Difference between r1.60 and the current

@@ -13,27 +13,41 @@

기타..
[[합성곱,convolution]]은 곱의 일종인가?
디리클레_곱 Dirichlet_product

'''Dirichlet product'''

합성곱과 같다고.
see https://freshrimpsushi.github.io/posts/dirichlet-product-of-arithmetical-function/ (Apostol)

... Ggl:"Dirichlet product" Bing:"Dirichlet product"

일반화된 디리클레 곱 = 일반화된 합성곱 generalized_Dirichlet_product = generalized_convolution ... [[일반화,generalization]]
see https://freshrimpsushi.github.io/posts/generalized-convolution/ (Apostol)
dyad product? // dyad_product

KmsE:dyad

dyad는 두 벡터의 '''곱'''인 2차(second order) [[텐서,tensor]]
이거? [[https://terms.naver.com/entry.naver?docId=1070998&cid=40942&categoryId=32204 두산백과: 기브스곱]] Gibbs' product

... Google:gibbs.product Google:dyad.product

https://planetmath.org/dyadproduct

... Google:gibbs.product

... Google:dyad.product

////위아래정확히MKL//// Ggl:"dyad product dyadic product" Bing:"dyad product dyadic product" .... see MathWorld:Dyad MathWorld:Dyadic

dyadic_product

https://en.citizendium.org/wiki/Dyadic_product

WpEn:Dyadics

WtEn:dyadic

1884년 Gibbs가 만든 단어.

Srch:dyadic_product

(이거 번역이 binary랑 겹칠 때가 많아서 ... 암튼 번역 tbd.)

KmsE:dyadic

[[곱집합,product_set]] (cartesian product)
$A\times B=\left{(a,b):a\in A,b\in B\right}$
2-[[튜플,tuple]]과 관련?
[[크로네커_곱,Kronecker_product]] - 작성중

rel. [[텐서곱,tensor_product]]

행렬의 크로네커 곱

https://freshrimpsushi.github.io/posts/kroneker-product-of-matrices/

rel. [[텐서곱,tensor_product]] [[행렬곱,matrix_product]] [[행렬곱셈,matrix_multiplication]] ...?

행렬의 크로네커 곱 https://freshrimpsushi.github.io/posts/kroneker-product-of-matrices/

[[MathNote:행렬의_크로네커_곱_(Kronecker_product)]]

[[WpKo:크로네커_곱]] = https://ko.wikipedia.org/wiki/크로네커_곱
... Google:크로네커+곱 Google:Kronecker+product Naver:크로네커+곱 Zeta:크로네커_곱
[[텐서곱,tensor_product]] - 작성중
[[무한곱,infinite_product]] - 작성중, ex. [[곱,product#s-3]]

직접곱,direct_product AKA 직적

~~kms~~ direct product : '직적, 직접곱' ~~... via https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=direct+product~~

[[direct_product]] - ? [[직접곱,direct_product]] AKA 직적

KmsE:"direct product" : '직적, 직접곱'

''직곱도 되지 않나? ... 왜냐면 저기서 direct sum은 직합. https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=direct+sum''
external_direct_product
internal_direct_product

@@ -50,6 +64,7 @@

tmp bmks ko:
군의 데카르트 곱 Cartesian Product of Groups https://freshrimpsushi.github.io/posts/cartesian-product-of-groups/
Twins:

Zeta:직접곱

[[WtEn:direct_product]] = https://en.wiktionary.org/wiki/direct_product
https://artofproblemsolving.com/wiki/index.php/Direct_product
https://mathworld.wolfram.com/DirectProduct.html

@@ -152,25 +167,29 @@

[[합,sum]]
[[최소항과_최대항,minterm_and_maxterm]]

= product term =

[[product_term]]

~~aka~~ minterm; curr see [[최소항과_최대항,minterm_and_maxterm]]

= 곱항 product term =

[[곱항,product_term]]

Rel [[최소항,minterm]]; curr see [[최소항과_최대항,minterm_and_maxterm]]

곱항 = 최소항이라는 곳도 있고

곱항 중에서 입력변수의 literal(각 변수 또는 그것의 complement)가 모두 곱해진 것만 최소항이라는 곳도 있음.

[[literal]]s들의 [[conjunction]]. 여기서 각 literal은 [[변수,variable]]이거나 그것의 [[부정,negation]]. (wpen)

'''곱항''': [[리터럴,literal]]s들의 [[논리곱,conjunction]]. 여기서 각 literal은 [[변수,variable]]이거나 그것의 [[부정,negation]]. (wpen)

Cmp: [[sum_term]] - curr see [[합,sum]]

Cmp: [[합항,sum_term]] - curr see [[합,sum]]

[[WpEn:Product_term]]

~~Google~~:product.term

NN:"product term" Ggl:"product.term"

----
바로 위 두 sections: 분야는 대충 [[불_논리,Boolean_logic]] [[불_대수,Boolean_algebra]] 이쪽, 관련단어는 Srch:canonical_normal_form Srch:canonical_form ...등 - 나중에 정확히

mklink: [[이항연산,binary_operation]], [[곱셈,multiplication]]
대충... '''곱'''은 이항연산인 곱셈의 결과물? chk

arithmetic/algebra의 '''product'''와 비슷한? : logic의 [[논리곱,conjunction]]

----
Twins:
https://mathworld.wolfram.com/Product.html

곱셈,multiplication의 결과.

