maple solution

This is implified version

 

Both versions are verified correct by odetest. The question is there is a way to obtain the simpler form from Maple.

 

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