simplification functions

type-a index cannot be "9".

[Graphics:../Images/index_gr_521.gif]
[Graphics:../Images/index_gr_522.gif]

using the above fact.

[Graphics:../Images/index_gr_523.gif]

raising -9 to 9 for a unique expression.

[Graphics:../Images/index_gr_524.gif]

further simplification

[Graphics:../Images/index_gr_525.gif]

Ignore [Graphics:../Images/index_gr_526.gif] terms for scalar

[Graphics:../Images/index_gr_527.gif]

Ignore [Graphics:../Images/index_gr_528.gif] terms for tensor.

[Graphics:../Images/index_gr_529.gif]

Series expansion for scalar ignoring [Graphics:../Images/index_gr_530.gif]

[Graphics:../Images/index_gr_531.gif]

Series expansion for tensor  ignoring [Graphics:../Images/index_gr_532.gif]

[Graphics:../Images/index_gr_533.gif]
[Graphics:../Images/index_gr_534.gif]
[Graphics:../Images/index_gr_535.gif]

Define an operator to separate the regular index into the type-a index and dim.

[Graphics:../Images/index_gr_536.gif]

Define differential operator (for type-a index)

[Graphics:../Images/index_gr_537.gif]


Converted by Mathematica      July 21, 2003