Ideas for new operators

[dloscutoff]

This issue is a place to brainstorm potentially useful new operators. Most of these, if they are implemented, will become 2-uppercase-letter operators; some will be 2-byte symbolic operators. Feel free to make suggestions in the comments. Also, if you see an idea you like, feel free to implement it and make a pull request!

• [x] Chop: split an iterable into n chunks of (roughly) equal size; unary version splits into two chunks (CH, or possibly >< because it's the converse of <>)
• [x] Flatten List (FL for flattening one level, FA for FlattenAll)
• [x] Map and flatten (MF)
• [x] Filter-enumerate: filters an iterable, but the first argument to the function is the index of the element and the second is the element itself (FE)
• [x] Filter-unpack: filters an iterable, but the arguments to the function are the elements of each element rather than the element itself (FU)
• [x] Filter negated: keeps elements for which the function returns a falsey value (FN)
• [x] Filter and join (FJ)
• [ ] Filter and flatten (FF)
• [x] Filter indexes: like FE, but returns a list of indexes instead of a list of elements (FX)
• [ ] Take-while and drop-while (TW and DW)
• [ ] Fold on function (FO for [left] Fold, FR for FoldRight)
• [ ] Iterate function (IW for Iterate While truthy, IU for Iterate Until truthy, IQ for Iterate while uniQue)
• [ ] Pad with spaces (LS for LeftSpace, RS for RightSpace, BS for BothSpace; or PL for PadLeft, PR for PadRight, PC for PadCentered)
• [ ] Left-pad with zeros (LZ for LeftZero; or ZP for ZeroPad)
• [ ] Base-conversion operator that takes a width and left-pads with zeros
• [ ] Pad with arbitrary character
• [ ] Wrap in parentheses (WP? or PN or PT for PareNThesize?)
• [x] Bit-length (how many bits are in the binary representation of a number) (BL)
• [ ] Rotate iterable left/right
• [x] Title-case (capitalize first letter of each run of letters) (TC)
• [x] Initial caps (capitalize first letter of string) (IC)
• [x] Round up, down, toward zero, to nearest (>| for round up, |< for round down, RZ for RoundZero, RN for RoundNearest)
• [ ] Keyed versions of MN and MX, analogous to SK (NK for MinKey, MK for MaxKey)
• [ ] String versions of MN and MX, analogous to SS (MS isn't available, so maybe LS for LeastString and GS for GreatestString)
• [x] Sort in descending order (DN for DescendingNumeric, DS for DescendingString)
• [x] Sort keyed in descending order (DK)
• [ ] Trim list (does the same thing as TM but works on Lists instead of Scalars) (TL)
• [ ] Join on list/element (concatenate list or insert element between consecutive elements of list) (JL and JE)
• [ ] Wrap in list (unary, binary, and maybe ternary versions) (WL or maybe WS for WrapSingleton, WP for WrapPair, WT for WrapTriple--maybe WL has unary and binary versions, but then there's also WS that's only unary?)
• [ ] Cartesian power (CW, or maybe CE by analogy to E for Exponential)
• [ ] Power set, i.e. list of all subsets (PS)
• [x] A version of Z that, given a list of strings, pads with spaces and returns a list of strings rather than a list of lists of characters (ZJ for ZipJoin, by quasi-analogy to MJ)
• [ ] Versions of zip and weave that cycle the shorter list(s) (ZC and WC)
• [x] A version of HV that rounds up instead of down (HU)
• [ ] Non-cyclically-indexing version of @ (returns nil when out of bounds; possibly extends iterable when out of bounds as an lvalue) (maybe EA for ElementAt, IA for ItemAt, or AI for AtIndex?)
• [ ] One-based indexing (\@, with a unary version that gets the last element)
• [x] Random shuffle (SH)
• [ ] Various triangular matrices
• [ ] Reversed identity matrix (RY, by analogy with EY?)
• [ ] Euclidean norm (ED for EuclideanDistance, or HY for HYpotenuse?)
• [ ] Dot product (DP)
• [ ] Convolution (CV, maybe also VT for ConvolutionTrimmed to the size of the bigger input)
• [x] Log base 2 and base 10 (LB for LogBinary, LD for LogDecimal)

[mathcat4]

• [ ] Factors
• [ ] Is prime?
• [ ] Prime factors
• [ ] Combinations with replacement
• [ ] Combinations without replacement
• [ ] All subsets