I expect that Robert is on the right tack to correctly guess the intention, with floor.

But I'll submit a joke answer, because the way the question was asked is terribly unclear.

> msolve({3*k-5=0},2);

                            {k = 1}

@mermeladeK I asked about Digits because I expected the results to change as the working precision was increased, on account of the range of magnitudes of the coefficiants, but didn't have the time to check. Then Axel corroborated this suspicion.

@Clare So The code for each is accessible from the alt tags on those inlined images.

What happens to the numeric results (from both/either) if you first raise Digits (eg. to 100)?

@Markiyan Hirnyk I only used method=[_RETURNVERBOSE] because I have noticed from perusing Library code that it forces all the methods to be tried and reported upon.

In Maple 15.01, the expanded integral is computed without specifying a method (though we now know, from that verbose view, that methods ftoc and ftocms would both return the same result).

> restart:

> int(expand(cos(a*x)*cos(x)^(a-2)),x=0..Pi/2) assuming a>1;

                                   0

So, the _RETURNVERBOSE method is not central to the result obtained, and was used as a convenience (to me). I inferred some behaviour of special values for the 'method' keyword parameter of the `int` routine by looking at the result of the following command.

   showstat((IntegrationTools::Definite)::ParseIntegrationMethod);

@Markiyan Hirnyk I only used method=[_RETURNVERBOSE] because I have noticed from perusing Library code that it forces all the methods to be tried and reported upon.

In Maple 15.01, the expanded integral is computed without specifying a method (though we now know, from that verbose view, that methods ftoc and ftocms would both return the same result).

> restart:

> int(expand(cos(a*x)*cos(x)^(a-2)),x=0..Pi/2) assuming a>1;

                                   0

So, the _RETURNVERBOSE method is not central to the result obtained, and was used as a convenience (to me). I inferred some behaviour of special values for the 'method' keyword parameter of the `int` routine by looking at the result of the following command.

   showstat((IntegrationTools::Definite)::ParseIntegrationMethod);

@Markiyan Hirnyk 

> restart:

> AD:=int(expand(cos(a*x)*cos(x)^(a-2)),x) assuming a>1:

> der:=diff(AD,x) assuming a>1, x>0, x<Pi/2:

> simplify(convert(eval(cos(a*x)*cos(x)^(a-2)-der,a=sqrt(2)),cos)) assuming x>0, x<Pi/2;

                                   0

@Markiyan Hirnyk 

> restart:

> AD:=int(expand(cos(a*x)*cos(x)^(a-2)),x) assuming a>1:

> der:=diff(AD,x) assuming a>1, x>0, x<Pi/2:

> simplify(convert(eval(cos(a*x)*cos(x)^(a-2)-der,a=sqrt(2)),cos)) assuming x>0, x<Pi/2;

                                   0

@remusmp Did you correctly add to LD_LIBRARY_PATH when succeeding with that mentioned gcc option?

Elsewhere, you wrote that you executed (hopefully, in the same shell from which you launch `simple`),

MAPLE=/usr/local/bin/maple15
export LD_LIBRARY_PATH=$MAPLE/bin.IBM_INTEL_LINUX

Did you do that here too? Is that path correct?

It's a bit unusual to install a whole application like Maple under /usr/local/bin/ instead of /usr/local/ or maybe /usr/local/lib/. It should not matter, though, as long as LD_LIBARARY_PATH includes it.

If it still doesn't work, try the following. On Linux, there are some additional subdirectories under $MAPLE/bin.IBM_INTEL_LINUX for specific architectures. Maybe your machines needs a specific one of these. If you issue the command getenv(LD_LIBRARY_PATH) from inside Maple then you could see which (if any) of those gets added when you launch Maple itself. You could also try prepending them both in LD_LIBRARY_PATH, in the specific order, in your shell.

Eg, replacing `ABCD` with the specific subdirectory name that you get from `getenv` (sorry, this is one long line which you can mouse-select with triple-click or something)

export LD_LIBRARY_PATH=$MAPLE/bin.IBM_INTEL_LINUX/ABCD:$MAPLE/bin.IBM_INTEL_LINUX:$LD_LIBRARY_PATH

@remusmp Did you correctly add to LD_LIBRARY_PATH when succeeding with that mentioned gcc option?

Elsewhere, you wrote that you executed (hopefully, in the same shell from which you launch `simple`),

MAPLE=/usr/local/bin/maple15
export LD_LIBRARY_PATH=$MAPLE/bin.IBM_INTEL_LINUX

Did you do that here too? Is that path correct?

