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Rank and Leading Axis Theory

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Manage episode 329990452 series 2926987
Content provided by bob therriault and The Array Cast. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by bob therriault and The Array Cast or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://ppacc.player.fm/legal.

Array Cast - May 27, 2022
Show Notes

[01] 00:02:00 APL logo https://aplwiki.com/wiki/APL_logo
[02] 00:02:24 APL Merch On Bonfire: https://bonfire.com/store/apl-stuff/
On Redbubble: https://redbubble.com/shop/ap/111813275
Aaron Hsu's site: https://www.bonfire.com/store/arcfide/[03] 00:03:00 BQN FFI XXXXXXXXXX
[04] 00:03:58 kx download https://kx.com/developers/download-licenses/
[05] 00:04:20 kx download request mailto:[email protected]
[06] 00:05:18 Rank https://aplwiki.com/wiki/Rank
Leading Axis Theory https://aplwiki.com/wiki/Leading_axis_theory
[07] 00:06:24 Adoption in APL https://aplwiki.com/wiki/Leading_axis_theory#Adoption_in_APL
[08] 00:08:27 APL https://aplwiki.com/wiki/Main_Page
BQN https://mlochbaum.github.io/BQN/
J https://www.jsoftware.com/#/README
[09] 00:10:19 + Rank 0 https://aplwiki.com/wiki/Add
Rank operator: https://apl.wiki/Rank_(operator)
Multidimensional arrays: https://apl.wiki/Array_model
Ravel order: https://apl.wiki/Ravel_order
[10] 00:10:53 ≡ Match Rank Infinity https://aplwiki.com/wiki/Match
APL: https://tryapl.org/?clear&q=a%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20b%E2%86%903%203%E2%8D%B4%E2%8D%B36%20%E2%8B%84%20a(%E2%89%A1%E2%8D%A41)b&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=YeKGkDPigL8z4qWKMSvihpU5IOKLhCBi4oaQM+KAvzPipYoxK+KGlTYg4ouEIGEg4omh4o6JMSBi
J: https://jsoftware.github.io/j-playground/bin/html2/#code=a%3D%3A%20i.%203%203%0Ab%3D%3A%203%203%20%24%20i.%206%0Aa%20-%3A%221%20b%0A
Function rank: https://apl.wiki/Function_rank
Raze (;): https://apl.wiki/Raze
[11] 00:12:23 Rank of verb in J https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm#_Toc191734331
Rank of noun in J https://www.jsoftware.com/help/jforc/declarations.htm#_Toc191734319
[12] 00:14:50 ". Do verb https://code.jsoftware.com/wiki/Vocabulary/quotedot
[13] 00:16:05 @ Atop https://code.jsoftware.com/wiki/Vocabulary/at
[14] 00:16:10 @: At https://code.jsoftware.com/wiki/Vocabulary/atco
[15] 00:18:53 Combinators https://mlochbaum.github.io/BQN/tutorial/combinator.html
Close composition: https://apl.wiki/Close_composition
[16] 00:19:32 The J diagram of composition patterns: https://code.jsoftware.com/wiki/File:Funcomp.png
[17] 00:20:10 Scalar APL https://aplwiki.com/wiki/Scalar
J https://code.jsoftware.com/wiki/Vocabulary/Nouns#Atom
BQN https://mlochbaum.github.io/BQN/doc/based.html#starting-from-atoms
Scalar function: https://apl.wiki/Scalar_function
Everything else: https://apl.wiki/Mixed_function
Atom: https://apl.wiki/Simple_scalar
Leading axis agreement: https://apl.wiki/Leading_axis_agreement
Scalar agreement: https://apl.wiki/Scalar_extension
[18] 00:25:50 Numpy https://numpy.org/
Julia https://julialang.org/
[19] 00:26:58 APL: https://tryapl.org/?clear&q=1%202%203(%2B%E2%8D%A41)2%203%E2%8D%B41%202%203&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=MeKAvzLigL8zK+KOiTEgMuKAvzPipYox4oC/MuKAvzM=
J: (3 3 $ 1 2 3) +"1 (1 2 3) https://jsoftware.github.io/j-playground/bin/html2/#code=%283%203%20%24%201%202%203%29%20%2B%221%20%281%202%203%29%0A
[20] 00:27:40 Reduce https://aplwiki.com/wiki/Reduce
Scan https://aplwiki.com/wiki/scan
Reverse https://aplwiki.com/wiki/reverse
Rotate https://aplwiki.com/wiki/rotate
[21] 00:33:00 ⍪ Catenate First https://aplwiki.com/wiki/Catenate
[22] 00:37:50 Major cells https://aplwiki.com/wiki/Major_cell
Cell: https://apl.wiki/Cell
"Items": https://apl.wiki/Major_cell
Arthur Whitney: https://apl.wiki/Arthur_Whitney
[23] 00:38:48 Operators and Enclosed Arrays https://www.jsoftware.com/papers/opea.htm
[24] 00:40:17 Original Iverson Notation http://www.jsoftware.com/papers/DFSP.htm
