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Question: Should this be considered a simplify bug?

Question:Should this be considered a simplify bug?

mmcdara 6730 Maple 2015
December 25 2023
3

A case where simplify(...) and simplify~(...) both return the wrong result.
Should we consider this a simplify bug?

> 

restart:


A simple case

> 

J := Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity)
     *
     Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity)

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity))

 (1)
> 

# OK

op(1, J) = simplify(op(1, J))

Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity) = Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity)

 (2)
> 

# OK

op(2, J) = simplify(op(2, J))

Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity) = Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity)

 (3)
> 

# But...
#
# Not OK

simplify(J)

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[1]^2*varphi[2](r[1]), r[1] = -infinity .. infinity))

 (4)
> 

# Not OK

simplify~(J)

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[1]^2*varphi[2](r[1]), r[1] = -infinity .. infinity))

 (5)
> 

# OK

map(simplify, J)

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity))

 (6)


A slightly more complex case

> 

J := (Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity))-(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]*varphi[2](r[2]), r[2] = -infinity .. infinity))^2;

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity))-(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]*varphi[2](r[2]), r[2] = -infinity .. infinity))^2

 (7)
> 

is(J=simplify(J))

false

 (8)
> 

is(J=simplify~(J))

false

 (9)
> 

is(J=map(simplify, J));
map(simplify, J);

false

  

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[1]^2*varphi[2](r[1]), r[1] = -infinity .. infinity))-(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[1]*varphi[2](r[1]), r[1] = -infinity .. infinity))^2

 (10)
> 

add(map(u -> map(simplify, u), [op(J)]));

is(J=%);

(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]^2*varphi[2](r[2]), r[2] = -infinity .. infinity))-(Int(r[1]^2*varphi[1](r[1]), r[1] = -infinity .. infinity))*(Int(r[2]*varphi[2](r[2]), r[2] = -infinity .. infinity))^2

  

true

 (11)
> 

 

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