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...l> between the coefficients of a Hypercomplex number and the corresponding Hypercomplex number.}} ...fficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number. '''This capability has been replaced by the [[Condense]] function

<td>converts <apll>R</apll> to a Hypercomplex array if <apll>(⍴R)[X]∊2 4 8</apll> or a Real array if <apll>(⍴R)[X]= .../apll>-axis of <apll>R</apll> as the coefficients of the resulting Real or Hypercomplex array. If

<td>extracts from <apll>R</apll> its Hypercomplex coefficients.</td> <td><apll>R</apll> is an arbitrary Real or Hypercomplex numeric array &mdash; otherwise, <apll>DOMAIN ERROR</apll>.</td>

<td valign="baseline"><b>Hypercomplex Point Notation</b>:</td> ...that is, infinite precision integers are actually represented as rational numbers with a denominator of <apll>1</apll>. However, this suffix cannot be used a

...Integers have <apll>63</apll> bits of precision and 64-bit Floating Point numbers have only <apll>53</apll>.<br /> The industry standard definition of the Floor function on Complex numbers is McDonnell's. However, McDonnell's Floor function isn't defined on Quate

* [[Rational and VFP Numbers|Rational Numbers]]: <apll>1<_r/>3</apll> and <apll>12345<_x/></apll>

...loating point values instead of a single representative. This allows such numbers to reflect their inexactness explicitly.

...er the number of bits per element (where appropriate), or for Hypercomplex numbers, the internal representation of the coefficients:</p> ...urned value <apll>Z</apll> may alternatively be: numeric scalar, vector of numbers, or a character string - depending on what the value of left argument <apll

...0 for GSL. The accuracy on both Multiple-Precision FP and Ball Arithmetic numbers is even more impressive because there the precision can be increased so as ...1..7</apll>. In practice, the above calculations are all done as Rational Numbers so as not to lose precision were they to be done in Floating Point.</i>

...hese variants are non-trivial only when multiplying <b>Non-commutative</b> numbers.<br />The following definitions on scalar <apll>L</apll> and <apll>R</apll> ...in the right operand, it is applied to the Index Origin; if there are two numbers, the first is applied to the Index Origin and the second to the Comparison