Hey and Thanks for your input.

Download function_evaluation_goes_wrong.mw

Am I doing something wrong?

Hi

I am having trouble in plotting the 3d plot of explicit expressions. Lets say

eq1:=f(z)

eq2:=g(z)

then how can I plot f(z) and g(z) together with z in 3d plot?

Thanks in advance

Regards

Sunit

Can I create a Groebner basis in Maple with system of inequalities and how should I do that?

For example: I have problem with 30 inequlities (all have to be binary {0,1}) and all inequalities are >=1 but if I put

F := [x1+x2+x3-1, x1+x5+x7-1 etc]; and after that I create Groebner basis, I get that system has no solutions, but I know it has. 

Thank you in advance!

in this ODE, with initial conditions, I am trying to verify my solution, but I can't figure how Maple obtained the final answer.  I can obtain same solution, but before using the initial conditions to find the constant of integrations. The problem comes in solving for the constant of integration from initial conditions. I do not know how Maple did it, becuause when I do the normal steps, I get division by zero.

restart;
ode:=diff(y(x),x)=x*ln(y(x)):
ic:=y(1)=1:
sol:=dsolve({ode,ic},y(x));

gives "sol := y(x) = 1"

Now I solve without IC, then try to find _C1 by hand

sol:=dsolve(ode,y(x));

       sol := y(x) = exp(RootOf(x^2+2*Ei(1, -_Z)+2*_C1))

Now used remove_RootOf

sol2:=DEtools:-remove_RootOf(sol);

            sol2 := x^2+2*Ei(1, -ln(y(x)))+2*_C1 = 0

Now I followed the steps I learned at school, which is to plugin y=1 and x=1 in the solution to get an equation to solve for _C1

eq := subs({y(x)=1,x=1},sol2);

            eq := 1+2*Ei(1, -ln(1))+2*_C1 = 0

But Ei(1, -ln(1)) is a division by zero. So can't solve for _C1

solve(eq,_C1);
       Error, (in Ei) numeric exception: division by zero

So how would you solve for _C1 in the above? Or how did the smart Maple do it?

I tried using limits, but that did not help.  I tried using allvalues instead of remove_RootOf, and that did not get rid of RootOf.  Next I tried not to remove RootOf and keep it there to see what happens

sol:=dsolve(ode,y(x));
eq := subs({y(x)=1,x=1},sol);
             eq := 1 = exp(RootOf(1+2*Ei(1, -_Z)+2*_C1))

c1:=solve(eq,_C1, AllSolutions);
              c1 := -1/2-Ei(1, -(2*I)*Pi*_Z1)

subs(_C1=c1,sol);
             y(x) = exp(RootOf(x^2+2*Ei(1, -_Z)-1-2*Ei(1, -(2*I)*Pi*_Z1)))

simplify(%);
            x^2+2*Ei(1, -ln(y(x)))-1-2*Ei(1, -(2*I)*Pi*_Z1) = 0

DEtools:-remove_RootOf(%);
           x^2+2*Ei(1, -ln(y(x)))-1-2*Ei(1, -(2*I)*Pi*_Z1) = 0

solve(%,y(x));
          exp(RootOf(x^2+2*Ei(1, -_Z)-1-2*Ei(1, -(2*I)*Pi*_Z1)))

So I can't figure how Maple obtained y(x)=1. Maple must have used different method to solve for _C1.

What would be the Maple commands to use to obtain y(x)=1, starting from

            sol:=dsolve(ode,y(x));

and given that y(1)=1 ?

In the calculation below, A and B both simplify to 1.  Why doesn't A*B simplify to 1?  Tested on Maple 2017 and 2018.

Can someone please explain in simple terms, why when I do

 r:=foo(r), where "r" is a Record, then the returned  "r" is not what is returned from foo()?  I want to write a proc foo() which takes in a Record variable, update some of its fields, and then return the updated Record to the caller

r:=Record('a','b');
foo:=proc(r)
    r:-b:=5;
    return(r);
end proc;

But now when I call the above as follows

r:-b:=99;
print(r);
r:=foo(r):
print(r);

The last print above just prints "r" and not the Record. It seems to have erased the Record.

But it works, if I change the name of the variable to return the result into, as 

r:-b:=99;
print(r);
r0:=foo(r):
print(r0);

When I do the same on say a Matrix, there is no problem

restart;
r:=<<1,1>>:
foo:=proc(r)
    r[1]:=5;
    return(r);
end proc;

And now

r;
r:=foo(r):
print(r);

Why it worked with a Matrix but not with Record? Why can't one overwrite the Record on the call return?

