Scalar function: Difference between revisions

A scalar function is one of a class of primitive functions that apply to arguments one [[element]] at a time. Dyadic scalar functions pair elements of their arguments based on [[conformability]] rules, and thus are subject to [[scalar extension]]. In [[Nested array model|nested]] array languages scalar functions recursively descend into nested arrays until they can be applied to [[simple scalars]]; in [[Flat array model|flat]] array languages they usually do not apply inside [[boxes]].

Only a particular [[valence]] of a function is labelled "scalar". The scalar monad [[Not]] usually shares the glyph <code>~</code> with non-scalar dyad [[Without]], and similarly scalar [[Roll]] and non-scalar [[Deal]] are both written <code>?</code>.

 

{|

| <code>-</code> || [[Negate]]

| <code>×</code> || [[Signum]] or Direction

| <code>÷</code> || [[Reciprocal]]

| <code>⌊</code> || [[Floor]]

| <code>⌈</code> || [[Ceiling]]

| <code>*</code> || [[Exponential]]

| <code>⍟</code> || [[Natural Logarithm]]

| <code><nowiki>|</nowiki></code> || [[Magnitude]]

| <code>!</code> || [[Factorial]]

| <code>○</code> || [[Pi Times]]

| <code>~</code> || [[Not]]

| <code>∊</code> || [[Type]]

|}

 

 

| <code>+</code> || [[Plus]]

| <code>-</code> || [[Minus]]

| <code>×</code> || [[Times]]

| <code>÷</code> || [[Divide]]

| <code>⌊</code> || [[Minimum]]

| <code>⌈</code> || [[Maximum]]

| <code>*</code> || [[Power function]]

| <code>⍟</code> || [[Logarithm]]

| <code><nowiki>|</nowiki></code> || [[Residue]]

| <code>!</code> || [[Binomial]] coefficient or combination function

| <code>○</code> || [[Circle function]]

| <code>∧</code> || [[Logical And]]

| <code>∨</code> || [[Logical Or]]

| <code>⍲</code> || [[Nand]]

| <code>⍱</code> || [[Nor]]

| <code><</code> || [[Less than]]