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

Asked by: nm 11353
August 11 2024
1  1

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

Remove the Warning...

Asked by: mehran rajabi 120
2dmath typesetting warning
August 10 2024
0  4

Hi everyone...

How can I remove the warning (Warning, (in anonymous procedure created in Typesetting:-FI) `m` is implicitly declared local
) from this for command in Maple 2024? I know the warning can be ignored but I want to remove it anyway.

for k from 1 to 4 do
    A[k] := Matrix(k, k, (i, j) -> local m; ifelse(i + j < k + 2, add(Y[i - m + j - 1]*binomial(i - 1, m)*(-1)^m, m = 0 .. i - 1), 0));
end do

tnx...

Frozen Maple 2023 document : I cannot input anythi...

Asked by: hexsol 30
August 10 2024
0  3

Hey!

I am having difficulties inputting in text and math mode in my Maple 2023 document. It was working fine in the beginning, but all of a sudden the problem occured. I was restarting maple initially which would temporarily solve the problem, now I cannot input anything after restart. I am doing exam excercises and have been copy/pasting text from a pdf into the document. 

I have tried to install Maple 2024 and open the file but to no avail.  Any help/ pointers would be greatly appreciated.

The attached file -

ml.mw

How to stop truncating?...

Asked by: Nicole Sharp 160
digits
August 10 2024
0  4

How do I stop truncation in Maple 2023?  Everything was working fine yesterday but today all of a sudden all assignments are truncated to only 10 digits.

If:

with(Units) :

a_Terra := 149598023.*Unit(km) :
A_Luna := 0.136 :
L_Sol := 3.75E28*Unit(lm) :
S_sphere := r -> 4*Pi*r^2 :

J_Luna := A_Luna*L_Sol/S_sphere(a_Terra) :

Then:

"" gives ""

but

"" gives ""

"" without "evalf" also provides a truncated number instead of showing the "Pi" for an exact value.  So something is wrong in the assignment settings.

Somehow the settings must have changed for how assignments are stored. The answer is irrational with a factor of "1/Pi" and so should not be truncated for calculations.  "a_Terra" is assigned with 9 significant digits ("" km) which I am wondering if maybe why "evalf" is truncating to 10 digits (though it should round and not truncate in that case) but it wasn't doing this before.

"Tools --> Options --> Precision" hasn't changed is set globally to round screen display to 32 decimal places and to round calculation to 64 significant digits.

strange new warning from dsolve Warning, only 1 sy...

Asked by: nm 11353
ode dsolve differential-equations
August 09 2024
1  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.

 

How to assign values to u[i] so that it can be use...

Asked by: Khair Muhammad Saraz 40
assign loop duplicate-question
August 09 2024
0  2

i am writing the code and unfortunately i am struck in a pb  where i assign initial condition values to u[i] from i 1 to N but when i use them in a loop it is not taking values of u[i] it is just taking value of u[1] only kindly help me in this regard i am attaching my file here.

automatic_differentiation.mw
 

> 

restart
> 

v := 1; a := 2; t := 0.1e-2; dt := 0.1e-3; N := 40; h := 1/40; K := 4
> 

NULL
> 

NULL
> 

for i from 0 to N do x[i] := i*h end do
> 

x[5]

1/8

 (1)
> 

initial_condition := []; for i to N do initial_condition := [op(initial_condition), evalf(2*v*Pi*sin(Pi*x[i])/(a+cos(Pi*x[i])))] end do
> 

initial_conditions := [.1644933719, .3289856976, .4934717144, .6579375992, .8223563570, .9866828090, 1.150848028, 1.314753051, 1.478261707, 1.641192349, 1.803308276, 1.964306617, 2.123805434, 2.281328760, 2.436289364, 2.587968970, 2.735495794, 2.877819368, 3.013682762, 3.141592654, 3.259788188, 3.366210070, 3.458472370, 3.533840560, 3.589220824, 3.621167336, 3.625916040, 3.599455182, 3.537643690, 3.436388151, 3.291886154, 3.100937330, 2.861312732, 2.572157998, 2.234388242, 1.851015873, 1.427342882, .9709526944, .4914580366, 0.]; u := proc (i) local u_x, u_xx, expr, j; u_x := (1/2)*(u[i+1]-u[i-1])/h; u_xx := (u[i-1]-2*u[i]+u[i+1])/h^2; expr := -alpha*u[i]*u_x+v*u_xx; expr end proc
NULL
> 

