The expression

The stope is a variant of the power

x + s * i. n [ x=: 7 [ n=: 5 [ s=: _1 7 6 5 4 3 (*/x + s * i. n);(x ^!.s n);(x ^!.0 n);(x^n) +----+----+-----+-----+ |2520|2520|16807|16807| +----+----+-----+-----+The phrase

P=: 1 : '+/@([ * ] ^!. x i.@#@[)"1 0' c=: 1 3 3 1 [ d=: 1 7 6 1 [ x=: 0 1 2 3 4 (c p. x);(c 0 P x);(d _1 P x);(d p.!._1 x) +-------------+-------------+-------------+-------------+ |1 8 27 64 125|1 8 27 64 125|1 8 27 64 125|1 8 27 64 125| +-------------+-------------+-------------+-------------+As illustrated above, stope polynomials are (for a suitable choice of coefficients) equivalent to ordinary polynomials. Moreover, the transformations between them are provided by a matrix product as follows:

VM=: 1 : '[ ^!.x/ i.@#@]' TO=: 2 : '(x VM %. y VM)~ @i.@#' (0 TO _1 c) +/ . * c 1 7 6 1The matrices

(0 TO _1 i.5);(_1 TO 0 i.5) +---------+------------+ |1 0 0 0 0|1 0 0 0 0| |0 1 1 1 1|0 1 _1 2 _6| |0 0 1 3 7|0 0 1 _3 11| |0 0 0 1 6|0 0 0 1 _6| |0 0 0 0 1|0 0 0 0 1| +---------+------------+The stope polynomial is also provided by the variant

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