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!