NULL
> 

odes := [seq(u(i, [seq(u[j], j = 1 .. N-1)]), i = 1 .. N-1)]
> 

for i to N-1 do assign(o[i] = odes[i]) end do
> 

for i to N-1 do printf("u_%d = %s\n", i, convert(u(i), string)) end do

u_1 = -alpha*u[1]*(20*u[2]-20*u[0])+1600*u[0]-3200*u[1]+1600*u[2]
u_2 = -alpha*u[2]*(20*u[3]-20*u[1])+1600*u[1]-3200*u[2]+1600*u[3]
u_3 = -alpha*u[3]*(20*u[4]-20*u[2])+1600*u[2]-3200*u[3]+1600*u[4]
u_4 = -alpha*u[4]*(20*u[5]-20*u[3])+1600*u[3]-3200*u[4]+1600*u[5]
u_5 = -alpha*u[5]*(20*u[6]-20*u[4])+1600*u[4]-3200*u[5]+1600*u[6]
u_6 = -alpha*u[6]*(20*u[7]-20*u[5])+1600*u[5]-3200*u[6]+1600*u[7]
u_7 = -alpha*u[7]*(20*u[8]-20*u[6])+1600*u[6]-3200*u[7]+1600*u[8]
u_8 = -alpha*u[8]*(20*u[9]-20*u[7])+1600*u[7]-3200*u[8]+1600*u[9]
u_9 = -alpha*u[9]*(20*u[10]-20*u[8])+1600*u[8]-3200*u[9]+1600*u[10]
u_10 = -alpha*u[10]*(20*u[11]-20*u[9])+1600*u[9]-3200*u[10]+1600*u[11]
u_11 = -alpha*u[11]*(20*u[12]-20*u[10])+1600*u[10]-3200*u[11]+1600*u[12]
u_12 = -alpha*u[12]*(20*u[13]-20*u[11])+1600*u[11]-3200*u[12]+1600*u[13]
u_13 = -alpha*u[13]*(20*u[14]-20*u[12])+1600*u[12]-3200*u[13]+1600*u[14]
u_14 = -alpha*u[14]*(20*u[15]-20*u[13])+1600*u[13]-3200*u[14]+1600*u[15]
u_15 = -alpha*u[15]*(20*u[16]-20*u[14])+1600*u[14]-3200*u[15]+1600*u[16]
u_16 = -alpha*u[16]*(20*u[17]-20*u[15])+1600*u[15]-3200*u[16]+1600*u[17]
u_17 = -alpha*u[17]*(20*u[18]-20*u[16])+1600*u[16]-3200*u[17]+1600*u[18]
u_18 = -alpha*u[18]*(20*u[19]-20*u[17])+1600*u[17]-3200*u[18]+1600*u[19]
u_19 = -alpha*u[19]*(20*u[20]-20*u[18])+1600*u[18]-3200*u[19]+1600*u[20]
u_20 = -alpha*u[20]*(20*u[21]-20*u[19])+1600*u[19]-3200*u[20]+1600*u[21]
u_21 = -alpha*u[21]*(20*u[22]-20*u[20])+1600*u[20]-3200*u[21]+1600*u[22]
u_22 = -alpha*u[22]*(20*u[23]-20*u[21])+1600*u[21]-3200*u[22]+1600*u[23]
u_23 = -alpha*u[23]*(20*u[24]-20*u[22])+1600*u[22]-3200*u[23]+1600*u[24]
u_24 = -alpha*u[24]*(20*u[25]-20*u[23])+1600*u[23]-3200*u[24]+1600*u[25]
u_25 = -alpha*u[25]*(20*u[26]-20*u[24])+1600*u[24]-3200*u[25]+1600*u[26]
u_26 = -alpha*u[26]*(20*u[27]-20*u[25])+1600*u[25]-3200*u[26]+1600*u[27]
u_27 = -alpha*u[27]*(20*u[28]-20*u[26])+1600*u[26]-3200*u[27]+1600*u[28]
u_28 = -alpha*u[28]*(20*u[29]-20*u[27])+1600*u[27]-3200*u[28]+1600*u[29]
u_29 = -alpha*u[29]*(20*u[30]-20*u[28])+1600*u[28]-3200*u[29]+1600*u[30]
u_30 = -alpha*u[30]*(20*u[31]-20*u[29])+1600*u[29]-3200*u[30]+1600*u[31]
u_31 = -alpha*u[31]*(20*u[32]-20*u[30])+1600*u[30]-3200*u[31]+1600*u[32]
u_32 = -alpha*u[32]*(20*u[33]-20*u[31])+1600*u[31]-3200*u[32]+1600*u[33]
u_33 = -alpha*u[33]*(20*u[34]-20*u[32])+1600*u[32]-3200*u[33]+1600*u[34]
u_34 = -alpha*u[34]*(20*u[35]-20*u[33])+1600*u[33]-3200*u[34]+1600*u[35]
u_35 = -alpha*u[35]*(20*u[36]-20*u[34])+1600*u[34]-3200*u[35]+1600*u[36]
u_36 = -alpha*u[36]*(20*u[37]-20*u[35])+1600*u[35]-3200*u[36]+1600*u[37]
u_37 = -alpha*u[37]*(20*u[38]-20*u[36])+1600*u[36]-3200*u[37]+1600*u[38]
u_38 = -alpha*u[38]*(20*u[39]-20*u[37])+1600*u[37]-3200*u[38]+1600*u[39]
u_39 = -alpha*u[39]*(20*u[40]-20*u[38])+1600*u[38]-3200*u[39]+1600*u[40]

  
> 

u := table(); for i to N do u[i] := initial_conditions[i] end do

.1644933719

  

.3289856976

  

.4934717144

  

.6579375992

  

.8223563570

  

.9866828090

  

1.150848028

  

1.314753051

  

1.478261707

  

1.641192349

  

1.803308276

  

1.964306617

  

2.123805434

  

2.281328760

  

2.436289364

  

2.587968970

  

2.735495794

  

2.877819368

  

3.013682762

  

3.141592654

  

3.259788188

  

3.366210070

  

3.458472370

  

3.533840560

  

3.589220824

  

3.621167336

  

3.625916040

  

3.599455182

  

3.537643690

  

3.436388151

  

3.291886154

  

3.100937330

  

2.861312732

  

2.572157998

  

2.234388242

  

1.851015873

  

1.427342882

  

.9709526944

  

.4914580366

  

0.

