the third expression uses this definition: "A saddle point of a matrix is an element which is both the largest element in its column and the smallest element in its row." -W
golfed: ⍉↑⍸(⌊/∘.=⌈⌿)NM
if IS means int scalar, this one makes no sense: (0,⍳(⍴XV)-IS)∘.+IS why the ∘. ?
probably a missing ⍳ after ∘.+
also, it relies on ⎕io←1
golfed: ↑IS,/⍳≢XV
"Number of ?s intersecting ?s". ?s = "intervals" or "segments"
"Repeat matrix" - i can see what it does but i don't understand how it could be useful
"XV[⍋BV++\BV] Rotate first elements (1⌽) of subvectors of XV indicated by BV." - as it says :) note that a 1 in BV marks the beginning of a subvector (unlike the first finnapl entry in which stretches of 1s were used to highlight whole subvectors)
the rest look boring. the ancient finns didn't have ⍤ and tao.
</ works on the vector of differences between two rows, and is supposed to report whether the first non-0 difference d is negative, but it fails when there's a 0<d<1
@Adám hard to describe with english words. it finds the beginning of each group of consecutive identical items in XV1, except that size-1 groups are ignored. then it gets the corresponding elements in XV2 and does ∘.= of them with XV2 itself
@Adám NV1 and NV2 describe segments on the real line. NV1 are the start points, NV2 are the end points. the expression computes how many of those segments intersect. perhaps it should be +/, instead of +/