2
edits
(small typo) |
No edit summary |
||
Line 1: | Line 1: | ||
{{Infobox array language | {{Infobox array language | ||
| logo = [[File:Nars2000.png]] | | logo = [[File:Nars2000.png]] | ||
Line 32: | Line 33: | ||
=== Functions === | === Functions === | ||
One feature of NARS2000 is its heavy use of experimental primitive functions & operators. In the table below, symbols which are unknown or obscure in the APL world are linked to the NARS2000 wiki rather than the APL wiki. | |||
{| class=wikitable | {| class=wikitable | ||
Line 38: | Line 41: | ||
| <source lang=apl inline>⍸</source> || [[Indices]] || Array Lookup (high-rank [[Index-Of]]) | | <source lang=apl inline>⍸</source> || [[Indices]] || Array Lookup (high-rank [[Index-Of]]) | ||
|- | |- | ||
| <source lang=apl inline><</source> || [ | | <source lang=apl inline><</source> || [http://wiki.nars2000.org/index.php?title=Condense Condense] || [[Less Than]] | ||
|- | |- | ||
| <source lang=apl inline>></source> || [ | | <source lang=apl inline>></source> || [http://wiki.nars2000.org/index.php?title=Dilate Dilate] || [[Greater Than]] | ||
|- | |- | ||
| <source lang=apl inline>\</source> || || [[Expand]] | | <source lang=apl inline>\</source> || || [[Expand]] | ||
Line 54: | Line 57: | ||
| <source lang=apl inline>⊂</source> || || [[Partitioned Enclose]] | | <source lang=apl inline>⊂</source> || || [[Partitioned Enclose]] | ||
|- | |- | ||
| <source lang=apl inline>π</source> || [ | | <source lang=apl inline>π</source> || [http://wiki.nars2000.org/index.php?title=Primes Prime Factors] || [http://wiki.nars2000.org/index.php?title=Primes Number Theory] | ||
|- | |- | ||
| <source lang=apl inline>⍴</source> || [[Shape]] || [[Reshape]] | | <source lang=apl inline>⍴</source> || [[Shape]] || [[Reshape]] | ||
Line 60: | Line 63: | ||
| <source lang=apl inline>√</source> || [[Square Root]] || [[Root]] | | <source lang=apl inline>√</source> || [[Square Root]] || [[Root]] | ||
|- | |- | ||
| <source lang=apl inline>..</source> || || [ | | <source lang=apl inline>..</source> || || [http://wiki.nars2000.org/index.php?title=Sequence Sequence] | ||
|- | |- | ||
| <source lang=apl inline>⊆</source> || || [ | | <source lang=apl inline>⊆</source> || || [http://wiki.nars2000.org/index.php?title=Sets#subset Subset] | ||
|- | |- | ||
| <source lang=apl inline>⊇</source> || || [ | | <source lang=apl inline>⊇</source> || || [http://wiki.nars2000.org/index.php?title=Sets#superset Superset] | ||
|- | |- | ||
| <source lang=apl inline>§</source> || || [ | | <source lang=apl inline>§</source> || || [http://wiki.nars2000.org/index.php?title=Sets#symmetric_difference Symmetric Difference] | ||
|- | |- | ||
| <source lang=apl inline>~</source> || [[Not]] || [[Without]] | | <source lang=apl inline>~</source> || [[Not]] || [[Without]] | ||
|- | |||
| <source lang=apl inline>≤</source> || [http://wiki.nars2000.org/index.php?title=Ball_Arithmetic#Contract Contract] || [[Less Than or Equal]] | |||
|- | |||
| <source lang=apl inline>≥</source> || [http://wiki.nars2000.org/index.php?title=Ball_Arithmetic#Distract Distract] || [[Greater Than or Equal]] | |||
|} | |} | ||
=== Operators === | === Operators === | ||
{| class=wikitable | {| class=wikitable | ||
! Glyph !! Valence !! Monadic call !! Dyadic call | ! Glyph !! Valence !! Monadic call !! Dyadic call | ||
|- | |- | ||
| <source lang=apl inline>⍣</source> || Dyadic ||colspan=2| [ | | <source lang=apl inline>⍣</source> || Dyadic ||colspan=2| [http://wiki.nars2000.org/index.php?title=Power Power] | ||
|- | |- | ||
| <source lang=apl inline>⍨</source> || Monadic || | | <source lang=apl inline>⍨</source> || Monadic || [http://wiki.nars2000.org/index.php?title=Commute-Duplicate Duplicate] || [http://wiki.nars2000.org/index.php?title=Commute-Duplicate Commute] | ||
|- | |- | ||
| <source lang=apl inline>⍥</source> || Dyadic ||colspan=2| Composition ([[Over]]) | | <source lang=apl inline>⍥</source> || Dyadic ||colspan=2| Composition ([[Over]]) | ||
Line 90: | Line 95: | ||
| <source lang=apl inline>‼</source> || Monadic || [http://wiki.nars2000.org/index.php/Combinatorial Combinatorial] || | | <source lang=apl inline>‼</source> || Monadic || [http://wiki.nars2000.org/index.php/Combinatorial Combinatorial] || | ||
|- | |- | ||