 (2)
> 

for i from 2 to N do T1[i] := (u[i+1]-u[i-1])/(2*h); T2[i] := u[i]*T1[i]; T3[i] := (u[i-1]-2*u[i]+u[i+1])/h^2; u[i][1] := v*T3[i]-T2[i] end do

20*u[3]-3.289867438

  

u[2]*(20*u[3]-3.289867438)

  

263.1893950-3200*u[2]+1600*u[3]

  

263.1893950-3200*u[2]+1600*u[3]-u[2]*(20*u[3]-3.289867438)

  

20*u[4]-20*u[2]

  

u[3]*(20*u[4]-20*u[2])

  

1600*u[2]-3200*u[3]+1600*u[4]

  

1600*u[2]-3200*u[3]+1600*u[4]-u[3]*(20*u[4]-20*u[2])

  

20*u[5]-20*u[3]

  

u[4]*(20*u[5]-20*u[3])

  

1600*u[3]-3200*u[4]+1600*u[5]

  

1600*u[3]-3200*u[4]+1600*u[5]-u[4]*(20*u[5]-20*u[3])

  

20*u[6]-20*u[4]

  

u[5]*(20*u[6]-20*u[4])

  

1600*u[4]-3200*u[5]+1600*u[6]

  

1600*u[4]-3200*u[5]+1600*u[6]-u[5]*(20*u[6]-20*u[4])

  

20*u[7]-20*u[5]

  

u[6]*(20*u[7]-20*u[5])

  

1600*u[5]-3200*u[6]+1600*u[7]

  

1600*u[5]-3200*u[6]+1600*u[7]-u[6]*(20*u[7]-20*u[5])

  

20*u[8]-20*u[6]

  

u[7]*(20*u[8]-20*u[6])

  

1600*u[6]-3200*u[7]+1600*u[8]

  

1600*u[6]-3200*u[7]+1600*u[8]-u[7]*(20*u[8]-20*u[6])

  

20*u[9]-20*u[7]

  

u[8]*(20*u[9]-20*u[7])

  

1600*u[7]-3200*u[8]+1600*u[9]

  

1600*u[7]-3200*u[8]+1600*u[9]-u[8]*(20*u[9]-20*u[7])

  

20*u[10]-20*u[8]

  

u[9]*(20*u[10]-20*u[8])

  

1600*u[8]-3200*u[9]+1600*u[10]

  

1600*u[8]-3200*u[9]+1600*u[10]-u[9]*(20*u[10]-20*u[8])

  

20*u[11]-20*u[9]

  

u[10]*(20*u[11]-20*u[9])

  

1600*u[9]-3200*u[10]+1600*u[11]

  

1600*u[9]-3200*u[10]+1600*u[11]-u[10]*(20*u[11]-20*u[9])

  

20*u[12]-20*u[10]

  

u[11]*(20*u[12]-20*u[10])

  

1600*u[10]-3200*u[11]+1600*u[12]

  

1600*u[10]-3200*u[11]+1600*u[12]-u[11]*(20*u[12]-20*u[10])

  

20*u[13]-20*u[11]

  

u[12]*(20*u[13]-20*u[11])

  

1600*u[11]-3200*u[12]+1600*u[13]

  

1600*u[11]-3200*u[12]+1600*u[13]-u[12]*(20*u[13]-20*u[11])

  

20*u[14]-20*u[12]

  

u[13]*(20*u[14]-20*u[12])

  

1600*u[12]-3200*u[13]+1600*u[14]

  

1600*u[12]-3200*u[13]+1600*u[14]-u[13]*(20*u[14]-20*u[12])

  

20*u[15]-20*u[13]

  

u[14]*(20*u[15]-20*u[13])

  

1600*u[13]-3200*u[14]+1600*u[15]

  

1600*u[13]-3200*u[14]+1600*u[15]-u[14]*(20*u[15]-20*u[13])

  

20*u[16]-20*u[14]

  

u[15]*(20*u[16]-20*u[14])

  

1600*u[14]-3200*u[15]+1600*u[16]

  

1600*u[14]-3200*u[15]+1600*u[16]-u[15]*(20*u[16]-20*u[14])

  

20*u[17]-20*u[15]

  

u[16]*(20*u[17]-20*u[15])

  

1600*u[15]-3200*u[16]+1600*u[17]

  

1600*u[15]-3200*u[16]+1600*u[17]-u[16]*(20*u[17]-20*u[15])

  

20*u[18]-20*u[16]

  

u[17]*(20*u[18]-20*u[16])

  

1600*u[16]-3200*u[17]+1600*u[18]

  

1600*u[16]-3200*u[17]+1600*u[18]-u[17]*(20*u[18]-20*u[16])

  

20*u[19]-20*u[17]

  

u[18]*(20*u[19]-20*u[17])