It's a bit unusual to install a whole application like Maple under /usr/local/bin/ instead of /usr/local/ or maybe /usr/local/lib/. It should not matter, though, as long as LD_LIBARARY_PATH includes it.

If it still doesn't work, try the following. On Linux, there are some additional subdirectories under $MAPLE/bin.IBM_INTEL_LINUX for specific architectures. Maybe your machines needs a specific one of these. If you issue the command getenv(LD_LIBRARY_PATH) from inside Maple then you could see which (if any) of those gets added when you launch Maple itself. You could also try prepending them both in LD_LIBRARY_PATH, in the specific order, in your shell.

Eg, replacing `ABCD` with the specific subdirectory name that you get from `getenv` (sorry, this is one long line which you can mouse-select with triple-click or something)

export LD_LIBRARY_PATH=$MAPLE/bin.IBM_INTEL_LINUX/ABCD:$MAPLE/bin.IBM_INTEL_LINUX:$LD_LIBRARY_PATH

@Markiyan Hirnyk Is part of this invalid, ie. expansion of integrand, or the methods?

I'd be willing to believe that :-limit might be accidentally producing a wrong intermediate result, somewhere deep inside int. The same result is not obtained from int (for the definite integral, I mean, rather than the manual FTOC application) when :-limit is replaced by MultiSeries:-limit before the int computation.

> restart:

> int(expand(cos(a*x)*cos(x)^(a-2)),x=0..Pi/2,method=[_RETURNVERBOSE]) assuming a>1;

[ftocms = 0, ftoc = 0, FAILS = (distribution, piecewise, series, 

  o, polynomial, ln, lookup, cook, ratpoly, elliptic, 

  elliptictrig, meijergspecial, improper, asymptotic, meijerg, 

  contour)]

> AD:=int(expand(cos(a*x)*cos(x)^(a-2)),x) assuming a>1:

> limit(AD,x=Pi/2) assuming a>1;

                               0

> limit(AD,x=0) assuming a>1;

                               0
> infolevel[int]:=1: #2;

> int(expand(cos(a*x)*cos(x)^(a-2)),x=0..Pi/2,method=[ftocms]) assuming a>1;

int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/trigon: case of integrand containing trigs
int/indef1: first-stage indefinite integration
int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/trigon: case of integrand containing trigs
int/rischnorm: enter Risch-Norman integrator
int/rischnorm: exit Risch-Norman integrator
int/risch: enter Risch integration
int/risch: exit Risch integration
                               0

When you ask how to show it with Maple which parts are we allowed to trust for this? Are you looking for a separate analysis?

@Markiyan Hirnyk Is part of this invalid, ie. expansion of integrand, or the methods?

I'd be willing to believe that :-limit might be accidentally producing a wrong intermediate result, somewhere deep inside int. The same result is not obtained from int (for the definite integral, I mean, rather than the manual FTOC application) when :-limit is replaced by MultiSeries:-limit before the int computation.

> restart:

> int(expand(cos(a*x)*cos(x)^(a-2)),x=0..Pi/2,method=[_RETURNVERBOSE]) assuming a>1;

[ftocms = 0, ftoc = 0, FAILS = (distribution, piecewise, series, 

  o, polynomial, ln, lookup, cook, ratpoly, elliptic, 

  elliptictrig, meijergspecial, improper, asymptotic, meijerg, 

  contour)]

> AD:=int(expand(cos(a*x)*cos(x)^(a-2)),x) assuming a>1:

> limit(AD,x=Pi/2) assuming a>1;

                               0

> limit(AD,x=0) assuming a>1;

                               0
> infolevel[int]:=1: #2;

> int(expand(cos(a*x)*cos(x)^(a-2)),x=0..Pi/2,method=[ftocms]) assuming a>1;

int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/trigon: case of integrand containing trigs
int/indef1: first-stage indefinite integration
int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/trigon: case of integrand containing trigs
int/rischnorm: enter Risch-Norman integrator
int/rischnorm: exit Risch-Norman integrator
int/risch: enter Risch integration
int/risch: exit Risch integration
                               0

When you ask how to show it with Maple which parts are we allowed to trust for this? Are you looking for a separate analysis?

But in general someobne might need to solve for particular variables, and not rely on the lexicographic ordering. It might not be ok, if he wanted to solve for x and got a solution containing x=x, etc.

But in general someobne might need to solve for particular variables, and not rely on the lexicographic ordering. It might not be ok, if he wanted to solve for x and got a solution containing x=x, etc.

@alex_01 Yes, that form can be obtained directly by replacing L' with U (or R') and L by U' (or R) literally, throughout (as mentioned).