Iverson Notation: https://apl.wiki/Iverson_notation
Roger Hui: https://apl.com/Roger_Hui
[25] 00:41:32 [] Bracket Axis https://aplwiki.com/wiki/Function_axis
[26] 00:43:32 Scan https://aplwiki.com/wiki/Scan
Scan with axis: https://tryapl.org/?clear&q=%E2%8E%95IO%E2%86%900%20%E2%8B%84%20m%E2%86%903%203%E2%8D%B41%202%203%20%E2%8B%84%20(%2B%5Cm)%20(%2B%5C%5B0%5Dm)%20(%2B%E2%8D%80m)&run
J: https://jsoftware.github.io/j-playground/bin/html2/#code=m%3D%3A%203%203%20%24%201%202%203%0Am%3B%28%2B%2F%5C%20m%29%0A%0A
[27] 00:48:32 A Programming Language http://www.jsoftware.com/papers/APL.htm
[28] 00:51:40 BQN to APL Translation https://mlochbaum.github.io/BQN/doc/fromDyalog.html
[29] 00:52:13 ˘ Cells https://mlochbaum.github.io/BQN/help/cells.html
Breve symbol: https://en.wikipedia.org/wiki/Breve
SHARP APL: https://apl.wiki/SHARP_APL
APL2: https://apl.wiki/APL2
[30] 00:53:34 Items J https://code.jsoftware.com/wiki/Vocabulary/Nouns#Item
[31] 00:54:59 ˝ Insert BQN https://mlochbaum.github.io/BQN/help/insert.html
[32] 00:56:09 Catenation https://aplwiki.com/wiki/Catenate
Concatenation reduction of a matrix:
APL: https://tryapl.org/?clear&q=%2C%2F3%203%E2%8D%B4%E2%8D%B39&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CuKIvsudbQ==
J: https://jsoftware.github.io/j-playground/bin/html2/#code=m%3D%3A%203%203%241%2Bi.9%0A%2C%2Fm
BQN with Each: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CuKIvsKoy51t
J with each: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A3%203%241%2Bi.9%0A%2C%2Feach%20m%0A
[33] 00:57:50 k language https://aplwiki.com/wiki/K
APL\360: https://apl.wiki/APL\360
[34] 01:00:34 / Insert J https://code.jsoftware.com/wiki/Vocabulary/slash
˝ Insert BQN https://mlochbaum.github.io/BQN/help/insert.html
J NuVoc: https://code.jsoftware.com/wiki/NuVoc
⌿ Reduce First APL https://aplwiki.com/wiki/Reduce
[35] 01:03:40 J for C Programmers Declarations https://www.jsoftware.com/help/jforc/declarations.htm#_Toc191734319
J for C Programmers Verbs have rank https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm#_Toc191734331
Summing rows:
APL: https://tryapl.org/?clear&q=%2B%2F3%203%E2%8D%B4%E2%8D%B39&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CivCtMuYbQ==
J: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A3%203%24%3E%3Ai.9%0A%2B%2F%221%20m%0A
Summing rows of coordinate pairs:
APL: https://tryapl.org/?clear&q=m%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20m%20(%E2%8A%96m)%20(%E2%8C%BDm)&run
BQN with insert: https://mlochbaum.github.io/BQN/try.html#code=K8udy5gxK+KGlTPigL8z
BQN with fold: https://mlochbaum.github.io/BQN/try.html#code=K8K0y5gxK+KGlTPigL8z
J: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A%7B%3B~%3E%3Ai.3%0A%2Beach%2F%20m%0A
[36] 01:07:00 Based Arrays https://aplwiki.com/wiki/Array_model#Based_array_theory
[37] 01:08:47 http://tryapl.com https://tryapl.org/
[38] 01:09:01 iota ⍳ https://aplwiki.com/wiki/Index_Generator
[39] 01:11:20 aplcart https://aplcart.info/
[40] 01:13:30 Einstein Summation Notation https://en.wikipedia.org/wiki/Einstein_notation
einsum: https://numpy.org/doc/stable/reference/generated/numpy.einsum.html
[41] 01:15:00 Dex programming language https://github.com/google-research/dex-lang#readme
[42] 01:18:00 ⍉ Transpose https://aplwiki.com/wiki/Transpose
Mirrors:
APL: https://tryapl.org/?clear&q=M%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20m%20(%E2%8A%96m)%20(%E2%8C%BDm)&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5IOKLhCDin6htLOKMvW0s4oy9y5ht4p+p
J:https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A%3E%3Ai.%203%203%0A%28%5D%20%3B%20%7C.%20%3B%20%7C.%221%29%20m%0A
[43] 01:20:00 BQN ⊸ Before https://mlochbaum.github.io/BQN/help/before_bind.html
⟜ After https://mlochbaum.github.io/BQN/help/after_bind.html
Conor's number of permutations tweet: https://twitter.com/code_report/status/1528844402046685187
Combinators: https://apl.wiki/Function_composition
[44] 01:31:30 Joel Kaplan on the ArrayCast https://www.arraycast.com/episodes/episode27-joel-kaplan

