Up to now my impression was that something declared via "operator" is
not automatically symmetric, i.e. T(X,Y) is not the same as T(Y,X).
cat bugNormalize.input |fricas -nosman > bugNormalize.out
It seems that normalize has a strange side effect on the application of
D. How else could there appear T_{,1,2}(Y(a,b),X(a,b)) in the output?
Ralf
PS: This is FriCAS revision 1506.
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)clear completely
T := operator 'T;X := operator 'X;Y := operator 'Y;
e := T(X(a,b),Y(a,b))
r1 := D(D(e,b),a)-D(D(e,a),b)
r2 := normalize r1
r3 := D(D(e,b),a)-D(D(e,a),b)
r1-r3
r2-r3
FriCAS Computer Algebra System
Version: FriCAS 518f5b10571e20d847efd2a54149ab7e8453153b
Timestamp: Friday February 22, 2013 at 20:59:43
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave FriCAS and return to shell.
-----------------------------------------------------------------------------
(1) -> )r bugNormalize.input
)clear completely
All user variables and function definitions have been cleared.
All )browse facility databases have been cleared.
Internally cached functions and constructors have been cleared.
)clear completely is finished.
T := operator 'T;X := operator 'X;Y := operator 'Y;
Type: BasicOperator
e := T(X(a,b),Y(a,b))
(2) T(X(a,b),Y(a,b))
Type: Expression(Integer)
r1 := D(D(e,b),a)-D(D(e,a),b)
(3)
T (X(a,b),Y(a,b))Y (a,b) - T (X(a,b),Y(a,b))Y (a,b)
,2 ,2,1 ,2 ,1,2
+
T (X(a,b),Y(a,b))X (a,b) - T (X(a,b),Y(a,b))X (a,b)
,1 ,2,1 ,1 ,1,2
+
(X (a,b)Y (a,b) - X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,2,1
+
(- X (a,b)Y (a,b) + X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,1,2
Type: Expression(Integer)
r2 := normalize r1
(4)
T (X(a,b),Y(a,b))Y (b,a) - T (X(a,b),Y(a,b))Y (a,b)
,2 ,1,2 ,2 ,1,2
+
T (X(a,b),Y(a,b))X (b,a) - T (X(a,b),Y(a,b))X (a,b)
,1 ,1,2 ,1 ,1,2
+
(X (a,b)Y (a,b) - X (a,b)Y (a,b))T (Y(a,b),X(a,b))
,1 ,2 ,2 ,1 ,1,2
+
(- X (a,b)Y (a,b) + X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,1,2
Type: Expression(Integer)
r3 := D(D(e,b),a)-D(D(e,a),b)
(5)
T (X(a,b),Y(a,b))Y (b,a) - T (X(a,b),Y(a,b))Y (a,b)
,2 ,1,2 ,2 ,1,2
+
T (X(a,b),Y(a,b))X (b,a) - T (X(a,b),Y(a,b))X (a,b)
,1 ,1,2 ,1 ,1,2
+
(X (a,b)Y (a,b) - X (a,b)Y (a,b))T (Y(a,b),X(a,b))
,1 ,2 ,2 ,1 ,1,2
+
(- X (a,b)Y (a,b) + X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,1,2
Type: Expression(Integer)
r1-r3
(6)
T (X(a,b),Y(a,b))Y (a,b) - T (X(a,b),Y(a,b))Y (a,b)
,2 ,2,1 ,2 ,1,2
+
- T (X(a,b),Y(a,b))Y (b,a) + T (X(a,b),Y(a,b))Y (a,b)
,2 ,1,2 ,2 ,1,2
+
T (X(a,b),Y(a,b))X (a,b) - T (X(a,b),Y(a,b))X (a,b)
,1 ,2,1 ,1 ,1,2
+
- T (X(a,b),Y(a,b))X (b,a) + T (X(a,b),Y(a,b))X (a,b)
,1 ,1,2 ,1 ,1,2
+
(X (a,b)Y (a,b) - X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,2,1
+
(- X (a,b)Y (a,b) + X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,1,2
+
(- X (a,b)Y (a,b) + X (a,b)Y (a,b))T (Y(a,b),X(a,b))
,1 ,2 ,2 ,1 ,1,2
+
(X (a,b)Y (a,b) - X (a,b)Y (a,b))T (X(a,b),Y(a,b))
,1 ,2 ,2 ,1 ,1,2
Type: Expression(Integer)
r2-r3
(7) 0
Type: Expression(Integer)