What would be the correct way to pass in a Record to a function, and have the function update some of its fields, and then return back the updated copy of the Record without having to make a new variable "r0" as above?

Ball_Maple.mwsBall_Maple.txt

Attached is code in Maple 7 and a text file.There is a for loop in which I want the plots to be output, and the printf command - but I am not getting a plot at all.  Any advice most appreciated.  David

I really like Maple Record. I think it is one of the hidden gems in Maple. Very useful.

But I have basic questions on it. I just started to learn how to use it. It is very similar to Pascal Record.

1)

r:=Record(a,b);
                       r := Record(a, b)
type(r,'record');
                              true
whattype(r);
                             symbol

Why  type(r,'record') says true, but whattype(r) says symbol?

2)
Why Maple displays the record content to the screen automatically only first time, after it is created, but second time, it only echos the name? So one has to use print() each time to display the content of the record.  Not a big deal, but it is little annoying

r:=Record(a,b);
                       r := Record(a, b)
r;
                               r

print(r);
                          Record(a, b)

r:-a:=5;
                             a := 5
r
                               r

print(r);
                        Record(a = 5, b)

Compare this to say a set type, where it displays the content each time

r:={1,2,3};
                         r := {1, 2, 3}
r
                           {1, 2, 3}

I tried changing max_record_depth but I must be doing something wrong. It still does not display the content

interface(max_record_depth=10)
                               10
r:=Record(a,b);
                       r := Record(a, b)
r;
                               r

3) Why are these two behave the same way

r:=Record("y");
r:-y:=4;

r:=Record('y');
r:-y:=4;

Giving the name of the field as string worked the same way as second example which is a name.  I thought the first one above will not work as field name should be a name according to help.

Hello,

I'm currently wondering about the "real" difference.

is() or type() can be used both for true/false checks. However when should what be used preferably?

For example I do not see what is better over the other when doing simple checks such as

is(2,'integer')

type(2,'integer')

Thanks for clarifying.

I can't workout the syntax to plot a sequence of arrow. See last line of document.

accel := plottools:-arrow(seq([M[j, 1][1], M[j, 1][2]], [M[j, 3][1], M[j, 3][2]], j = 1 .. i), colour = red)  Doesn't work and tried various things.

Would also appreciate an explination for how the lines are plotted. I found this line on Maple Primes. It works but I don't realy understant it.

orb := plot(([seq])([M[j, 1][1], M[j, 1][2]], j = 1 .. i), colour = blue)

Why is seq in square brackets?

Download plot_arrows_sequence.mw
 

Download plot_arrows_sequence.mw

I want to learn about why sometimes different algebraic expressions are ordered differently, and what would be the best way to instruct maple to chose a different "rule" for which a set of arithmetic functions are ordered, while still maintaining the axiom of uniqueness. 

I figured this would be accomplished on a case by case basis, and it may involve just using lists instead,defining a procedure to produce the desired ordering for any given set of functions, and using the "remove" command to replace the set "difference" operator and the Join command for the lists in place of the union operator. Then of course using the "Remove Duplicates" option from ListTools to impose the axiom of unique elements. 

Is this the best way to go about this, or is there a much simpler way, that includes an abstract algebra package that I'm unaware of thus far?

Dear sir, I hereby request you to suggest an appropriate method to plot phase portrait sketches for the above cited subject

in 2D and 3D for the problem  

With thanks and regards.

Mr M ANAND

Associate Profesoor in Mathematics.

This question is related to an answer I gave here:
So, please look at a simple worksheet containing only a few lines; the resuts are in the # comments.

restart;
evalf(frac(Pi^20));
#                              23.
restart;
printlevel:=40:
evalf(frac(Pi^20));
  ###  prinlevel stuff
#                              0.

And now the questions.
1. Why the first evalf(frac(Pi^20))  does not  call  `evalf/frac`?
     (the second does, trace(`evalf/frac`)  shows this  if inserted).
     Note that  `evalf/frac`(Pi^20)    returns  0.
2. Why evalf(frac(Pi^20))    depends on printlevel?
    Note that  if  printlevel is changed to 20 (say)  the result is again 23.
3. Why if we set interface(typesetting=standard)  in a fresh session
     the results are both 23?

I can't get a While do loop to work as expected.

For i from 2 while M[i,1]<>M[1,1] and i<25 do..   It doesn't catch row 15 where M[15,1] =M[1,1] but it does stop at i = 24 ok.
 

Download Test_While_do_loop.mw

I'm currently wondering about the cut I'm looking for in the following worksheet.

I evaluate it in 2 ways but get different answers. Any idea what the problem here is?

Thanks

Download CutErrorFunction.mw