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Piecewise function - How plot function with piece...

Asked by: Rariusz 30
plot piecewise
April 26 2018
0  2

Hi

I have the following piecewise function in Maple:

sigmaP:=piecewise(u < -1,-1,u >1,1,u);

Now we can plot this function:

plot(sigmaP,u=-5..5,size=[1200,300],gridlines,discont=[showremovable]);

Next, I define a new piecewise  function as

sigmaF:=u->piecewise(u < -1,-1,u >1,1,u);

and I use this function in 

Fun:=proc(x1,x2,u1,u2)
	2*x1*(1+x2)*sigmaF(u1)+(1+x2^2)*sigmaF(u2);
end proc:

Now I need to find a minimum of this function so I use the following code 

GlobalOptimization:-GlobalSolve(Fun,x1,x2,u1,u2);

where 

x1:=-5..5;
x2:=-10..100;
u1:=-1..1;
u2:=-1..1;

And I have the problem with plot function Fun. How to plot function Fun???

Best

 

Integral method ...

Asked by: John Eric 80
integration
April 26 2018
0  3

Hello,

Would you please help me with this integral : 


 

> 

restart
> 

int(exp(i*x*t)/((x-a)*(x+a)), x = -infinity .. infinity)

piecewise(Im(a) = 0, undefined, int(exp(i*x*t)/((x-a)*(x+a)), x = -infinity .. infinity, method = _UNEVAL))

 (1)
> 

``


 

Download Integrale.mw

Unable to plot" kx" vs "f "(maple code attached).....

Asked by: M Singh 10
plot plotting
April 26 2018
1  1

MAPLE CODE [below link]:


Dispersion.mw

range of "kx" variable [0 to 8x106] and range of "f" variable  [80x1012 to 220x1012]

Why different between calculate two form? ...

Asked by: assma 75
April 25 2018
1  2

Why different between calculate two form? I use maple 2017

evalf(sech(20)^2); evalf(sech(-20)^2);
                                     
                       1.699341702 *10^ -17  
                                     
                       1.699341702 *10^ -17  
evalf(1-tanh(20)^2); evalf(1-tanh(-20)^2);
                               0.
                               0.

 

what is the meaning of % ?...

Asked by: Lali_miani 70
April 25 2018
0  1

i want to calculate the eigenvalues and eigenvectors of two matrices ,i get these results, can anyone explain to me the meaning ?

A:=linalg[matrix](3,3,[-1,2,0,4,-2,3,0,1,-3]);
> B:=linalg[matrix](3,3,[2,0,1,4,-1,1,2,0,-5]);

> eigenvalues(A);

                  8                                    4
1/2 %2 + -------------------- - 2, - 1/4 %2 - --------------------
                      1/2 1/3                              1/2 1/3
         (20 + 4 I 231   )                    (20 + 4 I 231   )

                  1/2 /                  8          \
     - 2 + 1/2 I 3    |1/2 %2 - --------------------|, - 1/4 %2
                      |                      1/2 1/3|
                      \         (20 + 4 I 231   )   /

                4
     - -------------------- - 2
                    1/2 1/3
       (20 + 4 I 231   )

              1/2 /                  8          \
     - 1/2 I 3    |1/2 %2 - --------------------|
                  |                      1/2 1/3|
                  \         (20 + 4 I 231   )   /

               1
%1 := --------------------
                   1/2 1/3
      (20 + 4 I 231   )

                   1/2 1/3
%2 := (20 + 4 I 231   )

eigenvectors(B);
               1/2      [            1/2  65          1/2   ]
[- 3/2 + 1/2 57   , 1, {[7/4 + 1/4 57   , -- + 9/28 57   , 1]}],
                        [                 28                ]

                   1/2      [            1/2  65          1/2   ]
    [- 3/2 - 1/2 57   , 1, {[7/4 - 1/4 57   , -- - 9/28 57   , 1]}],
                            [                 28                ]

    [-1, 1, {[0, 1, 0]}]

what is the diffrence ?...

Asked by: Lali_miani 70
type has
April 25 2018
0  1

such a list H:=
                     [0, 4, 8, 1, 2, 1, 4, 2, 8]

what is the diffrence between these 2 commands ? has(H,integer), type(H,integer);

how to get this sequence ?...

Asked by: Lali_miani 70
April 25 2018
0  2

how to obtain the sequence of sin(((Kπ)/4)), where the integer K  is varying from 1 to 8, and then to delete the zeros.

Is this the true result ?...

Asked by: Lali_miani 70
April 25 2018
0  2

i'm triying to solve this sytem ,

solve({x^2+y^2=3,x^2+2*y^2=3},{x,y});
{y = 0, x = RootOf(_Z^2-3)}
what is the meaning of RootOf

maple gives me this, can anyone explain to me,the signification of the solutions ?

Solution of second order differential equation...

Asked by: Muhammad Usman 240
linear dsolve
April 25 2018
0  3

Dear Users!

Hope you would be fine with everying. I want to solve the following 2nd order linear differential equation. 

(1+B)*(diff(theta(eta), eta, eta))+C*A*(diff(theta(eta), eta)) = 0;
where A is given as

A := -(alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega+alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega-alpha*omega+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))-alpha-omega-1)/sqrt((omega+1)*omega*(M^2+alpha+1));
I want solution for any values of omega, alpha, M, B, C and L. The BCs are below:

BCs := (D(theta))(0) = -1, theta(L) = 0.

I am waiting your response, 

how can i obtain this ?...

Asked by: Lali_miani 70
homework list
April 25 2018
0  1

Write a command maple to count each two elements distincts of a list L ?

Error, (in unknown) invalid arguments to divide: 4...

Asked by: eager0626 55
eliminate
April 25 2018
1  2

Hello,

There is a error happened when i use the command "eliminate" ,

And,the target two equations is:

[190.0315457*d^6-7.601261828*d^4+344.0*c^2*d^2-2.677685950*c^4, 0.6830134554e-2*c^4+2084.317025*d^8-166.7453620*d^6+3.334907240*d^4-c^2*d^2]

The error is happened like that shown below.

Error, (in unknown) invalid arguments to divide: 4903.60312, 1.000000000 to use eliminate command!

I wonder why this error happened, could anyone help me!

Thanks!!!

how can i substitute these elements ?...

Asked by: Lali_miani 70
listlist max
April 25 2018
0  3

to get the list where all the elements of a list L equal to its largest element are replaced by 0 ?

How can I find the inverse of a function over a gi...

Asked by: sand15 847
solve
April 25 2018
0  9

Hi everyone,

I have a x -> y = f(x) function from R to R (you may suppose f is C(infinity)),  given by an explicit relation.
This function is not strictly monotonic over R.

I want to construct the global inverse of f over R by putting "side by side" local inverse functions.
Let a__0, ..., a__n values of x such that:

  1. -infinity =a__0 < a__1 < ... a__(n-1) < a__n = + infinity
  2. f is monotonic over ] a__p, a__(p+1) [   for each p=0..n-1

The idea is to define the global inverse g of f over R by
g := y ->  piecewise(y < f(a__1), g__0(y), ..., y < f(a__n), g__(n-1)(y))
where g__p(y), is the inverse function of the restriction of f to ] a__p, a__(p+1) [
 

Toy problem
f := x ->1-(1-x)^2;
x__1 := solve(diff(f(x), x);
y__1 := f(x__1);

# I thought one of these commands could work (but they don't return me a single branch as I had expected)
solve(f(x)=y, x) assuming y < y__1;
solve({f(x)=y, x < x__1}, x);

How can I obtain the inverse of a function f over an interval where f is bijective ?


TIA

 

 

 

latex code too long...

Asked by: Adam Ledger 360
sum evaluation latex
April 25 2018
1  7

I think that maple is actually evaluating this series into what ever ridiculously long closed form expression the expansion of the series has, but i just want the latex for what i have entered.

How do i tell maple to not evaluate something?
 

> 

latex(a[p, q] = sum(cos(2*Pi*(p+1)*(n-1)/q), n = 1 .. q))

a_{{p,q}}= \left( -4\, \left( \cos \left( {\frac {\pi }{q}} \right)
 \right) ^{2}+8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{
2}-8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {

\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right) +3-4\, \left( \cos \left( {\frac {
\pi \,p}{q}} \right)  \right) ^{2} \right)  \left( \cos \left( {\frac
{\pi \, \left( q+1 \right) }{q}} \right)  \right) ^{2}+ \left( -4\,
 \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}+8\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left(
\cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin \left( {
\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)
\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right) +3-4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \, \left( q+1
 \right) p}{q}} \right)  \right) ^{2}+ \left( 8\, \left( \cos \left( {
\frac {\pi }{q}} \right)  \right) ^{2}-16\, \left( \cos \left( {\frac
{\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q
}} \right)  \right) ^{2}+16\,\sin \left( {\frac {\pi \,p}{q}} \right)
\cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}}
 \right) \cos \left( {\frac {\pi }{q}} \right) -6+8\, \left( \cos
 \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \right)  \left(
\cos \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right)  \right)
^{2} \left( \cos \left( {\frac {\pi \, \left( q+1 \right) }{q}}
 \right)  \right) ^{2}+ \left( 8\,\sin \left( {\frac {\pi \,p}{q}}
 \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left(
{\frac {\pi }{q}} \right)  \right) ^{4}-4\, \left( \cos \left( {\frac
{\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right)
+8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}
 \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin
 \left( {\frac {\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}}
 \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left(
{\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p
}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{3} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{
2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{
q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right)
^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q
}} \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac
{\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right) \sin \left( {\frac {\pi \, \left( q+1 \right) }{q}}
 \right) \cos \left( {\frac {\pi \, \left( q+1 \right) }{q}} \right)
 \left( - \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2
}+ \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right)
^{-1}+ \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left(
{\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left(
\cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac
{\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos
 \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }
{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3
} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin
 \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4
}+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac
{\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right) \sin \left( {\frac {\pi \, \left( q+1 \right) p}{q}}
 \right) \cos \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right)
 \left( - \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2
}+ \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right)
^{-1}-2\, \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos
 \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }
{q}} \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left(
\cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac
{\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos
 \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }
{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3
} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin
 \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4
}+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac
{\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right)  \left( \cos \left( {\frac {\pi \, \left( q+1
 \right) p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi \,
 \left( q+1 \right) }{q}} \right) \cos \left( {\frac {\pi \, \left( q+
1 \right) }{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{
q}} \right)  \right) ^{2}+ \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{2} \right) ^{-1}-2\, \left( 8\,\sin \left( {\frac
{\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)
 \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4\,
 \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin
 \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8
\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac
{\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q
}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p}
{q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right)
\cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}
{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {
\frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi \,
 \left( q+1 \right) p}{q}} \right) \cos \left( {\frac {\pi \, \left( q
+1 \right) p}{q}} \right)  \left( \cos \left( {\frac {\pi \, \left( q+
1 \right) }{q}} \right)  \right) ^{2} \left( - \left( \cos \left( {
\frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos \left( {\frac {
\pi }{q}} \right)  \right) ^{2} \right) ^{-1}+ \left( -8\, \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{2}+16\, \left( \cos
 \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left(
{\frac {\pi }{q}} \right)  \right) ^{2}-16\,\sin \left( {\frac {\pi \,
p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( {
\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +6-8\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}
 \right) \sin \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right)
\cos \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right) \sin
 \left( {\frac {\pi \, \left( q+1 \right) }{q}} \right) \cos \left( {
\frac {\pi \, \left( q+1 \right) }{q}} \right) - \left( -4\, \left(
\cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}+8\, \left( \cos
 \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left(
{\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p
}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( {
\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +3-4\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}
 \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-
 \left( -4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2
}+8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}
 \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right) \sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {
\pi }{q}} \right) +3-4\, \left( \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \,p}{q}
} \right)  \right) ^{2}- \left( 8\, \left( \cos \left( {\frac {\pi }{q
}} \right)  \right) ^{2}-16\, \left( \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)
 \right) ^{2}+16\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos
 \left( {\frac {\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}}
 \right) \cos \left( {\frac {\pi }{q}} \right) -6+8\, \left( \cos
 \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \right)  \left(
\cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{2}- \left( 8\,\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4
\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin
 \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8
\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac
{\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q
}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p}
{q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right)
\cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}
{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {
\frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi }{q}}
 \right) \cos \left( {\frac {\pi }{q}} \right)  \left( - \left( \cos
 \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}- \left(
8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,
p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right)
^{4}-4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}
\sin \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac {
\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}
} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8
\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac
{\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q
}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p}
{q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right)
\cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}
{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {
\frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi \,p}{q}}
 \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( - \left(
\cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}+2\,
 \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {
\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left(
\cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac
{\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos
 \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }
{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p}{q}}
 \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3
} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin
 \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4
}+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}
 \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac
{\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin
 \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac
{\pi }{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right) ^{2}+ \left( \cos \left( {\frac {\pi }{q}} \right)
 \right) ^{2} \right) ^{-1}+2\, \left( 8\,\sin \left( {\frac {\pi \,p}
{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4\, \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {
\pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi \,p}{q}}
 \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)
 \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin \left( {
\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)
 \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin
 \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q}}
 \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p}
{q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi
\,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right)
\cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}
{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)
 \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {
\frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi \,p}{q}}
 \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left(
{\frac {\pi }{q}} \right)  \right) ^{2} \left( - \left( \cos \left( {
\frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos \left( {\frac {
\pi }{q}} \right)  \right) ^{2} \right) ^{-1}- \left( -8\, \left( \cos
 \left( {\frac {\pi }{q}} \right)  \right) ^{2}+16\, \left( \cos
 \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left(
{\frac {\pi }{q}} \right)  \right) ^{2}-16\,\sin \left( {\frac {\pi \,
p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( {
\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +6-8\,
 \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}
 \right) \sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {
\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}} \right) \cos
 \left( {\frac {\pi }{q}} \right)

 
> 

``


 

Download MAPLE_PLEASE_HELPS_BECOZ_MAPLE_IS_FRENS.mw

Monte Carlo integration...

Asked by: shaif 5
integration numeric monte-carlo
April 25 2018
1  5

I am trying to use Monte Carlo integration example given at: https://www.maplesoft.com/products/maple/new_features/maple15/examples/montecarlo.aspx.

After coding the procedure, the statement approxint(x^2, x = 1 .. 3)

gives error: Error, (in approxint) invalid input: `if` expects 3 arguments, but received 1

But I have used in exactly the same way as given in the page. What is the problem

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