  continue reading

109 episodes

Artwork

Rank and Leading Axis Theory

The Array Cast

24 subscribers

published

iconShare
 
Manage episode 329990452 series 2926987
Content provided by bob therriault and The Array Cast. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by bob therriault and The Array Cast or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://ppacc.player.fm/legal.

Array Cast - May 27, 2022
Show Notes

[01] 00:02:00 APL logo https://aplwiki.com/wiki/APL_logo
[02] 00:02:24 APL Merch On Bonfire: https://bonfire.com/store/apl-stuff/
On Redbubble: https://redbubble.com/shop/ap/111813275
Aaron Hsu's site: https://www.bonfire.com/store/arcfide/[03] 00:03:00 BQN FFI XXXXXXXXXX
[04] 00:03:58 kx download https://kx.com/developers/download-licenses/
[05] 00:04:20 kx download request mailto:[email protected]
[06] 00:05:18 Rank https://aplwiki.com/wiki/Rank
Leading Axis Theory https://aplwiki.com/wiki/Leading_axis_theory
[07] 00:06:24 Adoption in APL https://aplwiki.com/wiki/Leading_axis_theory#Adoption_in_APL
[08] 00:08:27 APL https://aplwiki.com/wiki/Main_Page
BQN https://mlochbaum.github.io/BQN/
J https://www.jsoftware.com/#/README
[09] 00:10:19 + Rank 0 https://aplwiki.com/wiki/Add
Rank operator: https://apl.wiki/Rank_(operator)
Multidimensional arrays: https://apl.wiki/Array_model
Ravel order: https://apl.wiki/Ravel_order
[10] 00:10:53 ≡ Match Rank Infinity https://aplwiki.com/wiki/Match
APL: https://tryapl.org/?clear&q=a%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20b%E2%86%903%203%E2%8D%B4%E2%8D%B36%20%E2%8B%84%20a(%E2%89%A1%E2%8D%A41)b&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=YeKGkDPigL8z4qWKMSvihpU5IOKLhCBi4oaQM+KAvzPipYoxK+KGlTYg4ouEIGEg4omh4o6JMSBi
J: https://jsoftware.github.io/j-playground/bin/html2/#code=a%3D%3A%20i.%203%203%0Ab%3D%3A%203%203%20%24%20i.%206%0Aa%20-%3A%221%20b%0A
Function rank: https://apl.wiki/Function_rank
Raze (;): https://apl.wiki/Raze
[11] 00:12:23 Rank of verb in J https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm#_Toc191734331
Rank of noun in J https://www.jsoftware.com/help/jforc/declarations.htm#_Toc191734319
[12] 00:14:50 ". Do verb https://code.jsoftware.com/wiki/Vocabulary/quotedot
[13] 00:16:05 @ Atop https://code.jsoftware.com/wiki/Vocabulary/at
[14] 00:16:10 @: At https://code.jsoftware.com/wiki/Vocabulary/atco
[15] 00:18:53 Combinators https://mlochbaum.github.io/BQN/tutorial/combinator.html
Close composition: https://apl.wiki/Close_composition
[16] 00:19:32 The J diagram of composition patterns: https://code.jsoftware.com/wiki/File:Funcomp.png
[17] 00:20:10 Scalar APL https://aplwiki.com/wiki/Scalar
J https://code.jsoftware.com/wiki/Vocabulary/Nouns#Atom