  

1600*u[17]-3200*u[18]+1600*u[19]

  

1600*u[17]-3200*u[18]+1600*u[19]-u[18]*(20*u[19]-20*u[17])

  

20*u[20]-20*u[18]

  

u[19]*(20*u[20]-20*u[18])

  

1600*u[18]-3200*u[19]+1600*u[20]

  

1600*u[18]-3200*u[19]+1600*u[20]-u[19]*(20*u[20]-20*u[18])

  

20*u[21]-20*u[19]

  

u[20]*(20*u[21]-20*u[19])

  

1600*u[19]-3200*u[20]+1600*u[21]

  

1600*u[19]-3200*u[20]+1600*u[21]-u[20]*(20*u[21]-20*u[19])

  

20*u[22]-20*u[20]

  

u[21]*(20*u[22]-20*u[20])

  

1600*u[20]-3200*u[21]+1600*u[22]

  

1600*u[20]-3200*u[21]+1600*u[22]-u[21]*(20*u[22]-20*u[20])

  

20*u[23]-20*u[21]

  

u[22]*(20*u[23]-20*u[21])

  

1600*u[21]-3200*u[22]+1600*u[23]

  

1600*u[21]-3200*u[22]+1600*u[23]-u[22]*(20*u[23]-20*u[21])

  

20*u[24]-20*u[22]

  

u[23]*(20*u[24]-20*u[22])

  

1600*u[22]-3200*u[23]+1600*u[24]

  

1600*u[22]-3200*u[23]+1600*u[24]-u[23]*(20*u[24]-20*u[22])

  

20*u[25]-20*u[23]

  

u[24]*(20*u[25]-20*u[23])

  

1600*u[23]-3200*u[24]+1600*u[25]

  

1600*u[23]-3200*u[24]+1600*u[25]-u[24]*(20*u[25]-20*u[23])

  

20*u[26]-20*u[24]

  

u[25]*(20*u[26]-20*u[24])

  

1600*u[24]-3200*u[25]+1600*u[26]

  

1600*u[24]-3200*u[25]+1600*u[26]-u[25]*(20*u[26]-20*u[24])

  

20*u[27]-20*u[25]

  

u[26]*(20*u[27]-20*u[25])

  

1600*u[25]-3200*u[26]+1600*u[27]

  

1600*u[25]-3200*u[26]+1600*u[27]-u[26]*(20*u[27]-20*u[25])

  

20*u[28]-20*u[26]

  

u[27]*(20*u[28]-20*u[26])

  

1600*u[26]-3200*u[27]+1600*u[28]

  

1600*u[26]-3200*u[27]+1600*u[28]-u[27]*(20*u[28]-20*u[26])

  

20*u[29]-20*u[27]

  

u[28]*(20*u[29]-20*u[27])

  

1600*u[27]-3200*u[28]+1600*u[29]

  

1600*u[27]-3200*u[28]+1600*u[29]-u[28]*(20*u[29]-20*u[27])

  

20*u[30]-20*u[28]

  

u[29]*(20*u[30]-20*u[28])

  

1600*u[28]-3200*u[29]+1600*u[30]

  

1600*u[28]-3200*u[29]+1600*u[30]-u[29]*(20*u[30]-20*u[28])

  

20*u[31]-20*u[29]

  

u[30]*(20*u[31]-20*u[29])

  

1600*u[29]-3200*u[30]+1600*u[31]

  

1600*u[29]-3200*u[30]+1600*u[31]-u[30]*(20*u[31]-20*u[29])

  

20*u[32]-20*u[30]

  

u[31]*(20*u[32]-20*u[30])

  

1600*u[30]-3200*u[31]+1600*u[32]

  

1600*u[30]-3200*u[31]+1600*u[32]-u[31]*(20*u[32]-20*u[30])

  

20*u[33]-20*u[31]

  

u[32]*(20*u[33]-20*u[31])

  

1600*u[31]-3200*u[32]+1600*u[33]

  

1600*u[31]-3200*u[32]+1600*u[33]-u[32]*(20*u[33]-20*u[31])

  

20*u[34]-20*u[32]

  

u[33]*(20*u[34]-20*u[32])

  

1600*u[32]-3200*u[33]+1600*u[34]

  

1600*u[32]-3200*u[33]+1600*u[34]-u[33]*(20*u[34]-20*u[32])

  

20*u[35]-20*u[33]

  

u[34]*(20*u[35]-20*u[33])

  

1600*u[33]-3200*u[34]+1600*u[35]

  

1600*u[33]-3200*u[34]+1600*u[35]-u[34]*(20*u[35]-20*u[33])

  

20*u[36]-20*u[34]

  

u[35]*(20*u[36]-20*u[34])

  

1600*u[34]-3200*u[35]+1600*u[36]

  

1600*u[34]-3200*u[35]+1600*u[36]-u[35]*(20*u[36]-20*u[34])

  

20*u[37]-20*u[35]

  

u[36]*(20*u[37]-20*u[35])

  

1600*u[35]-3200*u[36]+1600*u[37]

  

1600*u[35]-3200*u[36]+1600*u[37]-u[36]*(20*u[37]-20*u[35])

  

20*u[38]-20*u[36]

  

u[37]*(20*u[38]-20*u[36])