| <source lang=apl inline>⍡</source> || Dyadic || || [ | | <source lang=apl inline>⍡</source> || Dyadic || || [http://wiki.nars2000.org/index.php?title=Convolution Convolution] | ||
|- | |- | ||
| <source lang=apl inline>.</source> || Dyadic || [ | | <source lang=apl inline>.</source> || Dyadic || [http://wiki.nars2000.org/index.php?title=Determinant_Operator Determinant] || [[Inner Product]] | ||
|- | |- | ||
| <source lang=apl inline>∂</source> || Monadic ||colspan=2| Numerical [http://wiki.nars2000.org/index.php/Derivative Derivative] | | <source lang=apl inline>∂</source> || Monadic ||colspan=2| Numerical (Partial) [http://wiki.nars2000.org/index.php/Derivative Derivative] | ||
|- | |- | ||
| <source lang=apl inline>∫</source> || Monadic ||colspan=2| Numerical [http://wiki.nars2000.org/index.php/Integral Integral] | |||
|- | |||
| <source lang=apl inline>⌻</source> || Monadic ||colspan=2| [http://wiki.nars2000.org/index.php/Matrix Matrix] | | <source lang=apl inline>⌻</source> || Monadic ||colspan=2| [http://wiki.nars2000.org/index.php/Matrix Matrix] | ||
|- | |- | ||
Line 102: | Line 109: | ||
| <source lang=apl inline>⊙</source> || Monadic ||colspan=2| [http://wiki.nars2000.org/index.php/Null Null] | | <source lang=apl inline>⊙</source> || Monadic ||colspan=2| [http://wiki.nars2000.org/index.php/Null Null] | ||
|- | |- | ||
| <source lang=apl inline>a∘/</source> || Special || || [ | | <source lang=apl inline>a∘/</source> || Special || || [http://wiki.nars2000.org/index.php?title=Compose#Mask Mask] | ||
|- | |- | ||
| <source lang=apl inline>a∘⌿</source> || Special || || [ | | <source lang=apl inline>a∘⌿</source> || Special || || [http://wiki.nars2000.org/index.php?title=Compose#Mask Mask] First | ||
|- | |- | ||
| <source lang=apl inline>a∘\</source> || Special || || [[Mesh]] | | <source lang=apl inline>a∘\</source> || Special || || [[Mesh]] | ||
Line 110: | Line 117: | ||
| <source lang=apl inline>a∘⍀</source> || Special || || [[Mesh]] First | | <source lang=apl inline>a∘⍀</source> || Special || || [[Mesh]] First | ||
|- | |- | ||
| <source lang=apl inline>⍠</source> || Dyadic ||colspan=2| [[ | | <source lang=apl inline>⍠</source> || Dyadic ||colspan=2| [http://wiki.nars2000.org/index.php?title=Variant Variant] | ||
|- | |||
| <source lang=apl inline>≈</source> || Monadic ||colspan=2| [http://wiki.nars2000.org/index.php?title=Ball_Arithmetic Ball Arithmetic] | |||
|} | |||
== Datatypes == | |||
Along with the Real numbers, NARS2000 supports the rest of the four [https://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(composition_algebras) Normed Division Algebra] datatypes: Complex, Quaternion, and Octonion numbers, along with several Multi-Precision datatypes, and signed Infinities: | |||
{| class=wikitable | |||
! Notation !! Datatype | |||
|- | |||
| <source lang=apl inline>1i2</source> || [http://www.sudleyplace.com/APL/Hypercomplex%20Numbers%20in%20APL.pdf Complex] | |||
|- | |||
| <source lang=apl inline>1i2j3k4</source> || [http://www.sudleyplace.com/APL/Hypercomplex%20Numbers%20in%20APL.pdf Quaternion] | |||
|- | |||
| <source lang=apl inline>1i2j3k4l5ij6jk7kl8</source> || [http://www.sudleyplace.com/APL/Hypercomplex%20Numbers%20in%20APL.pdf Octonion] | |||
|- | |||
| <source lang=apl inline>2.2x</source> || [http://wiki.nars2000.org/index.php?title=Rational_and_VFP_Numbers Rational Numbers] | |||
|- | |||
| <source lang=apl inline>2.2v</source> || [http://wiki.nars2000.org/index.php?title=Rational_and_VFP_Numbers Variable-precision Floating Point Numbers] | |||
|- | |||
| <source lang=apl inline>2.2±</source> || [http://wiki.nars2000.org/index.php?title=Ball_Arithmetic Ball Arithmetic] | |||
|- | |||
| <source lang=apl inline>∞ and ¯∞</source> || [http://wiki.nars2000.org/index.php?title=Infinity Signed Infinities] | |||
|- | |||
| <source lang=apl inline>∅</source> || [http://wiki.nars2000.org/index.php?title=NaN Not-a-Number (NaN)] | |||
|} | |} | ||
Each of the 2, 4, or 8 coefficients of Hypercomplex numbers must all be the same Real number datatype (i.e., Boolean, Integer, Floating Point, Rational, Variable-precision Floating Point, or Ball Arithmetic), or else they will all be promoted to a single common Real number datatype. | |||
== External links == | == External links == |
edits