BQN https://mlochbaum.github.io/BQN/doc/based.html#starting-from-atoms
Scalar function: https://apl.wiki/Scalar_function
Everything else: https://apl.wiki/Mixed_function
Atom: https://apl.wiki/Simple_scalar
Leading axis agreement: https://apl.wiki/Leading_axis_agreement
Scalar agreement: https://apl.wiki/Scalar_extension
[18] 00:25:50 Numpy https://numpy.org/
Julia https://julialang.org/
[19] 00:26:58 APL: https://tryapl.org/?clear&q=1%202%203(%2B%E2%8D%A41)2%203%E2%8D%B41%202%203&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=MeKAvzLigL8zK+KOiTEgMuKAvzPipYox4oC/MuKAvzM=
J: (3 3 $ 1 2 3) +"1 (1 2 3) https://jsoftware.github.io/j-playground/bin/html2/#code=%283%203%20%24%201%202%203%29%20%2B%221%20%281%202%203%29%0A
[20] 00:27:40 Reduce https://aplwiki.com/wiki/Reduce
Scan https://aplwiki.com/wiki/scan
Reverse https://aplwiki.com/wiki/reverse
Rotate https://aplwiki.com/wiki/rotate
[21] 00:33:00 ⍪ Catenate First https://aplwiki.com/wiki/Catenate
[22] 00:37:50 Major cells https://aplwiki.com/wiki/Major_cell
Cell: https://apl.wiki/Cell
"Items": https://apl.wiki/Major_cell
Arthur Whitney: https://apl.wiki/Arthur_Whitney
[23] 00:38:48 Operators and Enclosed Arrays https://www.jsoftware.com/papers/opea.htm
[24] 00:40:17 Original Iverson Notation http://www.jsoftware.com/papers/DFSP.htm
Iverson Notation: https://apl.wiki/Iverson_notation
Roger Hui: https://apl.com/Roger_Hui
[25] 00:41:32 [] Bracket Axis https://aplwiki.com/wiki/Function_axis
[26] 00:43:32 Scan https://aplwiki.com/wiki/Scan
Scan with axis: https://tryapl.org/?clear&q=%E2%8E%95IO%E2%86%900%20%E2%8B%84%20m%E2%86%903%203%E2%8D%B41%202%203%20%E2%8B%84%20(%2B%5Cm)%20(%2B%5C%5B0%5Dm)%20(%2B%E2%8D%80m)&run
J: https://jsoftware.github.io/j-playground/bin/html2/#code=m%3D%3A%203%203%20%24%201%202%203%0Am%3B%28%2B%2F%5C%20m%29%0A%0A
[27] 00:48:32 A Programming Language http://www.jsoftware.com/papers/APL.htm
[28] 00:51:40 BQN to APL Translation https://mlochbaum.github.io/BQN/doc/fromDyalog.html
[29] 00:52:13 ˘ Cells https://mlochbaum.github.io/BQN/help/cells.html
Breve symbol: https://en.wikipedia.org/wiki/Breve
SHARP APL: https://apl.wiki/SHARP_APL
APL2: https://apl.wiki/APL2
[30] 00:53:34 Items J https://code.jsoftware.com/wiki/Vocabulary/Nouns#Item
[31] 00:54:59 ˝ Insert BQN https://mlochbaum.github.io/BQN/help/insert.html
[32] 00:56:09 Catenation https://aplwiki.com/wiki/Catenate
Concatenation reduction of a matrix:
APL: https://tryapl.org/?clear&q=%2C%2F3%203%E2%8D%B4%E2%8D%B39&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CuKIvsudbQ==
J: https://jsoftware.github.io/j-playground/bin/html2/#code=m%3D%3A%203%203%241%2Bi.9%0A%2C%2Fm
BQN with Each: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CuKIvsKoy51t