  

1600*u[36]-3200*u[37]+1600*u[38]

  

1600*u[36]-3200*u[37]+1600*u[38]-u[37]*(20*u[38]-20*u[36])

  

20*u[39]-20*u[37]

  

u[38]*(20*u[39]-20*u[37])

  

1600*u[37]-3200*u[38]+1600*u[39]

  

1600*u[37]-3200*u[38]+1600*u[39]-u[38]*(20*u[39]-20*u[37])

  

20*u[40]-20*u[38]

  

u[39]*(20*u[40]-20*u[38])

  

1600*u[38]-3200*u[39]+1600*u[40]

  

1600*u[38]-3200*u[39]+1600*u[40]-u[39]*(20*u[40]-20*u[38])

  

20*u[41]-20*u[39]

  

u[40]*(20*u[41]-20*u[39])

  

1600*u[39]-3200*u[40]+1600*u[41]

  

1600*u[39]-3200*u[40]+1600*u[41]-u[40]*(20*u[41]-20*u[39])

 (3)
> 

u[1]

.1644933719

 (4)
> 

u[2]

u[2]

 (5)
 

NULL

Download automatic_differentiation.mw

Function tan and FunctionAdvisor....

Asked by: Christian Wolinski 1650
August 09 2024
2  5

Why is this sum form for tan(x) not reported by FunctionAdvisor?
(sum = ''sum'')(-2/(2*Pi*n+Pi+2*x)-2/(-2*Pi*n-Pi+2*x), n = 0 .. infinity);
FunctionAdvisor(tan);

Function of a function: expressing derivatives of ...

Asked by: MaPal93 175
differentiation implicit
August 09 2024
1  10

Function X__2(y1,y2) is a function of X__1(y1,y2). How do I express (implicitly) d(X__2)/d(y1) and d(X__2)/d(y2) in terms of d(X__1)/d(y1) and d(X__1)/d(y2) and perhaps of X__1 and X__2 themselves?

I illustrate what I mean with an example for X__1(y1,y2), where d(X__1)/d(y1) and d(X__1)/d(y2) are written in a relatively compact form in terms of X__1 itself:
 

> 

restart;
> 

X1 := RootOf((8*y__1^14 + 32*y__1^12*y__2^2 + 48*y__1^10*y__2^4 + 32*y__1^8*y__2^6 + 8*y__1^6*y__2^8 + 16*y__1^12 + 80*y__1^10*y__2^2 + 160*y__1^8*y__2^4 + 160*y__1^6*y__2^6 + 80*y__1^4*y__2^8 + 16*y__1^2*y__2^10)*_Z^10 + (40*y__1^13*y__2^2 + 120*y__1^11*y__2^4 + 120*y__1^9*y__2^6 + 40*y__1^7*y__2^8 + 16*y__1^13 + 176*y__1^11*y__2^2 + 544*y__1^9*y__2^4 + 736*y__1^7*y__2^6 + 464*y__1^5*y__2^8 + 112*y__1^3*y__2^10)*_Z^9 + (84*y__1^12*y__2^4 + 168*y__1^10*y__2^6 + 84*y__1^8*y__2^8 - 20*y__1^14 + 28*y__1^12*y__2^2 + 552*y__1^10*y__2^4 + 1288*y__1^8*y__2^6 + 1132*y__1^6*y__2^8 + 348*y__1^4*y__2^10 - 48*y__1^12 - 192*y__1^10*y__2^2 - 272*y__1^8*y__2^4 - 128*y__1^6*y__2^6 + 48*y__1^4*y__2^8 + 64*y__1^2*y__2^10 + 16*y__2^12)*_Z^8 + (88*y__1^11*y__2^6 + 88*y__1^9*y__2^8 - 80*y__1^13*y__2^2 + 56*y__1^11*y__2^4 + 960*y__1^9*y__2^6 + 1432*y__1^7*y__2^8 + 608*y__1^5*y__2^10 - 48*y__1^13 - 416*y__1^11*y__2^2 - 944*y__1^9*y__2^4 - 736*y__1^7*y__2^6 + 16*y__1^5*y__2^8 + 256*y__1^3*y__2^10 + 80*y__1*y__2^12)*_Z^7 + (40*y__1^10*y__2^8 - 128*y__1^12*y__2^4 + 168*y__1^10*y__2^6 + 928*y__1^8*y__2^8 + 632*y__1^6*y__2^10 + 12*y__1^14 - 192*y__1^12*y__2^2 - 1084*y__1^10*y__2^4 - 1472*y__1^8*y__2^6 - 340*y__1^6*y__2^8 + 432*y__1^4*y__2^10 + 180*y__1^2*y__2^12 + 48*y__1^12 + 144*y__1^10*y__2^2 + 112*y__1^8*y__2^4 - 48*y__1^6*y__2^6 - 96*y__1^4*y__2^8 - 32*y__1^2*y__2^10)*_Z^6 + (-92*y__1^11*y__2^6 + 228*y__1^9*y__2^8 + 368*y__1^7*y__2^10 + 32*y__1^13*y__2^2 - 384*y__1^11*y__2^4 - 1272*y__1^9*y__2^6 - 704*y__1^7*y__2^8 + 376*y__1^5*y__2^10 + 224*y__1^3*y__2^12 + 48*y__1^13 + 304*y__1^11*y__2^2 + 432*y__1^9*y__2^4 + 16*y__1^7*y__2^6 - 288*y__1^5*y__2^8 - 128*y__1^3*y__2^10)*_Z^5 + (-24*y__1^10*y__2^8 + 96*y__1^8*y__2^10 + 24*y__1^12*y__2^4 - 412*y__1^10*y__2^6 - 576*y__1^8*y__2^8 + 164*y__1^6*y__2^10 + 160*y__1^4*y__2^12 + 4*y__1^14 + 172*y__1^12*y__2^2 + 532*y__1^10*y__2^4 + 252*y__1^8*y__2^6 - 328*y__1^6*y__2^8 - 216*y__1^4*y__2^10 - 16*y__1^12 - 32*y__1^10*y__2^2 + 32*y__1^6*y__2^6 + 16*y__1^4*y__2^8)*_Z^4 + (-8*y__1^11*y__2^6 - 192*y__1^9*y__2^8 + 28*y__1^7*y__2^10 + 60*y__1^5*y__2^12 + 16*y__1^13*y__2^2 + 232*y__1^11*y__2^4 + 296*y__1^9*y__2^6 - 168*y__1^7*y__2^8 - 184*y__1^5*y__2^10 - 16*y__1^13 - 64*y__1^11*y__2^2 - 32*y__1^9*y__2^4 + 64*y__1^7*y__2^6 + 48*y__1^5*y__2^8)*_Z^3 + (-15*y__1^10*y__2^8 + 9*y__1^6*y__2^12 + 24*y__1^12*y__2^4 + 116*y__1^10*y__2^6 - 36*y__1^8*y__2^8 - 80*y__1^6*y__2^10 - 4*y__1^14 - 40*y__1^12*y__2^2 - 48*y__1^10*y__2^4 + 40*y__1^8*y__2^6 + 52*y__1^6*y__2^8)*_Z^2 + (12*y__1^11*y__2^6 - 4*y__1^9*y__2^8 - 16*y__1^7*y__2^10 - 8*y__1^13*y__2^2 - 24*y__1^11*y__2^4 + 8*y__1^9*y__2^6 + 24*y__1^7*y__2^8)*_Z - y__1^10*y__2^8 - y__1^8*y__2^10 - 4*y__1^12*y__2^4 + 4*y__1^8*y__2^8):

