Imithetho ye-algebra yengqiqo

Iikhomputha zanamhlanje ezisekelwe kwiikhomputha zekhompyutheni, "njengoko imigaqo-siseko yomsebenzi isekelwe kwizikhundla ezithile. Zibizwa ngokuba yimithetho ye-algebra yengqiqo. Ngalokuqala ngolo hlobo ukuqeqeshwa okunjalo kuchazwe (ngokuqinisekileyo, kungekhona nje ngeenkcukacha ezinjengelimihla yanamhlanje) ngumfundi waseGrike wama-Aristotle.

Ukumelela icandelo elihlukeneyo leemathematika, apho i-calculus yeziphakamiso zifundwa ngayo, i-algebra yesigqibo sinombono wezigqibo ezizicaceleyo nezigqibo.

Ukuze siqonde kakuhle isihloko, siza kuhlalutya iingcamango eziya kunceda ukufunda imithetho ye-algebra yengqiqo kwixesha elizayo.

Mhlawumbi i-term ephambili ekufundiseni ukufundiswa yinkcazo. Le ngxelo ayinakubili yobuxoki neyinyaniso. Uhlala ehlala kwizinto ezifanayo kuphela. Kuyavunyelwa ngokuqhelekileyo ukunikezela inyaniso kwi-1, ukunyaniseka kwi-0, kwaye isivakalisi ngokwawo sibizwa ngokuba yileta yesiLatini: A, B, C. Ngamanye amazwi, ifomu A = 1 ithetha ukuba u-A uyinyaniso. Ngeengxelo ungenza ngezindlela ezahlukeneyo. Ngomfutshane, siya kuqwalasela izenzo ezinokuthathwa nazo. Siyaqaphela ukuba imithetho ye-algebra yengqiqo ayikwazi ukufundwa ngaphandle kokwazi le mithetho.

1. Ukudibanisa kweengxelo ezimbini kubangelwa ngumsebenzi "okanye". Inokuba yinyani okanye yinyaniso. Isimboli "v" sisetyenzisiweyo.

2. Ukudibanisa. Isiphumo saleso senzo, esenziwe ngeengxelo ezimbini, siya kuba sisitatimende esitsha, okwenyaniso kuphela ukuba zombini iintetho zokuqala ziyinyaniso. Umsebenzi "kunye", isimboli "^" sisetyenziswa.

3. Ingqalelo. Umsebenzi "ukuba A, B ke". Isiphumo sisitatimende esiyinyaniso kuphela ukuba u-A uyinyaniso kwaye u-F buxoki.

4. Ukulingana. Umsebenzi "A ukuba kwaye kuphela B, xa". Le nkcazo yinyani kwiimeko apho zombini iziguquko zinokulinganisela okufanayo. Isalathisi "<->" isetyenziswe.

Kukho nenani leemisebenzi esondeleyo kwintetho, kodwa ayiyi kuqwalaselwa kule nqaku.

Ngoku masiqwalasele ngokubanzi iinkcukacha ezisisiseko ze-algebra yengqiqo:

1. Ukuziphendulela okanye ukutshintshelwa ngokutsha ukuba utshintsho lweendawo zengqiqo ekusebenzisaneni okanye ukudibanisa kwisiphumo asichaphazeli.

2. Unxulumano okanye unxulumana. Ngokwalo mthetho, iinguqu ezinxulumene okanye izidibaniso zingabalwa kunye.

3. Ukusasazwa okanye ukuhambisa. Ingundoqo yomthetho kukuba iinguqu ezifanayo kwiibalo zingathathwa ngaphandle kweebakaki, ngaphandle kokutshintsha ingcamango.

4. Umthetho kaDor Morgan (inversion okanye ukunganaki). Ukulahlwa komsebenzi wokubambisana kufana nokuxhatshazwa kwezinto ezichaseneyo. Ukungabikho kokudibanisa, ngokukhawuleza, kulingana nokuhlanganyelwa kwezinto ezingafaniyo.

5. Ukungahoxiswa kabini. Ukunyanzelwa kwezwi elithile kabini linikeza ngenxa yesigqibo sokuqala, kathathu ukuphika kwayo.

6. Umthetho we-idempotency ukhangeleka njengolu xwebhu olongezelelweyo: xvxvxvx = x; Ukuphindaphinda: x ^ x ^ x ^ = x.

7. Umthetho wokungahambisani nokuchasana uthi: iingxelo ezimbini, ukuba ziphikisana, azikwazi ukunyaniseka ngexesha elifanayo.

8. Umthetho wokukhutshwa kwesithathu. Phakathi kweengxelo ezimbini eziphikisanayo, omnye uhlala eqinisile, enye inkohliso, okwesithathu ayinikiweyo.

9. Umthetho wokunyuselwa ungabhalwa ngale ndlela ukwenzela ukongezelela okunengqiqo: xv (x ^ y) = x, ngokuphindaphinda: x ^ (xvy) = x.

10. Umthetho we-gluing. Izihlanganisi ezimbini ezikufutshane ziyakwazi ukuqokelela kunye, ukwenza umdibaniso wezinga elincinci. Kule meko, uguquko, ngokubhekiselele kuzo zonke izihlanganisi zokuqala eziye zahlanjululwa, zinyamalalala. Umzekelo wokongezelela okunengqiqo:

(X ^ y) v (-x ^ y) = y.

Siye saqwalasela kuphela imithetho eqhelekileyo esetyenziswayo ye-algebra yengqiqo, eqinisweni inokuba yinto emininzi, kuba ngokuphindaphindiweyo ukulingana okulinganayo kufumana ukubonakala kwexesha elide kunye neentyatyambo, ezinokunciphisa ngokusebenzisa imithetho eminye.

Njengomgaqo, ukulungelelwa kokubala nokuchonga iziphumo, iitafile ezikhethekileyo zisetyenzisiweyo. Yonke imithetho ekhoyo ye-algebra yengqiqo, itheyibhile enesakhiwo esifanayo somxube wegridi, icwecwe ngaphandle, ihambisa isantlukwano ngasinye kwisitya esahlukileyo. Eyona nkulu i-equation, kulula ukuyijamelana nayo usebenzisa iitafile.