HaloO,
Ruud H.G. van Tol wrote:
Yes, it could use a step:
^42.7 = (0, 7, 14, 21, 28, 35)
^42.-7 = (35, 28, 21, 14, 7, 0)
OK, fine if the step sign indicates reversal after creation.
That is, the modulus is 7 in both cases.
^-42.7 = (-35, -28, -21, -14, -7, 0)
^-42.-7 = (0, -7, -14, -21, -28, -35)
I would make these
^-42.7 == (-42, -35, -28, -21, -14, -7)
^-42.-7 == ( -7, -14, -21, -28, -35, -42)
and (^-42.7 + ^42.7) has length 11, maybe better expressed as ^-42.7.42,
And the fact that you concatenate two six-element lists and get one with
*11* elements doesn't strike you as odd? I find it very disturbing! E.g.
when shifting by 42 rightwards I would expect
^-42.7.42 == (-42, -35, -28, -21, -14, -7, 0, 7, 14, 21, 28, 35)
to become
^84.7 == (0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77)
and of course
^84.7 »- 42;
or to more resemble your notation
-42 +« ^84.7;
beeing two other forms to write this kind. Ahh, and should there be
a warning about a remainder for
^45.7 == (0, 7, 14, 21, 28, 35, 42) # rest 3
and how should a negative---err---endpoint be handled? I opt for
^-45.7 == (-49, -35, -28, -21, -14, -7) # rest 4
But the warning could be avoided with some dwimmery after we
observe that 45 == 42 + 3 and -45 == -49 + 4 the respective rests
mean to shift the list rightwards accordingly
^45.7 == (3, 10, 17, 24, 31, 38, 45) # shift right 3
^-45.7 == (-46, -39, -30, -23, -18, -11, -4) # same
^-45.7 == (-45, -38, -31, -24, -17, -10, -3) # shift right 4
^45.7 == (4, 11, 18, 25, 32, 39, 46) # same
If you find the above odd, than use the homogenious cases
^45.7 == ( 3, 10, 17, 24, 31, 38, 45) # shift right 3
and
^-45.-7 == (-3, -10, -17, -24, -31, -38, -45) # reversed shift right -3
== -« ^45.7
which results in pairwise nullification as expected
^45.7 »+« ^-45.-7 == ^7.0 == (0,0,0,0,0,0,0)
Let's switch to a shorter example list and use the , to build
some subsets of int
^-21.7.0 , ^21.7.0 == (-21, -14, -7, 0, 7, 14) # length: 42/7 == 6
^-21.7.1 , ^21.7.1 == (-20, -13, -6, 1, 8, 15)
^-21.7.2 , ^21.7.2 == (-19, -12, -5, 2, 9, 16)
^-21.7.3 , ^21.7.3 == (-18, -11, -4, 3, 10, 17)
^-21.7.4 , ^21.7.4 == (-17, -10, -3, 4, 11, 18)
^-21.7.5 , ^21.7.5 == (-16, -9, -2, 5, 12, 19)
^-21.7.6 , ^21.7.6 == (-15, -8, -1, 6, 13, 20)
^-21.7.7 , ^21.7.7 == (-14, -7, 0, 7, 14, 21)
If the lists where extended on both sides to infinity then a
shift of 7 changes anything, as can be seen from the last line.
Hmm, the syntax is ambigous with respect to the . if we want to
allow steps < 1. Looks like a jobs for the colon:
^21:7:0 == (0, 7, 14)
^1:0.25 == (0, 0.25, 0.5, 0.75)
^1:0.2:0.2 == (0.2, 0.4, 0.6, 0.8, 1.0)
which perhaps just mean
^1:step(0.2):shift(0.2)
Please note that all of the above are *list literals* not
prefix ^ operator invocations. If one wants to become variable
in this type/kind then a @var is needed. A ^$x might be just
a short form of capturing the kind of $x into ^x which not
auto-listifies. Thus
my ^x $x = 7;
say ^x; # Int
say +$x; # 7
but
my ^a @a = (0,0,0);
say [EMAIL PROTECTED]; # 3
say ^a; # Array is shape(3) of Int
# Array[^3] of Int
# Array[ shape => 3, kind => Int ]
or however the structure of an array is printed.
which makes '^5' the short way to write '^5.1.0'.
And ^0 is *the* empty list. Hmm, and ^Inf.0 the infinite
list full of zeros (0, 0, 0, ...), ^Inf.1 are of course
the non-negative integers in a list (0, 1, 2, ...). Then
if we hyperate it and pick the last entry (^Inf.1 »+ 1)[-1]
we get the first transfinite ordinal Omega[0]. From there we
keep counting transfinitely...
And of course 10 * ^0.pi == 3.14...
--
$TSa.greeting := "HaloO"; # mind the echo!
