Parametrization (geometry)

A cikin ilmin lissafi, kuma musamman a cikin lissafi, parametrization (ko parameterization; kuma parameterization, parametrisation) shine tsari na gano daidaitattun daidaitattun ma'auni na layin, farfajiyar, ko, gabaɗaya, manifold ko iri-iri, wanda aka Bayyanawa ta hanyar daidaitattun. Ana kiran tsari mai juyawa da implicitization. "Don parameterize" da kansa yana nufin "bayyana dangane da sigogi".

Parametrization tsari ne na lissafi wanda ya kunshi bayyana yanayin tsarin, tsari ko samfurin a matsayin aiki wasu adadi masu zaman kansu da ake kira sigogi. Yanayin tsarin gabaɗaya an ƙayyade shi ta hanyar ƙayyadaddun ƙayyadadden ƙayyadamuran, kuma ƙaddamarwa ta ƙunshi aiki ɗaya na masu canji na ainihi don kowane ƙayyadama. Adadin sigogi shine adadin digiri na 'yanci na tsarin.

Misali, matsayin wani batu wanda ke motsawa a kan karkata a cikin sararin samaniya uku an ƙayyade shi ta lokacin da ake buƙata don isa wurin lokacin da aka fara daga asalin da aka daidaita. Idan x, y, z sune daidaitattun ma'anar, ana bayyana motsi ta hanyar daidaitattun daidaitattun 

inda shine siginar kuma yana nuna lokaci. Irin wannan ma'auni na ma'aunin gaba ɗaya yana ƙayyade layin, ba t da buƙat kowane fassarar t a matsayin lokaci ba, kuma saboda haka ana kiransa ma'aikatar ma'aunar ma'aunonin (wannan wani lokacin ana taƙaita shi ta hanyar cewa mutum yana da layin ma'aini). Hakanan yana samun daidaitattun ma'auni na farfajiyar ta hanyar la'akari da ayyukan sigogi biyu t da u.

 Girma 
Gabaɗaya, mafi ƙarancin adadin sigogi da ake buƙata don bayyana samfurin ko abu na lissafi daidai yake da girman, kuma ikon sigogi - a cikin iyakar da aka ba su - shine sararin sigogi. Kodayake kyakkyawan saiti na sigogi yana ba da iz gano kowane aya a cikin sararin abu, yana iya z cewa, don ƙaddamar da sigogi, ƙimar sigogi daban-daban na iya komawa zuwa wannan batu. Irin waɗannan taswirar suna da tsinkaye amma ba injective ba. Misali shine nau'i biyu na ma'aunin ma'auni (ρ, φ, z) da (ρ,φ + 2π, z).      

 Rashin canji 
Kamar yadda aka nuna a sama, akwai son rai a cikin zaɓin sigogi na samfurin da aka ba shi, abu na lissafi, da dai sauransu. Sau da yawa, mutum yana so ya ƙayyade kaddarorin wani abu wanda ba ya dogara da wannan son rai, wanda saboda haka ya kasance mai zaman kansa daga kowane zaɓi na sigogi. Wannan shi ne musamman lamarin a cikin kimiyyar lissafi, inda ƙarancin ƙididdiga (ko 'maido da ƙarancin') ƙa'ida ce mai jagora a cikin binciken ka'idojin da za a yarda da su a jiki (musamman a cikin ma'auni na gaba ɗaya).

Misali, yayin da wurin da aka daidaita a kan wasu layin da aka yi amfani da shi zai iya ba da saiti na lambobi waɗanda ƙimarsu ta dogara da yadda aka tsara layin, tsawon (wanda aka bayyana yadda ya kamata) na layin tsakanin irin waɗannan maki biyu zai kasance mai zaman kansa daga takamaiman zaɓi na parametrization (a wannan yanayin: hanyar da wani ma'anar da aka tsara a kan layin). Saboda haka, tsawon layin yana da yawa. A irin waɗannan lokuta parametrization kayan aiki ne na lissafi wanda aka yi amfani da shi don cire sakamakon wanda darajarsa ba ta dogara da shi ba, ko yin nuni ga, cikakkun bayanai na parametrization. Fiye da haka, ƙarancin ƙididdigar ka'idar jiki yana nuna cewa ko dai girmansa ko girman sararin siginar ya fi girma fiye da yadda ya kamata don bayyana kimiyyar lissafi (yawan mahimmancin jiki) da ake tambaya.

Kodayake ana iya bayyana ka'idar ma'auni na gaba ɗaya ba tare da ambaton tsarin daidaitawa ba, lissafin abubuwa na zahiri (watau abin lura) kamar ƙuƙwalwar sararin samaniya koyaushe yana ƙunshe da gabatar da wani tsarin daidaitawa don komawa ga maki na sararin samaniya da ke cikin lissafin. A cikin mahallin ma'auni na gaba ɗaya to, za a iya ɗaukar zaɓin tsarin daidaitawa a matsayin hanyar 'parametrizing' sararin samaniya, kuma rashin tausayi na sakamakon lissafin ƙididdigar ma'ana ta jiki ga wannan zaɓin za a iya ɗauka a matsayin misali na rashin daidaituwa.

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