Ok, I think I am starting to get the hang of this. So in Maple, structured types is like a pattern in Mathematica. To find some subexpression one needs to first define a structured type which match that subexpression, and then use  select(type,.....).  

This works well so far (but it is not as easy as setting up a pattern).

But one small problem is that select() starts looking at the operands of the expression to look for a match.

So if the whole expression itself matches the structured type, it will not detect the whole expression, since select goes over each operand, missing that the whole thing actually matches the type.

May be an example helps shows what I mean. I want to find if an expression has cos(anything)*sin(anything) so I made a structured type for this 

mytype_3 :=  ''`*`'( {'specfunc'(cos),'specfunc'(sin)})';

btw, I do not know if I should use `&*` or '`*`' but that is a side point, I'll try to find this out.   

Now I want to use the above to check if expression has the same "structured type", or "pattern". The expression is expr:=cos(x)*sin(x); clearly it matches it. But since select looks at the operands, it will only see cos(x) by itself, and then sin(x) by itself and hence not find the structured type. 

restart;
mytype_3 :=  ''`*`'( {'specfunc'(cos),'specfunc'(sin)})';
expr:=cos(x)*sin(x);
type(expr,mytype_3);  # true
select(type, expr, mytype_3); # does not work, does not find it.

Since I am doing this in code, and I do not know what the expression is, I think I have to now do the following 

restart;
mytype_3 :=  ''`*`'( {'specfunc'(cos),'specfunc'(sin)})';
expr:=cos(x)*sin(x);
if type(expr,mytype_3) then
   print("The whole expression is a match! nothing to do. no need to use select");
else
   select(type, expr, mytype_3);
fi;

Which is OK. I can do this, But it will be nice if there was a way to have select (or another function like it) starts at the top level before looking at the operands?  

How do others handle such cases? does the above sound like an OK solution to this?

I am learning how to use select with my own types defined, to find parts of expression. This is instead of using patmach.

For example, given   3+x^2*sin(x) and then I want to find any POLYNIMAL*sin function, if present. So I did the following

restart;
expr_1:=3+x^2*sin(x):
mytype_1 := `&*`( polynom(And(algebraic, satisfies(u -> not has(u, I))),x),specfunc('sin')):
select( z->type(z,mytype_1),expr_1);

Which works. Maple returned 

The problem is that if I change the order of multiplication, and also at same time change the polynomial by adding one more term, it no longer works!

I have no idea why. It seems Maple rememebrs something.  Here is a screen shot, followed by plain text code.

code

restart;
expr_1:=3+(1+x)*sin(x):
mytype_1 := `&*`( polynom(And(algebraic, satisfies(u -> not has(u, I))),x),specfunc('sin')):
select( z->type(z,mytype_1),expr_1);
expr_1:=3+sin(x)*(1+x):
select( z->type(z,mytype_1),expr_1);

#change polynomial but keep same order, it works
expr_2:=3+(1+x+x^2)*sin(x):
select( z->type(z,mytype_1),expr_2);

#change order BUT keep same polynomial, it works
expr_3:=3+sin(x)*(1+x+x^2):
select(z->type(z, mytype_1),expr_3);

#keep same order as above, but change polynomial, now it does not works
expr_4:=3+sin(x)*(1+x+x^2+x^4):
select(z->type(z, mytype_1),expr_4);

#keep same order as first one  but change polynomial, it does not work
expr_5:=3+(1+x+x^2+x^4)*sin(x):
select(z->type(z, mytype_1),expr_5);

#keep same order as first one but change polynomial back to what it was, now it works
expr_6:=3+(1+x)*sin(x):
select(z->type(z, mytype_1),expr_6);

What Am I doing wrong?

Maple 2021.1

I need to check if an expression is polynomial in x but with coefficients that are either symbolic, or do not include the complex numebr I.

The problem is that maple considers integers and reals complex also.   

type(1,complex) gives true. so I can't use

restart;
type(1+2*x,polynom(Not(complex),x))

Since this gives false. 

I could instead list all the types to be accepted using Or, like this

restart;
type(1+2*x,polynom(Or(float,realcons,rational,integer),x))

But I might overlook something if I have to enumerate every type accepted. It is easier to just exclude complex numbers. 

What is the correct way to tell Maple to check if expression is polynomial in x where coefficients do not have the complex I in them? It it ok if the coefficient are any other numeric value, or a known Maple constant, or a parameter (symbol). I just want to exclude complex numbers.

I know I could do this

restart;
the_poly:=1+2*x;
if not has(the_poly,I) then
   type(the_poly,polynom(anything,x))
else
   print("not allowed");
fi;

But I wanted to learn how to make a type which excludes complex numbers.

Maple 2021.1

Given an expressions such as 

expr:=sin(x)+cos(x)*exp(x)+x*tan(x)*f(x)+x+y;

I want to use indets to find only the mathematical functions in it, and also symbol but only x symbol in this above. I can do the following to find the mathematical functions and symbols, but I do not know how to tell it to find type symbol which happend to be x. Since x is not a type.

expr:=sin(x)+cos(x)*exp(x)+x*tan(x)*f(x)+x+y;
type_1:={function,typefunc(mathfunc)};
type_2:=symbol;
lis:=indets(expr,  Or( And(type_1),  type_2 ))

Which gives

But I really wanted this output

I know I can post process the outout using has or remove, to remove symbol y. But is it possible to do that using indets? something similar to specfunc but specsymbol ? I looked at the help page for Definition of a Structured Type in Maple but do not see anything there so far.

I tried

expr:=sin(x)+cos(x)*exp(x)+x*tan(x)*f(x)+x+y;
type_1:={function,typefunc(mathfunc)};
type_2:={symbol,identical(x)};
lis:=indets(expr,  Or( And(type_1),  And(type_2) ))

but it gives same output.

given one equation where both sides are polynomials in one variable x, like this

eq:=c1*(x^2+x)+c2*(2+2*x)+c3=-4*x^2+2*x+6;

And we want to solve for the coefficients on the LHS, which are c1,c2,c3.  By hand, this is solved by expanding both sides, and then comparing the coefficient of each power of x. This generates 3 equations (in this example) and then these are solved for c1,c2,c3.

Is there a way to automatically do this in Maple without the user having to do the first manual step of generating the equations needed to solve for c1,c2,c3?

eq1:=c1=-4;eq2:=c1+2*c2=2;eq3:=2*c2+c3=6;
PDEtools:-Solve([eq1,eq2,eq3],[c1,c2,c3])

gives

              {c1 = -4, c2 = 3, c3 = 0}

But It will be nice if there is a command in Maple which will do it starting from the first equation. Ofcourse one has to tell Maple what to solve for. PDEtools:-Solve(eq,[c1,c2,c3]); or solve(eq,[c1,c2,c3]) does not work, because Maple does not know it needs to expand and compare coefficients as we do by hand.

It is not hard to write code to generate these equations, but I am asking if there is already a command in Maple which somehow does it automatically. I looked at SolveTools, but did not spot something yet there.

edit

Ok, I think this is easy to do. I found a command

eq:=c1*(x^2+x)+c2*(2+2*x)+c3=-4*x^2+2*x+6;
eqs:=PolynomialTools:-CoefficientList((lhs-rhs)(eq),x);
PDEtools:-Solve(eqs,[c1,c2,c3])

{c1 = -4, c2 = 3, c3 = 0}