## 15202 Reputation

12 years, 70 days

## Ambiguity...

Formulation of the problem is unclear!  What is 10P4?

## Another variant...

I agree that the machinery of the bug is still unclear. But why my code can not be treated as a workaround? Here's another variant for any range:

restart;

X:=[seq(k, k=-20..20, 0.1)]:

Y:=[]:

for k from 1 to 401 do

a:=solve(eval(sqrt(x^2+y^2)=sqrt((x-4)^2+(y-3)^2)+5, x=X[k])):

if a<>NULL then

Y:=[op(Y), [X[k], a]]: fi:

od:

plot(Y, thickness=3, scaling=constrained, view=[-20..20, -16..16]);

## Variant...

Your plot can be constructed as follows:

X:=[seq(k, k=4..10, 0.1)]:

Y:=[]:

for k from 1 to 61 do

solve(eval(sqrt(x^2+y^2)=sqrt((x-4)^2+(y-3)^2)+5, x=X[k])):

Y:=[op(Y), [X[k], %]]:

od:

plot(Y, thickness=3, view=[-1..10, -1..8]);

## 1) To Alejandro Jakubi. Thanks for the...

1) To Alejandro Jakubi.

Thanks for the detailed explanation! It is unfortunate that Maple unable to cope with checking obvious statements.

Another example:

is(2*х^5 +1>0) assuming x>=0, x<=1;

false

This is just a bug!

2) To Markiyan Hirnyk.

I think that the use of  continuous=true option, without proof of the convergence of the improper integral, is unacceptable because may result in an error.

An example:

int(1/x, x=-1..2, continuous=true);

-Pi*I+ln(2)

## 1) To Alejandro Jakubi. Thanks for the...

1) To Alejandro Jakubi.

Thanks for the detailed explanation! It is unfortunate that Maple unable to cope with checking obvious statements.

Another example:

is(2*х^5 +1>0) assuming x>=0, x<=1;

false

This is just a bug!

2) To Markiyan Hirnyk.

I think that the use of  continuous=true option, without proof of the convergence of the improper integral, is unacceptable because may result in an error.

An example:

int(1/x, x=-1..2, continuous=true);

-Pi*I+ln(2)

1) Why was the combinat package called, if in the code it is not used?

2) Your procedure s does not work in the classic interface, as left single quotes should be used: print(`Invalid input`) . In standard interface s works - Maple interprets a blank as multiplication.

3) A simple exhaustive search program more effective (running at least 10 times faster)

s1:=proc(L::list)

local n, N, i, j;

n:=nops(L);

if nops(convert(L,set))=n then

N:=0;

for i to n-1 do

for j from i+1 to n do

if L[i]>L[j] then N:=N+1; fi;

od; od;

else print(`Invalid input`); fi;

(-1)^N;

end proc;

Examples:

L:=combinat[randperm](1000):

st:=time():

s1(L), time()-st;

1,  0.967

st:=time():

s(L), time()-st;

1,  11.981

1) Why was the combinat package called, if in the code it is not used?

2) Your procedure s does not work in the classic interface, as left single quotes should be used: print(`Invalid input`) . In standard interface s works - Maple interprets a blank as multiplication.

3) A simple exhaustive search program more effective (running at least 10 times faster)

s1:=proc(L::list)

local n, N, i, j;

n:=nops(L);

if nops(convert(L,set))=n then

N:=0;

for i to n-1 do

for j from i+1 to n do

if L[i]>L[j] then N:=N+1; fi;

od; od;

else print(`Invalid input`); fi;

(-1)^N;

end proc;

Examples:

L:=combinat[randperm](1000):

st:=time():

s1(L), time()-st;

1,  0.967

st:=time():

s(L), time()-st;

1,  11.981

s([1, 2, 3, 4]);

-1

s([1, 2, 3, 4]);

-1

## Computation in Mathematica...

Mathematica immediately finds the correct answer:

N[FractionalPart[10^9*Exp[1]], 10]

0.4590452354

## Re...

The coordinates of T and E are the rational numbers, what you would like!

## Re...

The coordinates of T and E are the rational numbers, what you would like!