It possible to expand numbers in general bases.
Here we expand 111 in base 5. This means
10^2+10^1+10^0 = 4 * 5^2+2 * 5^1 + 5^0
111::RadixExpansion(5)
421
Type: RadixExpansion 5
You can expand fractions to form repeating expansions.
(5/24)::RadixExpansion(2)
__
0.00110
Type: RadixExpansion 2
(5/24)::RadixExpansion(3)
__
0.012
Type: RadixExpansion 3
(5/24)::RadixExpansion(8)
__
0.152
Type: RadixExpansion 8
(5/24)::RadixExpansion(10)
_
0.2083
Type: RadixExpansion 10
For bases from 11 to 36 the letters A through Z are used.
(5/24)::RadixExpansion(12)
0.26
Type: RadixExpansion 12
(5/24)::RadixExpansion(16)
_
0.35
Type: RadixExpansion 16
(5/24)::RadixExpansion(36)
0.7I
Type: RadixExpansion 36
For bases greater than 36, the ragits are separated by blanks.
(5/24)::RadixExpansion(38)
_____
0 . 7 34 31 25 12
Type: RadixExpansion 38
The RadixExpansion type provides operations to obtain the individual ragits. Here is a rational number in base 8.
a := (76543/210)::RadixExpansion(8)
____
554.37307
Type: RadixExpansion 8
The operation wholeRagits returns a list of the ragits for the integral part of the number.
w := wholeRagits a
[5,5,4]
Type: List Integer
The operations prefixRagits and cycleRagits return lists of the initial and repeating ragits in the fractional part of the number.
f0 := prefixRagits a
[3]
Type: List Integer
f1 := cycleRagits a
[7,3,0,7]
Type: List Integer
You can construct any radix expansion by giving the whole, prefix and cycle parts. The declaration is necessary to let FriCAS know the base of the ragits.
u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1)
____
554.37307
Type: RadixExpansion 8
If there is no repeating part, then the list [0] should be used.
v: RadixExpansion(12) := fractRadix([1,2,3,11], [0])
_
0.123B0
Type: RadixExpansion 12
If you are not interested in the repeating nature of the expansion, an infinite stream of ragits can be obtained using fractRagits.
fractRagits(u)
_______
[3,7,3,0,7,7]
Type: Stream Integer
Of course, it’s possible to recover the fraction representation:
a :: Fraction(Integer)
76543
-----
210
Type: Fraction Integer
See Also: