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10 years, 56 days
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theta...

vv 14037
June 09 2017
0 0

@Markiyan Hirnyk 

Ypu forgot theta = Pi/6.

f...

vv 14037
June 09 2017
0 0

@Markiyan Hirnyk 

f is OP's integrand of course.

divergence...

vv 14037
June 09 2017
0 0

@Markiyan Hirnyk 

A brief inspection confirms divergence:
int(f, k=1..10) assuming cos(p)>-1, cos(p)<-1/2, Z>0, Z<1/10;
         infinity

But the justification for extrema is eas...

vv 14037
June 08 2017
0 0

But the justification for extrema is easy: the feasible region is compact and the function is differentiable there.

@Kitonum 

code...

vv 14037
June 06 2017
0 0

@Cham 

You make a mistake in this case (if you want to use modern Maple and efficient code).
See also "angle bracket" in  https://en.wikipedia.org/wiki/Bracket.

examples...

vv 14037
June 05 2017
0 0

@John Fredsted 

Do you have an example where delayed evaluation does not work?

BTW,

Tools > Options > Display > Typesetting level = Standard (instead of Extended) 

implies that your original construct works!

 

But indeed, the situation is strange:

 

 

> 

A:=Vector(2,(a) -> Matrix(2,2,(b,c) -> m||a||b||c)):
> 

%;

Error, (in Vector[column]) number of elements on right side must match subselection on left side

  
> 

A[1];

Matrix(2, 2, {(1, 1) = m111, (1, 2) = m112, (2, 1) = m121, (2, 2) = m122})

 (1)
> 

A;

Error, (in Vector[column]) number of elements on right side must match subselection on left side

  
> 

lprint(A);

Vector[column](2, {1 = Matrix(2, 2, {(1, 1) = m111, (1, 2) = m112, (2, 1) = m121, (2, 2) = m122}, datatype = anything, storage = rectangular, order = Fortran_order, shape = []), 2 = Matrix(2, 2, {(1, 1) = m211, (1, 2) = m212, (2, 1) = m221, (2, 2) = m222}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

  
> 

 

> 

 

> 

################
> 

restart;
> 

f:=(a) -> 'Matrix'(2,2,(b,c) -> m||a||b||c):
> 

V:=Vector(2,F);

V := Vector(2, {(1) = F(1), (2) = F(2)})

 (2)
> 

eval(V, F=f);

Error, (in Vector[column]) number of elements on right side must match subselection on left side

  
> 

V:=Vector(2, 'f');

V := Vector(2, {(1) = Matrix(2, 2, {(1, 1) = m111, (1, 2) = m112, (2, 1) = m121, (2, 2) = m122}), (2) = Matrix(2, 2, {(1, 1) = m211, (1, 2) = m212, (2, 1) = m221, (2, 2) = m222})})

 (3)
> 

V:=Vector(2):
> 

for i to 2 do V[i]:=f(i) od: V;

Error, (in Vector[column]) number of elements on right side must match subselection on left side

  
> 

for i to 2 do V[i]:='f'(i) od: V;

Vector(2, {(1) = Matrix(2, 2, {(1, 1) = m111, (1, 2) = m112, (2, 1) = m121, (2, 2) = m122}), (2) = Matrix(2, 2, {(1, 1) = m211, (1, 2) = m212, (2, 1) = m221, (2, 2) = m222})})

 (4)
> 

 

or ......

vv 14037
June 02 2017
0 0

@Kitonum 

You forgot the case f(a,b)=0, g(a,b)=0, h(a,b)>0.

int...

vv 14037
June 02 2017
0 0

@Kitonum 

Of course the integral can be computed. My point was that without a general algorithm implemented, many functions with simple elementary antiderivatives will need consistent help from the user to be integrated.

Just luck...

vv 14037
June 02 2017
0 3

It was a pure luck that expanding the integrand was successful (the three resulting integrals have cancelled).
For example, for:

f := (3*(x+exp(x))^(2/3)+(x^2+3*x)*exp(x)+4*x^2)/((x+exp(x))^(2/3)*x);

IntegrationTools:-Expand(int(f, x));

will not work.

[ The integral is   3*(x+exp(x))^(1/3)*x+3*ln(x)  ]

AFAIK the Risch algorithm is not (fully) implemented for functions involving roots.

 

 

OK, I quit, anyway you are going to pers...

vv 14037
June 01 2017
0 0

OK, I quit, anyway you are going to persist in error ad infinitum.

@Markiyan Hirnyk 

Nothing to understand....

vv 14037
June 01 2017
0 0

@Markiyan Hirnyk 

Example:

 

 

 

> 

f:=sin(1/x)/x;

sin(1/x)/x

 (1)
> 

GlobalSearch(f, {x = 0.01 .. 1}, solutions = 3);

Array([[-80.1168531456592, [x = 0.124807962966356e-1], 19], [-23.5831306496334, [x = 0.423651896147433e-1], 17], [-17.3076086078585, [x = 0.576821758588231e-1], 20]])

 (2)
> 

GlobalOptima(f, {x = 0.01 .. 1});

[HFloat(-98.9652206531187), [x = HFloat(0.010104044142551094)], 138]

 (3)

If you refuse to accept such a clear sit...

vv 14037
June 01 2017
0 0

If you refuse to accept such a clear situation, it's OK for me.

@Markiyan Hirnyk 

help...

vv 14037
June 01 2017
0 0

@Markiyan Hirnyk 

The help is very clear: for global extrema, use GlobalOptima. You found 3 extrema which could be global or local.

partial workaround only...

vv 14037
June 01 2017
0 0

@Markiyan Hirnyk 

This is only a partial workaround, DS fails. You have asked 3 local extrema, you cannot know whether 1 is global or not.

DS...

vv 14037
May 31 2017
0 0

@Markiyan Hirnyk 

DS is a very good package, but i doubt that you have never seen a fail.

f:=ln(ln( exp(exp(exp(10^10*(x-1/7)))) + y)):
absminmax(f,{x>=1/7,y>=0,x<=3/7,y<=1});

gives the correct result min=1.
In DS, min=Float(infinity) and  sometimes min=0.

 

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