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sand15

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I update my answer...

sand15 1249
November 14 2025
0 0

@Math-dashti 

look at it

Is this you are looking for?...

sand15 1249
November 13 2025
0 0

@Math-dashti 

> 

restart; with(plots); f := proc (u, v) options operator, arrow; v*(2*chi*u^2+p) end proc; g := proc (u, v) options operator, arrow; -beta[2]*u^5-2*chi*u*v^2+u*p*k^2-beta[1]*u^3+u*w end proc; equilibria := solve({f(u, v) = 0, g(u, v) = 0}, {u, v}, explicit)
> 

# Find the parameters in f(u, và and g(u, v)

indE := convert( indets({f(u, v) = 0, g(u, v) = 0}, name) minus {u, v}, list)

[chi, k, p, w, beta[1], beta[2]]

 (1)
> 

# Define a function 'Equilibria" whch maps 'indE' to 'equilibria'

Equilibria := unapply({equilibria}, indE):
> 

# Example of use: a change of name

Equilibria(X, k, p, alpha[1], alpha[2], alpha[3])

{{u = 0, v = 0}, {u = -(1/2)*(-(2*alpha[2]+2*(4*k^2*p*alpha[3]+4*alpha[1]*alpha[3]+alpha[2]^2)^(1/2))/alpha[3])^(1/2), v = 0}, {u = (1/2)*(-(2*alpha[2]+2*(4*k^2*p*alpha[3]+4*alpha[1]*alpha[3]+alpha[2]^2)^(1/2))/alpha[3])^(1/2), v = 0}, {u = -(1/2)*2^(1/2)*((-alpha[2]+(4*k^2*p*alpha[3]+4*alpha[1]*alpha[3]+alpha[2]^2)^(1/2))/alpha[3])^(1/2), v = 0}, {u = (1/2)*2^(1/2)*((-alpha[2]+(4*k^2*p*alpha[3]+4*alpha[1]*alpha[3]+alpha[2]^2)^(1/2))/alpha[3])^(1/2), v = 0}, {u = -(1/2)*(-2*X*p)^(1/2)/X, v = -(1/4)*2^(1/2)*(X*(4*X^2*k^2*p+4*X^2*alpha[1]+2*X*p*alpha[2]-p^2*alpha[3]))^(1/2)/X^2}, {u = -(1/2)*(-2*X*p)^(1/2)/X, v = (1/4)*2^(1/2)*(X*(4*X^2*k^2*p+4*X^2*alpha[1]+2*X*p*alpha[2]-p^2*alpha[3]))^(1/2)/X^2}, {u = (1/2)*(-2*X*p)^(1/2)/X, v = -(1/4)*2^(1/2)*(X*(4*X^2*k^2*p+4*X^2*alpha[1]+2*X*p*alpha[2]-p^2*alpha[3]))^(1/2)/X^2}, {u = (1/2)*(-2*X*p)^(1/2)/X, v = (1/4)*2^(1/2)*(X*(4*X^2*k^2*p+4*X^2*alpha[1]+2*X*p*alpha[2]-p^2*alpha[3]))^(1/2)/X^2}}

 (2)
> 

# Example of use: some parameters are numeric

Equilibria(chi, k, p, 1, 3/5, -7)

{{u = 0, v = 0}, {u = -(1/2)*(6/35+(2/7)*(-28*k^2*p-691/25)^(1/2))^(1/2), v = 0}, {u = (1/2)*(6/35+(2/7)*(-28*k^2*p-691/25)^(1/2))^(1/2), v = 0}, {u = -(1/2)*2^(1/2)*(3/35-(1/7)*(-28*k^2*p-691/25)^(1/2))^(1/2), v = 0}, {u = (1/2)*2^(1/2)*(3/35-(1/7)*(-28*k^2*p-691/25)^(1/2))^(1/2), v = 0}, {u = -(1/2)*(-2*chi*p)^(1/2)/chi, v = -(1/4)*2^(1/2)*(chi*(4*chi^2*k^2*p+(6/5)*chi*p+7*p^2+4*chi^2))^(1/2)/chi^2}, {u = -(1/2)*(-2*chi*p)^(1/2)/chi, v = (1/4)*2^(1/2)*(chi*(4*chi^2*k^2*p+(6/5)*chi*p+7*p^2+4*chi^2))^(1/2)/chi^2}, {u = (1/2)*(-2*chi*p)^(1/2)/chi, v = -(1/4)*2^(1/2)*(chi*(4*chi^2*k^2*p+(6/5)*chi*p+7*p^2+4*chi^2))^(1/2)/chi^2}, {u = (1/2)*(-2*chi*p)^(1/2)/chi, v = (1/4)*2^(1/2)*(chi*(4*chi^2*k^2*p+(6/5)*chi*p+7*p^2+4*chi^2))^(1/2)/chi^2}}

 (3)
 

 

Download Is_this_you_are_looking_for.mw

?...

sand15 1249
November 13 2025
0 0

@Math-dashti 

I'm not sure I trully understand what you are saying.
Read carefully this worksheet and let me know if it answers your problem simpler_sand15.mw

No problem...

sand15 1249
November 12 2025
0 0

with Maple 2015, worksheet mode , input display = Maple Notation, output display = 2-D Math Notation

> 

restart
> 

kernelopts(version)

`Maple 2015.2, APPLE UNIVERSAL OSX, Dec 20 2015, Build ID 1097895`

 (1)
> 

with(Units):
> 

d := 10*Unit('cm');
c__w := 0.47;
F__luft := 0.040146*Unit('N');

10*Units:-Unit('cm')

  

.47

  

0.40146e-1*Units:-Unit('N')