J with each: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A3%203%241%2Bi.9%0A%2C%2Feach%20m%0A
[33] 00:57:50 k language https://aplwiki.com/wiki/K
APL\360: https://apl.wiki/APL\360
[34] 01:00:34 / Insert J https://code.jsoftware.com/wiki/Vocabulary/slash
˝ Insert BQN https://mlochbaum.github.io/BQN/help/insert.html
J NuVoc: https://code.jsoftware.com/wiki/NuVoc
⌿ Reduce First APL https://aplwiki.com/wiki/Reduce
[35] 01:03:40 J for C Programmers Declarations https://www.jsoftware.com/help/jforc/declarations.htm#_Toc191734319
J for C Programmers Verbs have rank https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm#_Toc191734331
Summing rows:
APL: https://tryapl.org/?clear&q=%2B%2F3%203%E2%8D%B4%E2%8D%B39&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CivCtMuYbQ==
J: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A3%203%24%3E%3Ai.9%0A%2B%2F%221%20m%0A
Summing rows of coordinate pairs:
APL: https://tryapl.org/?clear&q=m%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20m%20(%E2%8A%96m)%20(%E2%8C%BDm)&run
BQN with insert: https://mlochbaum.github.io/BQN/try.html#code=K8udy5gxK+KGlTPigL8z
BQN with fold: https://mlochbaum.github.io/BQN/try.html#code=K8K0y5gxK+KGlTPigL8z
J: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A%7B%3B~%3E%3Ai.3%0A%2Beach%2F%20m%0A
[36] 01:07:00 Based Arrays https://aplwiki.com/wiki/Array_model#Based_array_theory
[37] 01:08:47 http://tryapl.com https://tryapl.org/
[38] 01:09:01 iota ⍳ https://aplwiki.com/wiki/Index_Generator
[39] 01:11:20 aplcart https://aplcart.info/
[40] 01:13:30 Einstein Summation Notation https://en.wikipedia.org/wiki/Einstein_notation
einsum: https://numpy.org/doc/stable/reference/generated/numpy.einsum.html
[41] 01:15:00 Dex programming language https://github.com/google-research/dex-lang#readme
[42] 01:18:00 ⍉ Transpose https://aplwiki.com/wiki/Transpose
Mirrors:
APL: https://tryapl.org/?clear&q=M%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20m%20(%E2%8A%96m)%20(%E2%8C%BDm)&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5IOKLhCDin6htLOKMvW0s4oy9y5ht4p+p
J:https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A%3E%3Ai.%203%203%0A%28%5D%20%3B%20%7C.%20%3B%20%7C.%221%29%20m%0A
[43] 01:20:00 BQN ⊸ Before https://mlochbaum.github.io/BQN/help/before_bind.html
⟜ After https://mlochbaum.github.io/BQN/help/after_bind.html
Conor's number of permutations tweet: https://twitter.com/code_report/status/1528844402046685187
Combinators: https://apl.wiki/Function_composition
[44] 01:31:30 Joel Kaplan on the ArrayCast https://www.arraycast.com/episodes/episode27-joel-kaplan

  continue reading

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