isControllable and isObservable maple functions: Is there a way to make them show steps?

So we can use isObservable to work with some systems but I wonder If we can make tham show staps or do something like that. Is开发者_运维知识库 that possible?

I'm supposing that you are actually referring to the Observable and Controllable commands which are part of the DynamicSystems package.

Some Maple routines have so-called userinfo messages, which are optionally displayed and which can show partial steps. Those would typically be enabled with a call like infolevel[DynamicSystems]:=6 where 6 is the highest level of detail. With a lower value less detail might be displayed. Unfortunately, these particular DynamicSystems routines don't seem to have any userinfo messages in them. So this won't help directly in your case.

Sometimes one package calls another. The routine LinearAlgebra:-Rank is called, at some point, when Controllable is called. I'm guessing that you don't wish to see userinfo messages in Rank, which would be enabled by issuing infolevel[LinearAlgebra]:=n for some n between 1 and 6.

An alternative is to set printlevel high. But doing so will make all Maple internal calls also be verbose. The resulting output of setting, say, printlevel:=20 is overwhelming. I doubt that you'd find this approach useful.

Another alternative is to set certain routines as option trace. Sometimes doing so entails knowing the names of the appropriate internal routines. And this is made more complicated by the fact that not all non-exported module locals are visible by default. You could try first issuing the call, trace(DynamicSystems::ControllableSS): before invoking Controllable on your system. That shows some intermediary results, but those might not make much sense to you unless you know what source lines are generating those results. You can see the source by issuing the command, showstat(DynamicSystems::ControllableSS);

Here's an example,

restart:
with( DynamicSystems ):
aSys := StateSpace( <<1,2>|<3,4>>, <<2,3>>, <<1,0>|<0,1>>, <<0,0>> ):
aSys:-a, aSys:-b, aSys:-c:
trace(DynamicSystems::ControllableSS):
Controllable( aSys );
showstat(DynamicSystems::ControllableSS);

By looking at the source of the ControllableSS routine, you can deduce that it calls DynamicSystems:-StaircaseTransformation when the staircase method is specified. So here too you could issue showstat(DynamicSystems::StaircaseTransformation) to see the source of that internal (local) routine. Or you could trace that routine as well.

As a general rule, you can refer to exports of a module or package using the :- notation. And you can pass such names to trace and showstat using the :: notation instead of :-, unless you have first set kernelopts(opaquemodules=false). If an inner submodule member has more than one :- in its name then you'd have to use round-bracket delimiters to refer to it with the :: syntax. Sorry, that that's not so easy to express.