Ctadel: Symbolic Simplification
Generation of efficient codes for numerical problems requires extensive simplification of commuting operators
(through operator commuting diagrams).
For example, the rule
|
|
æ
è
|
B
å
I = A
|
X |
ö
ø
|
+ |
æ
è
|
B
å
I = A
|
Y |
ö
ø
|
Þ |
B
å
I = A
|
(X+Y) |
|
is specified in Ctadel as
sum(X,I=A..B) + sum(Y,I=A..B) => sum(X+Y,I=A..B)
can be applied on the expression
|
|
æ
è
|
m
å
j = 1
|
|
æ
è
|
n
å
i = 1
|
uij |
ö
ø
|
ö
ø
|
+ |
æ
è
|
n
å
i = 1
|
vi |
ö
ø
|
|
|
resulting in
|
|
n
å
i = 1
|
|
æ
è
|
æ
è
|
m
å
j = 1
|
uij |
ö
ø
|
+vi |
ö
ø
|
|
|
because the sum operation is ``self-commuting''.
This means that LHS of transformation rules can be specified independently of the operator commuting properties.
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File translated from TEX by TTH, version 2.21.
On 8 Oct 1999, 14:27.