1 chain with 2 bits set
Notation:
@(.) means 2^(.)
p,q are free nonnegative integer variables
A,B are also free nonnegative integer variables
* in the index-list as a right sub_index indicates a doubling step.
: is a delimiter in the sub-index to refine this sub-index by a further 'value'.
Such a 'value' is in general a polynomial of degree 0 or 1 in one variable
[i.e. an affine form with integer coefficients and dimension less or equal 1].
This 'value' indicates either in a doubling step how many doubling steps are here,
or when using a doubling step in another index how many doubling steps are used there.
If a doubling step is used with exactly as many doubling steps it was generated then this
delimiter and 'value' is optional [E.g. It may be left out in the left sub-index for every star-chain].
In all two-power-sum representations the two-power-exponents are always strictly monotonic decreasing and >= 0.
Shortest Addition Chains with 1 Small Step
2* @(p)+@(q)
A=p, B=q
0( ) 1
1( 0, *:A) @(A)
2( 1, 1:B) @(A)+@(B)