 (2)
> 

F__luft = 1/2*rho__luft*A*c__w*v^2;

0.40146e-1*Units:-Unit('N') = .2350000000*rho__luft*A*v^2

 (3)
> 

A := Pi*(d/2)^2

25*Pi*Units:-Unit('cm')^2

 (4)
> 

rho__luft := 1.2*Unit('kg/m^3')

1.2*Units:-Unit(('kg')/('m')^3)

 (5)
> 

under_radical := 2*F__luft/(rho__luft*A*c__w);

under_radical := simplify(under_radical);
 

0.1812605488e-2*Units:-Unit('N')/(Units:-Unit(('kg')/('m')^3)*Units:-Unit('cm')^2)

  

18.12605488*Units:-Unit(('m')^2/('s')^2)

 (6)
> 

v = simplify(surd(under_radical, 2))

v = 4.257470479*Units:-Unit(('m')/('s'))

 (7)
 

 

Download No_problem_with_Maple_2015.mw
 

> 

restart
> 

kernelopts(version)

`Maple 2015.2, APPLE UNIVERSAL OSX, Dec 20 2015, Build ID 1097895`

 (1)
> 

with(Units):
> 

d := 10*Unit('cm');
c__w := 0.47;
F__luft := 0.040146*Unit('N');

10*Units:-Unit('cm')

  

.47

  

0.40146e-1*Units:-Unit('N')

 (2)
> 

F__luft = 1/2*rho__luft*A*c__w*v^2;

0.40146e-1*Units:-Unit('N') = .2350000000*rho__luft*A*v^2

 (3)
> 

A := Pi*(d/2)^2

25*Pi*Units:-Unit('cm')^2

 (4)
> 

rho__luft := 1.2*Unit('kg/m^3')

1.2*Units:-Unit(('kg')/('m')^3)

 (5)
> 

under_radical := 2*F__luft/(rho__luft*A*c__w);

under_radical := simplify(under_radical);
 

0.1812605488e-2*Units:-Unit('N')/(Units:-Unit(('kg')/('m')^3)*Units:-Unit('cm')^2)

  

18.12605488*Units:-Unit(('m')^2/('s')^2)

 (6)
> 

v = simplify(surd(under_radical, 2))

v = 4.257470479*Units:-Unit(('m')/('s'))

 (7)
 

 

Download No_problem_with_Maple_2015.mw

Adjust scales...

sand15 1249
November 12 2025
0 0

@Andiguys 

The things you will have to adjust for future data are pink written in the attached file Scalling_issue_fixsd.mw
.

Explanation...

sand15 1249
November 11 2025
0 0

@acer 

When I posted my answer I have no clue at all about what the OP wanted.
I simply guessed he wanted to identify the regions where some TM dominates the others: so I proposed him this notional inequal plot without knowing if it asked or not its question (what puzzed me by the time was the image he joined at the end if its question).
And doing so I didn't pay attention to the phrase "(TM1, TM2, TM3 are all positive)"

So you're likely right that the conditions TMs > 0 should be included in some inequal plot... which I see you did in your answer.

@acer Thanks for your reply. S...

sand15 1249
November 10 2025
0 0

@acer 

Thanks for your reply. 

See you soon on another thread

Not the same problem as the original one...

sand15 1249
November 10 2025
0 0

@Andiguys 

... implies not the same code to apply.

Indeed in your initial question you had L := something = 0, now you have L := M1=M2 (with M2 <> 0).
So you have to replace the line

A := expand(lhs(L)):

by the line

A := expand(M1-M2):

to be in the same conditions than previously.

Here is your file corrected.mw

Great...

sand15 1249
November 10 2025
0 0

@acer 

I vote up

Thanks...

sand15 1249
November 10 2025
0 0

@acer 

By the way, do you know whether modern Maple versions enable giving an axis a color, and the associated label another one, or yet, enable using attributes 'linestyle' or 'transparency' for an axis?

Hum......

sand15 1249
November 10 2025
0 0

@AHSAN 

As I use Maple 2015 I wasn't capable to find any simple way to add the contour lines to the projected surface.
Maybe more recent versions have such feature?

Meanwhile there is a workaround:
With_Maple_2015.mw



By the way, have a look to the posts  @acer  wrote in the last two years and to the answers he gave to, if I'm not mistaken, quite similar problems.

A suggestion...

sand15 1249
November 10 2025
0 0

@acer 



All_plots_Combined_sand15.mw

About the unit stuff......

sand15 1249
November 09 2025
0 0

@WD0HHU 

You can write all the quantities with the units you are the most at ease with and, before defining your system to solve, convert all of them in SI units.
For instance you can define Mars armospheric density in g/m3 , Mars mass in Kg, distances in Km and convert all of them in [Km, Kg, s].

Thanks for the feedback...

sand15 1249
November 06 2025
0 0

@C_R 

Shouldn't you send a SCR?

Workaround...

sand15 1249
November 05 2025
0 0

This won't answer your question, but using `#mi("&#8240;")` instead fixes the issue.
Don't ask me why...
(I always use this kind of syntax which enables managing font and color.)

> 

kernelopts(version)

`Maple 2015.2, APPLE UNIVERSAL OSX, Dec 20 2015, Build ID 1097895`

 (1)
> 

`&permil;`;
`#mi("&permil;")`

`&permil;`

  

`#mi("&permil;")`

 (2)
> 

`&#x2030;`;
`#mi("&#x2030;")`;

`&#x2030;`

  

`#mi("&#x2030;")`

 (3)
> 

`&#8240;`;
`#mi("&#8240;")`;

`&permil;`

  

`#mi("&permil;")`

 (4)
 

 

Download mi.mw

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