nm

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These are questions asked by nm

help on structured type says

| identical(expr) an expression identical to expr

and

The type identical(expr) matches the expression expr identically. If there is more than one expr (i.e. identical(expr1,expr2,...)), then this type matches any one of the exprN identically.
 

Then why does the following produce the same output?

restart;
expr:=x*A[2]+A[1];
select(type,expr,'`*`'({anything, identical(x^2)}));
select(type,expr,'`*`'({anything, identical(x)}))

x*A[2]

x*A[2]


I would have expected only the second select to find x*A[2].

What do I need to only select anything*x^2 without selecting anything*x ?

Actually anything in identical gives same result

select(type,expr,'`*`'({anything, identical(zzzzz)}));

x*A[2]

So I must be misunderstanding something about identical and how it works.  I want to match only anything*x^2 and nothing else. How to do that?

all these things are trivial to do use pattern matching. But in Maple, one is supposed to use structured types.

 

I can't figure this one out.

I need to pick out the subexpression   anything*sin(3*x) from an expression.

it works, when the expression is   anything*sin(3*x)+something else. But when the expression is exactly  anything*sin(3*x) then select returns and not anything*sin(3*x) as I was expecting.

So I must be doing something silly, but do not see it.

restart;
TypeTools:-AddType('type_1', '`*`'({anything,identical(exp(3*x))}));
expr:=25*A[1]*exp(3*x);
type(expr,type_1);

returns true. good. Now I test it on 

select(type,expr+sin(x),type_1) ;

and this returns what is expected. 25*A[1]*exp(3*x) but when I type

select(type,expr,type_1) ;

it return

reading select help page did not help.  Tried flatten, inplace.

I can do this using patmatch

patmatch(expr,a::anything*exp(3*x),'la');la

But why is select not working in the above? What is the correct way to do this so it works for a*expr+anything and also for a*expr only? This is done inside a function and not interactive. So I need it to work for both cases, since the input can be anything, but I only need the term anything*exp(3*x) pulled out.

 

I want to have a proc, which returns an expression using an indexed symbol. The proc needs to basically generate constansts to use to build an expression, similar to how dsolve uses _Cn.  But I do not want to use _Cn for this so not to confuse the expression with another one that was generated using _Cn already.

So I thought to use a local symbol say A.  (I could have used _Zn also, but I think _Z is also used by Maple).

The symbol A is first declared local to the proc, and then the proc returns the expression using A[n]. For example  A[0]*x+A[1]*x^2 etc... The number of A[n]'s is not known before hand, but should not be more than 10. 

I want to make sure that A[n] returned is really part of the local symbol and not different symbol to avoid clash with any global A[n] 

When I do the following check

restart;
foo:=proc()
 local A;
 return A[99]
end proc;

expr:=foo()

type(expr,`global`)

gives

good. So Maple says that A[99] is not global. But when I do

type(expr,`local`)

it also says false!

My question is: When making local A , will A[1] and A[2] also be local, or are they different symbols? Maplemint says nothing about it, so I assume A[n] is local also?

maplemint(foo)
Procedure foo() 
  These local variables were used but never assigned a value:  A

It did not say that A[99] was never declared local. This tells me that A[99] is local, because A is local. But then why did type(expr,`local`)  say false?

Given an expression, how to best find the constants _C1, _C2, etc.... in this expression?  Currently I do the following, but I think there should be a better way.

restart;
sol:=dsolve(diff(y(x),x$2)+y(x)=1);
indets(sol);
select(x->`if`(type(x,symbol) and convert(x,string)[1..2]="_C",true,false),indets(sol))

The above works, at least on the few examples I tried it on, but is there a better way to do it?  All constants will have the form _Cn where n is integer. 

 

 

Which one of these two versions, is the recommened one to use? For example, to check for type  integer*x, where x is literal x. i.e. identical(x)

restart;
TypeTools:-AddType('type_1', `&*`(integer,identical(x)));
type(3*x,type_1);

restart;
TypeTools:-AddType('type_1', '`*`'({integer,identical(x)}));
type(3*x,type_1)

Both work.  The difference is that `*` needs {} while `&*` does not.

I read the help page  and I do not understand what it says about the difference, and when is one supposed to use `*` vs. `&*`. it says 

              | `*`(type)  a product of factors of the given type
              | `&*`(type*)  a product of factors in which the nth factor is of the nth type specified in type*

Could possibly someone please explain in simple plain english what is the difference? If I use `&*`  vs. `*` with {}, will they work the same all the time or are there cases when to use one vs. the other?  Any rules of thumb to follow?

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