여러 가지 product들이 있는데,

수,number의 곱
벡터,vector의 스칼라배 곱 (한 벡터)
내적,inner_product (이하 두 벡터)
외적,outer_product
스칼라곱,scalar_product,dot_product
벡터곱,vector_product,cross_product
삼중곱,triple_product (세 벡터에 대해)

스칼라 삼중곱: A·(B×C)
벡터 삼중곱: A×(B×C)

기타..

합성곱,convolution은 곱의 일종인가?
디리클레_곱 Dirichlet_product

Dirichlet product
합성곱과 같다고.
see https://freshrimpsushi.github.io/posts/dirichlet-product-of-arithmetical-function/ (Apostol)
...

Dirichlet product

일반화된 디리클레 곱 = 일반화된 합성곱 generalized_Dirichlet_product = generalized_convolution ... 일반화,generalization

see https://freshrimpsushi.github.io/posts/generalized-convolution/ (Apostol)

dyad product? // dyad_product

dyad
dyad는 두 벡터의 곱인 2차(second order) 텐서,tensor
이거? [https]

두산백과: 기브스곱 Gibbs' product
https://planetmath.org/dyadproduct
...

gibbs.product
...

dyad.product

////위아래정확히MKL////

dyad product dyadic product

dyad product dyadic product .... see

Dyad

Dyadic
dyadic_product

https://en.citizendium.org/wiki/Dyadic_product

Dyadics

dyadic

1884년 Gibbs가 만든 단어.

dyadic_product
(이거 번역이 binary랑 겹칠 때가 많아서 ... 암튼 번역 tbd.)

dyadic

곱집합,product_set (cartesian product)

$A\times B=\left{(a,b):a\in A,b\in B\right}$
2-튜플,tuple과 관련?

크로네커_곱,Kronecker_product - 작성중

rel. 텐서곱,tensor_product 행렬곱,matrix_product 행렬곱셈,matrix_multiplication ...?
행렬의 크로네커 곱 https://freshrimpsushi.github.io/posts/kroneker-product-of-matrices/

행렬의_크로네커_곱_(Kronecker_product)

크로네커_곱 = https://ko.wikipedia.org/wiki/크로네커_곱
...

텐서곱,tensor_product - 작성중
무한곱,infinite_product - 작성중, ex. 곱,product#s-3
direct_product - ? 직접곱,direct_product AKA 직적

direct product : '직적, 직접곱'
직곱도 되지 않나? ... 왜냐면 저기서 direct sum은 직합. https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=direct sum
external_direct_product
internal_direct_product
cf. semidirect_product - curr see https://everything2.com/title/semidirect product
semi_direct_product or semidirect_product or semi-direct_product ?

https://artofproblemsolving.com/wiki/index.php/Semi-direct_product

group_direct_product

https://mathworld.wolfram.com/GroupDirectProduct.html

group_direct_product

ring_direct_product

https://mathworld.wolfram.com/RingDirectProduct.html

ring_direct_product

Compare: direct_sum
tmp bmks ko:
군의 데카르트 곱 Cartesian Product of Groups https://freshrimpsushi.github.io/posts/cartesian-product-of-groups/
Twins:

직접곱

direct_product = https://en.wiktionary.org/wiki/direct_product
https://artofproblemsolving.com/wiki/index.php/Direct_product
https://mathworld.wolfram.com/DirectProduct.html

Direct_product

직접곱
https://wiki.haskell.org/Combinatory_logic#Direct_product - ,combinatory_logic
https://everything2.com/title/direct product
https://encyclopediaofmath.org/wiki/Direct_product

- linked from https://encyclopediaofmath.org/wiki/Cartesian_product

Compare: ,direct_sum - curr at 덧셈,addition#합

오일러 곱(Euler product)? 오일러_곱,Euler_product

see 리만_제타함수,Riemann_zeta_function
rel. 디리클레_급수,Dirichlet_series
https://artofproblemsolving.com/wiki/index.php/Euler_Product

Euler_product

= https://en.wikipedia.org/wiki/Euler_product

https://mathworld.wolfram.com/EulerProduct.html

euler product

행렬,matrix의 곱 - 행렬곱,matrix_product / 행렬곱셈,matrix_multiplication

일반적인 곱
스칼라배 곱
아다마르_곱,Hadamard_product
Frobenius_product or
Frobenius_inner_product - 작성중

쌍대곱,coproduct - 작성중
코시_곱,Cauchy_product
그래프 곱? - 그래프,graph 곱,product -

Graph_product https://mathworld.wolfram.com/GraphProduct.html

cartesian_product (graph Cartesian product)
tensor_product
lexicographical_product
strong_product ... 그래프 페이지에 작성중,

strong_product

https://mathworld.wolfram.com/GraphStrongProduct.html

자유곱,free_product - 군론. 작성중.
smash_product - 위상,topology.

Smash_product

분쇄곱
https://ncatlab.org/nlab/show/smash product

ultraproduct - model_theory. 작성중
category_product - https://mathworld.wolfram.com/CategoryProduct.html
fiber_product aka fibre_product aka pullback - writing
대칭곱 symmetric_product vs (왜대칭곱 skew-symmetric_product = 외적 exterior_product ... 외적,outer_product의 일반화??)

Wallis_product - writing; 원주율,pi을 구하는 공식,formula.