alias(X__1=X1);

X__2 := -y__1*y__2^2*X__1*(8*X__1^7*y__1^10 + 24*X__1^7*y__1^8*y__2^2 + 24*X__1^7*y__1^6*y__2^4 + 8*X__1^7*y__1^4*y__2^6 + 24*X__1^6*y__1^9*y__2^2 + 48*X__1^6*y__1^7*y__2^4 + 24*X__1^6*y__1^5*y__2^6 + 26*X__1^5*y__1^8*y__2^4 + 26*X__1^5*y__1^6*y__2^6 + 8*X__1^4*y__1^7*y__2^6 + 32*X__1^7*y__1^8 + 128*X__1^7*y__1^6*y__2^2 + 192*X__1^7*y__1^4*y__2^4 + 128*X__1^7*y__1^2*y__2^6 + 32*X__1^7*y__2^8 + 16*X__1^6*y__1^9 + 192*X__1^6*y__1^7*y__2^2 + 480*X__1^6*y__1^5*y__2^4 + 448*X__1^6*y__1^3*y__2^6 + 144*X__1^6*y__1*y__2^8 - 16*X__1^5*y__1^10 + 32*X__1^5*y__1^8*y__2^2 + 392*X__1^5*y__1^6*y__2^4 + 624*X__1^5*y__1^4*y__2^6 + 280*X__1^5*y__1^2*y__2^8 - 36*X__1^4*y__1^9*y__2^2 + 72*X__1^4*y__1^7*y__2^4 + 396*X__1^4*y__1^5*y__2^6 + 288*X__1^4*y__1^3*y__2^8 - 28*X__1^3*y__1^8*y__2^4 + 84*X__1^3*y__1^6*y__2^6 + 156*X__1^3*y__1^4*y__2^8 - 7*X__1^2*y__1^7*y__2^6 + 33*X__1^2*y__1^5*y__2^8 - 64*X__1^5*y__1^8 - 192*X__1^5*y__1^6*y__2^2 - 192*X__1^5*y__1^4*y__2^4 - 64*X__1^5*y__1^2*y__2^6 - 32*X__1^4*y__1^9 - 288*X__1^4*y__1^7*y__2^2 - 480*X__1^4*y__1^5*y__2^4 - 224*X__1^4*y__1^3*y__2^6 + 8*X__1^3*y__1^10 - 88*X__1^3*y__1^8*y__2^2 - 408*X__1^3*y__1^6*y__2^4 - 312*X__1^3*y__1^4*y__2^6 + 12*X__1^2*y__1^9*y__2^2 - 108*X__1^2*y__1^7*y__2^4 - 196*X__1^2*y__1^5*y__2^6 + 4*X__1^2*y__1^3*y__2^8 + 2*X__1*y__1^8*y__2^4 - 46*X__1*y__1^6*y__2^6 + 4*X__1*y__1^4*y__2^8 - y__1^7*y__2^6 + y__1^5*y__2^8 + 32*X__1^3*y__1^8 + 64*X__1^3*y__1^6*y__2^2 + 32*X__1^3*y__1^4*y__2^4 + 16*X__1^2*y__1^9 + 96*X__1^2*y__1^7*y__2^2 + 80*X__1^2*y__1^5*y__2^4 + 32*X__1*y__1^8*y__2^2 + 64*X__1*y__1^6*y__2^4 + 16*y__1^7*y__2^4)/(-8*X__1^7*y__1^11*y__2^2 - 24*X__1^7*y__1^9*y__2^4 - 24*X__1^7*y__1^7*y__2^6 - 8*X__1^7*y__1^5*y__2^8 - 32*X__1^6*y__1^10*y__2^4 - 64*X__1^6*y__1^8*y__2^6 - 32*X__1^6*y__1^6*y__2^8 - 50*X__1^5*y__1^9*y__2^6 - 50*X__1^5*y__1^7*y__2^8 - 28*X__1^4*y__1^8*y__2^8 + 