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In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using Excel. Because the sum has only eleven 1s after the decimal, the true difference when ‘1’ is subtracted is three 0s followed by a string of eleven 1s.
Set up an interim digit and initialize it to 0. Process the number digit by digit: Use the number's digit as column index and the interim digit as row index, take the table entry and replace the interim digit with it. The number is valid if and only if the resulting interim digit has the value of 0. [1]
Leading zeros are also present whenever the number of digits is fixed by the technical system (such as in a memory register), but the stored value is not large enough to result in a non-zero most significant digit. [7] The count leading zeros operation efficiently determines the number of leading zero bits in a machine word. [8]
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
All rows having only zero entries are at the bottom. [1] The leading entry (that is, the left-most nonzero entry) of every nonzero row, called the pivot, is on the right of the leading entry of every row above. [2] Some texts add the condition that the leading coefficient must be 1 [3] while others require this only in reduced row echelon form.
or the non-zero rows are all above the (eventual) zero rows, and the leading coefficient of a non-zero row which is not the first one is stricly to the right of the leading coefficent of the row above it.--Zebulon64 14:29, 7 March 2008 (UTC) A separate issue: In the current version, leading coefficients have to be 1.
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For each table, insert an alpha-prefix on each column (making each row-token "|-" to sort as column zero, like prefix "Row124col00"), then sort into a new file, and then de-prefix the column entries. Again, bear in mind, the tedious hand-editing of items in each row is often faster than the potential delay of automated edits gone awry.