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Question: Compared behaviours of type and pat match

Question:Compared behaviours of type and pat match

mmcdara 7349 Maple
multiplication patmatch type addition
February 09 2025
2

Could you explain me why the three forms of patmatch behave identically (which seems natural) but the three forms of type do not.
Is there a way to define the type in type such that this latter returns the same thing for a*f(x)+b, f(x)*a+b, b+a*f(x), b+f(x)*a ?

> 

Z := f(x)*a+b;
t1 = type(Z, `&+`(algebraic, `&*`(algebraic, function)));
t2 = type(Z, `&+`(`&*`(algebraic, function), algebraic));
t3 = type(Z, `&+`(`&*`(function, algebraic), algebraic));

f(x)*a+b

  

t1 = false

  

t2 = false

  

t3 = true

 (1)
> 

p1 = patmatch(Z, A::algebraic*f(X::algebraic) + B::algebraic, 'pat');
pat;
p2 = patmatch(Z, B::algebraic + A::algebraic*f(X::algebraic), 'pat');
pat;
p2 = patmatch(Z, B::algebraic + f(X::algebraic)*A::algebraic, 'pat');
pat;

p1 = true

  

[A = a, B = b, X = x]

  

p2 = true

  

[A = a, B = b, X = x]

  

p2 = true

  

[A = a, B = b, X = x]

 (2)
 

 

Download type_vs_patmatch.mw

TIA
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