Kitonum

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8 years, 228 days

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These are questions asked by Kitonum

How to put programmatically 2 dots above the first and the last digit  as in the example?

http://s017.radikal.ru/i419/1610/55/958cd75b6b34.png

 

Since the new editor for some reason I cannot upload any pictures or files from my computer.

 

Quite accidentally I discovered incorrect calculation of the simple definite integral:

int(1/(x^4+4), x=0..1);  

evalf(%);

                            1/8*ln(2)-1/16*ln(5)+1/32*Pi+1/8*arctan(1/3)   # This is incorrect result

                                                   0.1244471178

Is this a known bug?

 

If  first we calculate corresponding indefinite integral, and then by the formula of Newton - Leibniz, that everything is correct:

F:=int(1/(x^4+4), x):

eval(F, x=1)-eval(F, x=0);

evalf(%);

                                             1/16*ln(5)+1/8*arctan(2)

                                                     0.2389834593

 

 

When generating the list of all the permutations of  [$1..10]  we get an error:

combinat[permute]([$ 1 .. 10]);

    Error, (in combinat:-permute) Maple was unable to allocate enough memory to complete this computation. Please see ?alloc

 

But if the same problem to solve using a simple custom procedure, there is no any problems:

restart;

Permute := proc (L::list)

local n;

n := nops(L);

if nops(L) = 1 then return [L[1 .. 1]] else

[seq(seq([op(p[1 .. k-1]), L[1], p[k .. n-1][]], k = 1 .. n), p = Permute(L[2 .. n]))] end if;

end proc:

L := CodeTools[Usage](Permute([$ 1 .. 10])):

nops(L);

        

 

 

In Maple 2015.1 we have

restart;

solve([sin(2*x)/cos(x+3*Pi/2)=1,  x>-4*Pi, x<-5*Pi/2], x, allsolutions, explicit);

solve([sin(2*x)/cos(x+3*Pi/2)=1, x>0, x<2*Pi], x, allsolutions, explicit);

 

 

In the first example, the error message is not clear (actually there exists a unique root  x=-11*Pi/3), in the second example, one root  (x=5*Pi/3) is lost.

 

Is there in Maple a command to verify that one segment on the real axis is a subset of another segment?  For example  RealRange(2, 4)  is subset of  RealRange(2, 5)

Of course easy to write a procedure that makes it:

Subset:=proc(r1::RealRange, r2::RealRange)

local a, b, c, d;

a, c:= op~(1,[r1, r2])[];

b, d:= op~(2,[r1, r2])[];

if a>=c and b<=d then true else false fi;

end proc:

 

Example of use:

Subset(RealRange(2,4), RealRange(2,5));

Subset(RealRange(2,5), RealRange(2,4));

                            true

                            false

 

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