The expressions for column order and row order computations are given below.
5) When all the columns have been placed, repeat the procedure on the rows using row order computation expression.
The column computation started as first and computes the optimal column order sequence and starts the row computation and computes the optimal row order sequence.
This fact motivated us to introduce a new stronger definition of a row-reduced system based on row orders (see Definitions 4 and 6).
Find, according to Definition 4, the row orders of system (5) as [mu] = (1,2).
Note that the difference stems from the difference between the row degrees and the row orders: the row orders [[mu].
mu]] are ordered with respect to row orders starting from the lowest and denote the rows by [L.
Then the equivalence transformation of system (1) can be found by solving the system of partial differential equations (17), resulting in the new system having the same row orders, except the (i + 1)th one which, by (18), is strictly less than [beta]i+1.
According to Definition 4, compute the row orders [mu] = ([[mu].