Iskudhufasho

Iskudhufasho (sidoo kale loo yaqaan ku dhufasho) waa hawlgal xisaabeed oo laba tiro laga soo saaro tiro saddexaad oo la yidhaahdo badeel ama wax-soo-saarka (product). Astaanta caadiga ah ee loo isticmaalo waa × ama ·, kombuyuutarkana badanaa waxaa loo qoraa *. Tirooyinka la isku dhufanayo waxaa la yidhaahdaa factor-yo (qaybiyayaal).

Tirooyinka dabiiciga ah, iskudhufashadu waxay u dhigantaa isku-darid soo noqnoqota: 4 × 3 waxay ka dhigan tahay in 4 saddex jeer la isku daro (4 + 4 + 4 = 12). Fasiraaddaas kama shaqeyso si toos ah marka la isticmaalayo jajab, tiro taban ama tiro dhab ah, sidaas darteed xisaabta sare waxaa lagu qeexaa si guud oo ku salaysan hantida hawlgalka.

Hantida aasaasiga ah

Iskudhufashada tirooyinka caadiga ah waxay leedahay dhowr hanti: waa is-beddelan (commutative), taas oo la micno ah a × b = b × a; waa isku-urursan (associative), (a × b) × c = a × (b × c); waxayna ku qaybsantaa isku-darka (distributive), a × (b + c) = a × b + a × c. Tirada 1 waa cunsurka dhexdhexaadka ah, maadaama a × 1 = a, halka eber uu had iyo jeer bixiyo eber.

Habab lagu xisaabiyo

Dugsiyada waxaa caadi ahaan lagu barta jadwalka ku dhufashada iyo habka tiirarka (long multiplication), oo lambarrada la kala qaybiyo halbeegyada tobanle. Waxaa kale oo jira habab kale sida habka shabaqa (lattice) iyo habka Masaarida hore ee laba-laabidda. Kombuyuutarrada casriga ah waxay isticmaalaan algorithm-yo dheeraad ah, sida habka Karatsuba, kuwaas oo yaraynaya tirada ku dhufashooyinka loo baahan yahay marka lambarradu aad u dhaadheer yihiin.

Ballaarinta xisaabta sare

Fikradda iskudhufashada waxaa loo ballaariyay walxo aan tiro ahayn. Tusaale ahaan, matrix-yada waa la isku dhufan karaa, laakiin natiijadu ma aha mid is-beddelan: A × B badanaa kama simna B × A. Sidoo kale waxaa jira ku dhufashada tirooyinka isku-dhafan (complex), vector-yada, iyo kooxaha abstract-ka ah ee cilmiga algebra-da. Xisaabta guud, hawlgal kasta oo buuxiya shuruudo gaar ah ayaa loo aqoonsan karaa nooc ka mid ah iskudhufashada.