32*X__1^8*y__1^10 + 160*X__1^8*y__1^8*y__2^2 + 320*X__1^8*y__1^6*y__2^4 + 320*X__1^8*y__1^4*y__2^6 + 160*X__1^8*y__1^2*y__2^8 + 32*X__1^8*y__2^10 + 160*X__1^7*y__1^9*y__2^2 + 640*X__1^7*y__1^7*y__2^4 + 960*X__1^7*y__1^5*y__2^6 + 640*X__1^7*y__1^3*y__2^8 + 160*X__1^7*y__1*y__2^10 - 8*X__1^6*y__1^12 - 24*X__1^6*y__1^10*y__2^2 + 328*X__1^6*y__1^8*y__2^4 + 1048*X__1^6*y__1^6*y__2^6 + 1056*X__1^6*y__1^4*y__2^8 + 352*X__1^6*y__1^2*y__2^10 - 24*X__1^5*y__1^11*y__2^2 - 48*X__1^5*y__1^9*y__2^4 + 400*X__1^5*y__1^7*y__2^6 + 848*X__1^5*y__1^5*y__2^8 + 424*X__1^5*y__1^3*y__2^10 - 38*X__1^4*y__1^10*y__2^4 - 54*X__1^4*y__1^8*y__2^6 + 274*X__1^4*y__1^6*y__2^8 + 290*X__1^4*y__1^4*y__2^10 - 44*X__1^3*y__1^9*y__2^6 - 32*X__1^3*y__1^7*y__2^8 + 104*X__1^3*y__1^5*y__2^10 - 27*X__1^2*y__1^8*y__2^8 + 15*X__1^2*y__1^6*y__2^10 - 64*X__1^6*y__1^10 - 256*X__1^6*y__1^8*y__2^2 - 384*X__1^6*y__1^6*y__2^4 - 256*X__1^6*y__1^4*y__2^6 - 64*X__1^6*y__1^2*y__2^8 - 256*X__1^5*y__1^9*y__2^2 - 768*X__1^5*y__1^7*y__2^4 - 768*X__1^5*y__1^5*y__2^6 - 256*X__1^5*y__1^3*y__2^8 + 16*X__1^4*y__1^12 + 32*X__1^4*y__1^10*y__2^2 - 408*X__1^4*y__1^8*y__2^4 - 848*X__1^4*y__1^6*y__2^6 - 424*X__1^4*y__1^4*y__2^8 + 48*X__1^3*y__1^11*y__2^2 + 48*X__1^3*y__1^9*y__2^4 - 352*X__1^3*y__1^7*y__2^6 - 352*X__1^3*y__1^5*y__2^8 + 54*X__1^2*y__1^10*y__2^4 - 150*X__1^2*y__1^6*y__2^8 + 22*X__1*y__1^9*y__2^6 - 30*X__1*y__1^7*y__2^8 - 2*y__1^8*y__2^8 + 32*X__1^4*y__1^10 + 96*X__1^4*y__1^8*y__2^2 + 96*X__1^4*y__1^6*y__2^4 + 32*X__1^4*y__1^4*y__2^6 + 96*X__1^3*y__1^9*y__2^2 + 192*X__1^3*y__1^7*y__2^4 + 96*X__1^3*y__1^5*y__2^6 - 8*X__1^2*y__1^12 - 8*X__1^2*y__1^10*y__2^2 + 104*X__1^2*y__1^8*y__2^4 + 104*X__1^2*y__1^6*y__2^6 - 16*X__1*y__1^11*y__2^2 + 48*X__1*y__1^7*y__2^6 - 8*y__1^10*y__2^4 + 8*y__1^8*y__2^6):


Synthetic representation of derivatives


derivatives for X__1 okay: written in terms of y__1, y__2, and X__1 itself.

