janhardo

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These are questions asked by janhardo

Well , honestly I can't make sense of how to do this.

Interactive can be done step by step , but now generalize via a procedure , but can't get a handle on it
How to get the right procedure ?

"maple.ini in users"

(1)

NULL

" restart: with(plots):with(DEtools):with(Student[ODEs]):infolevel[Student]:=3 ;"

"maple.ini in users"

 

3

(2)

DV := y(x)*(diff(y(x), x)) = exp(x)

y(x)*(diff(y(x), x)) = exp(x)

(3)

opl_1 := dsolve({DV, RV1}, y(x))

y(x) = (1-2*exp(1)+2*exp(x))^(1/2)

(4)

opl_2 := dsolve({DV, RV2}, y(x))

y(x) = -(1-2*exp(1)+2*exp(x))^(1/2)

(5)

opl := plot({rhs(opl_1), rhs(opl_2)}, x = 0 .. 5, y = -10 .. 10, thickness = 3)

lijnelement := dfieldplot(DV, y(x), x = 0 .. 5, y = -10 .. 10, title = "lijnelementveld met intergaalkromme door (1,1)(1,-1)")

display({opl, lijnelement})

 

NULL

" restart: with(plots):with(DEtools):with(Student[ODEs]):infolevel[Student]:=3 ;"

"maple.ini in users"

 

3

(6)

NULL

DV, RV1, RV2

y(x)*(diff(y(x), x)) = exp(x), y(1) = 1, y(1) = -1

(7)

``

NULL

NULL

"restart: with(plots):with(DEtools):with(Student[ODEs]):infolevel[Student]:=3 ; "

"maple.ini in users"

 

3

(8)

DVplot:=proc(DVA,RV1A,RV2A)
          local DV;RV1;RV2;opl_1;opl_2;opl;lijnelement;
          DV:
          RV1:
          RV2:
          opl_1 := dsolve({DV, RV1}, y(x)):
          opl_2 := dsolve({DV, RV2}, y(x)):
          opl:= plot({rhs(opl_1), rhs(opl_2)}, x = 0 .. 5, y = -10 .. 10, thickness = 3):
          lijnelement:=dfieldplot(DV, y(x), x = 0 .. 5, y = -10 .. 10, title = "lijnelementveld met                intergaalkromme door (1,1)(1,-1)"):
          display({opl, lijnelement});
end proc:

NULL

DVA := y(x)*(diff(y(x), x)) = exp(x)

y(x)*(diff(y(x), x)) = exp(x)

(9)

RV1A := y(1) = 1

y(1) = 1

(10)

RV2A := y(1) = -1

y(1) = -1

(11)

DVplot(DVA, RV1A, RV2A)

Error, (in dsolve) not a system with respect to the unknowns [y(x)]

 
 

NULL

Download DV_plotten-_procedure.mw

I have here a function  
                           "sin(x)/x"

and suppose sin(x)/x = 0 
Can I now use MapleAI to retrieve the correct command for this in Maple..could I?

The intersection points with the x-axis are positive and negative multiples of Pi
I have put these in an ordered list, but Maple gives this:
For x domain = -20...20 
X := {x = Pi}, {x = 2*Pi}, {x = 3*Pi}, {x = 4*Pi}, {x = 5*Pi}, {x = 6*Pi}, {x = -6*Pi}, {x = -5*Pi}, {x = -4*Pi}, {x = -3*Pi}, {x = -2*Pi}, {x = -Pi};

 
X := sort(eval~(x, [X]));
 X := [, -6 Pi, -5 Pi, -4 Pi, -3 Pi, -2 Pi, -Pi, 2 Pi, 3 Pi, 4 Pi, 5 Pi, 6 Pi]


A strange ranking that Maple comes up with ? 

with(NaturalLanguage);
        [Explain, GetCommand, GetMath, Query, RawQuery]



GetCommand("give for Maple solve command all options?");
            "solve(equations, variables, options);"

Explain("give for Maple solve command all options?");

"Maple is a symbolic and numeric computing environment. Its 

   "solve" command is used to find solutions (roots) of a given 

   equation or a system of equations.
  

  There are a number of options (or "parameters") which can be 

   specified in this command to alter its behavior:

  

  1. `Allsolutions`: This option makes Maple to generate all 

   possible solutions of an equation.

  

  2. `Real`: This option only provides the real solutions. If 

   equations do not have real solutions, it will return an 

   empty set.

  

  3. `Positive`: It only includes positive solutions in the 

   output.

  

  4. `explicit`: If specified, Maple attempts to isolate roots 

   and provide an explicit solution for each variable.

  

  5. `assume = real`: This option restrict the solutions to 

   only real numbers.

  

  6. `parametric`: This option allows Maple to write the 

   solutions in a parametric form. 

  

  7. `avoid ={x = a}`: This option makes solve exclude the 

   possibility `x = a` as a solution.

  

  8. `MaxDegree = d`: This option allows you to limit the 

   degree of the polynomial equations to be considered.

  

  9. `maxdepth = d`: This sets a limit on recursive depth to 

   which the computation should go to seek a solution.

  

  10. `multiplicities`: This option reports multiplicity of the 

   roots.

  

  11. `solutions = vars`: This option tells Maple to look for 

   solutions for specific variables.

  

  12. `numeric`: This option makes solve find a numeric 

   solution to the equation.

  

  13. `symbolic`: This option makes solve find a symbolic 

   solution to the equation.

  

  14. `simplify`: This option simplifies the solutions returned 

   by solve.

  

  15. `sqrt`: This option allows square roots in the output.

  

  It is important to note that not all options are suited for 

   use with all types of equations. Also, the "solve" command 

   in Maple can be occasionally limited by the complexity of 

   the equation, and may sometimes fail to find solutions that 

   more specialized software or methods can find."



 

 

I want to have a 14 larger font instead of Times New Roman 12 for the whole worksheet or else a different font later. 
Can't make sense of how this is all organized in Maple 
You would say set a template , but ?

For Mathematica  math software app,there is a plugin to use in chatGPT pro ( paid subscription ) and maybe this can be done for Maple too ? 

Haven't used the plugin for Mathematica yet, am curious about it.
Let me have the AI look at the Riemann Hypothesis :)  
Have a few books on it, but can't get through that math with all those special functions.

How to get a general expression here ?

restart

 

f(s) is the function value  expressed as a integral around s  (singularity)  of a complex function.

f(s) = (int(f(z)/(z-s), z))/(2*Pi*I)

f(s) = -((1/2)*I)*(int(f(z)/(z-s), z))/Pi

(1)

f(s) = int(f(z)/(z - s), z)/((2*Pi)*I):

"(->)"

diff(f(s), s) = -((1/2)*I)*(int(f(z)/(z-s)^2, z))/Pi

(2)

"(->)"

diff(diff(f(s), s), s) = -((1/2)*I)*(int(2*f(z)/(z-s)^3, z))/Pi

(3)

"((ⅆ)^(n))/(ⅆn) f(s)   =  "
                                      

NULL

NULL

                 .......

quote : "Important consequence.

Above it actually says: "If there is a function f(s) that is somewhere analytic, then you can use such an integral as above to make a new function f '(s), which is also analytic there. And from that a new function f '' and so on.
That means something revolutionary for complex numbers:   "

 

================================

Question: how to get the "((ⅆ)^(n))/(ⅆn) f(s)  "?
===============================

Note : again the form of the answers in Maple : Its not possible to force Maple to come up with this form of answer, ex

``  NULL

Download Maple_primes_bvraag_hoger_orde_singulariteit_henk_hofstede.mw

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