Maple V Questions and Posts

These are Posts and Questions associated with the product, Maple V

Above in the figure, the trapezoid method. How to fix the error?

And how to solve this interval using the method of rectangles?


 

sin(Pi/12);

(1/4)*6^(1/2)*(1-(1/3)*3^(1/2))

(1)

 


 

Download calculation.mws

can anyone explain to me this result ?

in the book "maple by example" they said that sin(Pi/12);
sin (1/12 π)
returns sin(π/12) because it does not know a formula for the explicit value of sin(π/12). but when i'm calculated this in maple i had got , this result, what does this result mean ?

 

we know that the exponotial function is represented as a taylor series, that means that the exponontial of any value is approximatvly evaluated ,the same thing of sinus function when i calcute sin(Pi/6) it give me the exacte result,
 

sum(0^i/i!,i=0..infinity);

0

(1)

exp(0);

1

(2)

sin(0.2);

.1986693308

(3)

sin(Pi/6);

1/2

(4)

sin(Pi/2);

1

(5)

 


 

Download trying.mws

,can anyone explain to me these results ?

 we know that  maple evaluate an expression as a tree, for example if i have the expression:

f:=x^2*exp(3/2)*sin(Pi/3-1/x);

i want to get all the tree, is there a command to obtain this !!

can anyone tell me the difference between subs and eval and  evalf ?

Hello dear Maple,

My name is Bulat, I'm student of Kazan National Research Technical University ( Russia). In our High Program we used your product ( Maple V, Release 4). Now I have two problems and I haven't no idea how I resolve their. I am forced to ask for your help. I upload PrintScreen of my two problems. Please help me to solve them. I' ll be grateful for your help. Sorry for my English :(.

Yours very truly, Bulat

In Maple V, Release 4 (1996):

 

T:=table():
i:=1:N:=5000;

for i from i to N  
do
   T[i]:=T[i+1]:
   T[i+1]:=1;
   eval(T[1]);
od:
print(i);

for i from i to N  
do
   T[i]:=T[i+1]:
   T[i+1]:=1;
   eval(T[1]);
od:
print(i);

I receive this output:

N := 5000
Error, too many levels of recursion
3607
5001

Can You explain this occurence, as well as the following one:

In Maple V, Release 4 (1996):

 

T:=table():
i:=1:N:=5000;

for i from i to N  
do
  T[i]:=T[i+1]:
  eval(T[1]);
od:
print(i);
 
for i from i to N  
do
  T[i]:=T[i+1]:
  eval(T[1]);
od:
print(i);;

gives:

N := 5000
Error, too many levels of recursion
3607
Error, too many levels of recursion
3607

How does one control allowance for recursion depth?

In Maple V, Release 4 (1996):

 

_EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end();
_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end();;

gives:
                                 0, 0
                                 0, 1

In newer Maple:

 

_EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end proc();
_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end proc();

?

Code & result:

> map((a::uneval,b)->'args',[a,b,c,d],1..4,x);       
['a, 1 .. 4, x', 'b, 1 .. 4, x', 'c, 1 .. 4, x', 'd, 1 .. 4, x']

> map((a,b::uneval)->'args',[a,b,c,d],1..4,x);           
[a, 1 .. 4, x, b, 1 .. 4, x, c, 1 .. 4, x, d, 1 .. 4, x]

Why is the output not:
['a', 1 .. 4, x, 'b', 1 .. 4, x, 'c', 1 .. 4, x, 'd', 1 .. 4, x]
and
[a, '1 .. 4', x, b, '1 .. 4', x, c, '1 .. 4', x, d, '1 .. 4', x]
?

How do I write a procedure to find a root of f(x)=0 in the vicinity of a given value x0. The procedure should initially use the rearrangement method to produce a linearly convergent sequence of values, and should, when appropriate, switch to Aitkin's Method. The input for the procedure should be the re-arranged function and the velue for x0. The output should be the root and the number of iteration taken. The procedure should check that re-arrangement will converge. This program should do in Maple V Release5.

Thank you for your help.

 

I am trying to obtain the splitting field of New_polyq. evala@AFactor did not complete. Applying splitting sequentially produced independent extensions from the first 2 (3?) factors. evala@Indep did not complete for the union of all 4 extensions.

What libraries would handle this better?

restart; _EnvExplicit:=false;interface(labelwidth=200);
Rho_polys:=rho[3,1]^3-2, rho[3,2]^2+rho[3,2]*rho[3,1]+rho[3,1]^2, 2*rho[6,1]^3+rho[6,1]^6-2, rho[12,1]^2+rho[6,1]^2-1, 2*rho[12,2]^2-rho[6,1]^2*rho[3,2]*rho[3,1]^2-2*rho[6,1]^2-2;
New_poly:=1/16*(-rho[6,1]^4*rho[3,2]*rho[3,1]-2-rho[3,1]^2*rho[6,1]^4-2*rho[6,1]*rho[3,2]*rho[3,1]-2*rho[3,1]^2*rho[6,1]+2*lambda^2)*(rho[6,1]^4*rho[3,2]*rho[3,1]+2*rho[6,1]*rho[3,2]*rho[3,1]-2+2*lambda^2)*(-2+2*rho[3,1]^2*rho[6,1]+rho[3,1]^2*rho[6,1]^4+2*lambda^2)*(-2+rho[6,1]^2*rho[3,2]*rho[3,1]^2+2*lambda^2);
sol:=solve({Rho_polys});
alias(op(sol));
New_polyq:=subs(sol,New_poly);

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
  local no_points,x_old,x_new,y_old,y_new,i:
  no_points:=round(evalf((xn-x0)/h)):
  x_old:=x0:
  y_old:=y0:
 
  for i from 1 to no_points do
      x_new:=x_old+h:
      y_new:=y_old+evalf(h*f(x_old,y_old)):
      x_old:=x_new:
      y_old:=y_new:
  od:
  y_new:
end:


Thanks

I am also having trouble with limits when I have indexed
variables.   That is, how do I tell Maple to assume every element of
an indexed variable is positive?

uxb3% maple < te7a

    |\^/|     Maple V Release 3 (Governors State University)



Here, I show that normal limits work.
> int (exp(-x^2),x=3..infinity);

                                1/2         1/2

                          1/2 Pi    - 1/2 Pi    erf(3)



> assume(a>0);

> int(exp(-a*x^2...

A curve has the equation y=f(x).

Find the eqn of the normal to the curve at the point x=xin the form y=g(x, x0) and write a procedure to plot curve y=f(x) with its normal at any point on the curve.

Animate the plot so that the normal is seen sliding along the curve.

I use the eqn feature from Maple to generate troff output.

Each equation is longer than one line. How does one get the eqn/troff
combination to automatically break the equation into multiple lines.

(I tried finding the division point myself and could not do it. I am
generating the output and I have a perl script that puts together the indivdual
equations into the document to be printed. Thus, I need something automatic)

I tried Google and...
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