> 

derX1_y1 := diff(X1, y__1):
derX1_y2 := diff(X1, y__2):

Diff('X__1(y__1,y__2)', y__1) = collect~(normal(eval(derX1_y1, X1 = 'X__1(y__1,y__2)')), 'X__1(y__1,y__2)');
Diff('X__1(y__1,y__2)', y__2) = collect~(normal(eval(derX1_y2, X1 = 'X__1(y__1,y__2)')), 'X__1(y__1,y__2)');


derivatives for X__2 not okay (X__2 is itself a function of X__1): how do I write them in terms of y__1, y__2, X__1 AND the derivatives for X__1 just found? What's the most compact way to express these two derivatives below?

> 

derX2_y1 := diff(X__2, y__1):
derX2_y2 := diff(X__2, y__2):

Diff('X__2(y__1,y__2)', y__1) = collect~(normal(eval(eval(derX2_y1, derX1_y1='Diff('X__1(y__1,y__2)', y__1)'), X__1 = 'X__1(y__1,y__2)')), 'X__1(y__1,y__2)');
Diff('X__2(y__1,y__2)', y__2) = collect~(normal(eval(derX2_y2, X__1 = 'X__1(y__1,y__2)')), 'X__1(y__1,y__2)');
> 

``

 

Download compact_derivatives.mw


Thank you for the help.

DEplot losses slope line when changing the ode's...

Asked by: nm 11353
ode differential-equations deplot
August 08 2024
2  2

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

 

 

 

fsolve problem with seq...

Asked by: emrantohidikub 15
fsolve
August 08 2024
1  2

Hello everyone

I want to use some limitations in fsolve by using seq command, but I can not achieve to any solution.

Can you help me?

I provided my maple codes here

restart;
f := sin(x[1] + x[2]) - exp(x[1])*x[2] = 0;
g := x[1]^2 - x[2] - 2 = 0;
cond := {seq(x[i] = -1 .. 1, i = 1 .. 2)};

fsolve({f, g}, cond);

why DynamicSystems uses GLOBAL user variables?...

Asked by: nm 11353
dynamicsystems global
August 08 2024
1  1

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

 

How to solve such a system ?...

Asked by: JAMET 425
August 08 2024
0  7

eq1 := x = (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)/((-a + b + c)*(a + b - c)*(a - b + c)*(a + b + c));
eq2 := y = (-a^2 + b^2 + c^2)*(a^2 + b^2 - c^2)/((-a + b + c)*(a + b - c)*(a - b + c)*(a + b + c));
eq3 := z = (-a^2 + b^2 + c^2)*(a^2 - b^2 + c^2)/((-a + b + c)*(a + b - c)*(a - b + c)*(a + b + c));
sol := solve({eq1, eq2, eq3, x + y + z = 1}, {a, b, c}, explicit);
No resolution. To find the Cartesian coordinates from barycentric coordinates;

Slow series summation...

Asked by: Rio 25
performance sum series
August 08 2024
2  6

Hello, I trying to sum up a series which involves several binomial terms, Maple simply gets stuck and give no results. I think I am not being smart to improve Maple performance. Please, see my code below:
 

>n1 := 423; x := 16; n2 := 81; y := 35; s1 := 0.1; b1 := 7; beta1 := 2.1; s2 := 0.1; b2 := 7; beta2 := 2.1;

>A := (h, v) -> Sum(Sum(binomial(n1 - x, j)*binomial(n2 - y, l)*(-1)^(j + l)*GAMMA(s1 + h + 1)*GAMMA(s2 + v + 1)*(-1)^(h + v)*(beta1 - 1)^h*(beta2 - 1)^v/(h!*GAMMA(s1 + 1)*v!*GAMMA(s2 + 1)*(x + b1*s1 + j + b1*h + y + b2*s2 + l + b2*v)*(r + x + b1*s1 + j + b1*v)), j = 0 .. n1 - x), l = 0 .. n2 - y);

>B := (h, v) -> Sum(Sum(binomial(n1 - x, j)*binomial(n2 - y, l)*(-1)^(j + l)*GAMMA(s1 + v + 1)*GAMMA(s2 + h + 1)*(-1)^(h + v)*(beta1 - 1)^v*(beta2 - 1)^h/(v!*GAMMA(s1 + 1)*h!*GAMMA(s2 + 1)*(y + b2*s2 + l + b2*h + x + b1*s1 + j + b1*v)*(y + b2*s2 + l + b2*h - r)), j = 0 .. n1 - x), l = 0 .. n2 - y)

>f := (r, upto) -> sum(sum(A(h, v) + B(h, v), v = 0 .. upto), h = 0 .. upto);

>f(0,30);

Summing up to 30 is very slow, I have left it running over many hours and no result was provided. Could we improve the way it is summing up? thanks in advance.

 

 

 

Why do I have to use expand to combine this expres...

Asked by: C_R 3412
August 08 2024
1  5

My (intutive) interpretation of combine was so far in line with the combine help page

The combine function applies transformations which combine terms in sums,...

For the expression below I have to do the opposite (i.e. expand)

1/2 + cos(2*x)/2
                         1   1         
                         - + - cos(2 x)
                         2   2         

expand(%,trig)
                                  2
                            cos(x)

Why is this and why does the context pannel offer (the ineffective) combine,trig on the first expression but not (the effective) expand,trig?

This cannot be a bug (this trig identity is so elementary) but I cannot make sense of it.

 

labels for plots do not use Typesetting....

Asked by: nm 11353
typesetting label deplot
August 07 2024
1  2

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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