blob: e807f91f34cc576b66d2b67b52f94f1ecdc8ee0b (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
|
% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
\newcommand{\HexadecimalExpansionXmpTitle}{HexadecimalExpansion}
\newcommand{\HexadecimalExpansionXmpNumber}{9.33}
%
% =====================================================================
\begin{page}{HexadecimalExpansionXmpPage}{9.33 HexadecimalExpansion}
% =====================================================================
\beginscroll
All rationals have repeating hexadecimal expansions.
The operation \spadfunFrom{hex}{HexadecimalExpansion} returns these
expansions of type \spadtype{HexadecimalExpansion}.
Operations to access the individual numerals of a hexadecimal expansion can
be obtained by converting the value to \spadtype{RadixExpansion(16)}.
More examples of expansions are available in the
\downlink{`DecimalExpansion'}{DecimalExpansionXmpPage}\ignore{DecimalExpansion},
\downlink{`BinaryExpansion'}{BinaryExpansionXmpPage}\ignore{BinaryExpansion}, and
\downlink{`RadixExpansion'}{RadixExpansionXmpPage}\ignore{RadixExpansion}.
\showBlurb{HexadecimalExpansion}
\xtc{
This is a hexadecimal expansion of a rational number.
}{
\spadpaste{r := hex(22/7) \bound{r}}
}
\xtc{
Arithmetic is exact.
}{
\spadpaste{r + hex(6/7) \free{r}}
}
\xtc{
The period of the expansion can be short or long \ldots
}{
\spadpaste{[hex(1/i) for i in 350..354] }
}
\xtc{
or very long!
}{
\spadpaste{hex(1/1007) }
}
\xtc{
These numbers are bona fide algebraic objects.
}{
\spadpaste{p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9) \bound{p}}
}
\xtc{
}{
\spadpaste{q := D(p, x) \free{p}\bound{q}}
}
\xtc{
}{
\spadpaste{g := gcd(p, q) \free{p}\free{q}}
}
\endscroll
\autobuttons
\end{page}
%
|
