Dear all,
In writing a routine for QR decomposition of matrices
(http://rosettacode.org/wiki/QR_decomposition#Axiom), I needed a domain that
combined Fields (+,-,*,/), RadicalCategory (sqrt - for normed length of a
vector) and OrderedRing (sign). I satisfied this using:
if not(R has OrderedRing) and R has ConvertibleTo(Float) then
sign(x:R):Integer == sign(convert(x)$R @ Float)
Pleasantly, this allows a QR decomposition using Integers, Fractions or
AlgebraicNumbers (as well as Float and DoubleFloat):
m := matrix [[12, -51, 4], [6, 167, -68], [-4, 24, -41]];
qr m
+ 6 69 58 +
|- - --- --- |
| 7 175 175 |
| | +- 14 - 21 14 +
| 3 158 6 | | |
(2) [q= |- - - --- - ---|,r= | 0 - 175 70 |]
| 7 175 175| | |
| | + 0 0 - 35+
| 2 6 33 |
| - - -- -- |
+ 7 35 35 +
Type: Record(q: Matrix(AlgebraicNumber),r: Matrix(AlgebraicNumber))
Is there a better solution to this problem?
Kindly, Mark.
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