Teburin Abubuwan Ciki[Boye][Nuna]
Babu samun kusanci da ilimin lissafi, ko kai dalibin jami'a ne ko kuma kana aiki a kimiyyar bayanai.
Mutum na iya ma yin gardama cewa kimiyyar bayanai wani nau'in lissafin lissafi ne. NumPy, SciPy, Scikit-Koyi, Da kuma TensorFlow kadan ne daga cikin dakunan karatu na Python wadanda ke magana da lissafi a adadi mai yawa.
Koyaya, akwai mai fafatawa ɗaya kawai don yin ma'amala da alamomin lissafi a sarari: SymPy.
Bari mu gano komai game da SymPy.
Mene ne SymPy?
SymPy babban ɗakin karatu ne na lissafin lissafi. Yana fatan zama cikakken tsarin algebra na kwamfuta (CAS) yayin da yake kiyaye lambar a matsayin asali kamar yadda zai yiwu don zama mai fahimi da sauƙin faɗaɗawa.
An rubuta shi cikakke da Python. Abu ne mai sauƙi don amfani tunda kawai ya dogara da mpmath, babban ɗakin karatu na Python don ƙididdige ƙididdiga na iyo.
A matsayin ɗakin karatu, an ƙirƙira shi tare da mahimmancin mahimmancin amfani a zuciya. Extensibility yana da mahimmanci a cikin ƙirar ƙirar shirin aikace-aikacen sa (API).
Sakamakon haka, ba ya yin ƙoƙari don haɓaka harshen Python. Manufar ita ce masu amfani su sami damar yin amfani da shi tare da wasu Dakunan karatu na Python a cikin aikin su, ko a cikin yanayi mai ma'amala ko a matsayin tsarin da aka tsara na babban tsarin.
SymPy, a matsayin ɗakin karatu, ba shi da ginanniyar hoto mai amfani mai amfani (GUI). Laburare shine:
- Kyauta, duka game da magana da giya, saboda yana da lasisi ƙarƙashin lasisin BSD.
- Python tushen: An haɓaka shi gabaɗaya a cikin Python kuma yana ɗaukar Python a matsayin harshensa.
- Mai nauyi saboda kawai ya dogara da mpmath, mai tsabta Python library don lissafi na sabani na iyo, wanda ya sauƙaƙa don amfani.
- Ana iya shigar da su cikin wasu shirye-shirye kuma a gyara su tare da ayyuka na al'ada ban da yin amfani da su azaman kayan aiki na mu'amala.
Me yasa ake amfani da SymPy?
Sage, tsarin algebra na kwamfuta, kuma yana amfani da Python a matsayin harshen shirye-shirye. Sage, a gefe guda, yana da girma, yana buƙatar saukewa fiye da gigabyte. Yana da fa'idar kasancewa mara nauyi.
Bugu da ƙari, kasancewarsa ƙanƙara, ba shi da wani abin dogaro face Python, yana ba da damar amfani da shi a zahiri a ko'ina.
Bugu da ƙari, manufofin Sage da SymPy ba iri ɗaya ba ne. Sage yana fatan zama cikakken tsarin ilimin lissafi, kuma yana yin haka ta hanyar haɗa dukkan manyan tsarin lissafin buɗe tushen tushen zuwa ɗaya.
Lokacin da kake amfani da aikin Sage, kamar haɗaka, yana kiran ɗaya daga cikin fakitin buɗe ido wanda ya ƙunshi. A gaskiya, an gina shi a cikin Sage. SymPy, a gefe guda, yana burin zama tsarin da ya dace da kansa, tare da aiwatar da dukkan ayyuka a cikinsa.
Ƙarfinsa na aiki azaman ɗakin karatu wani muhimmin fasali ne. Yawancin tsarin algebra na kwamfuta ana nufin a yi amfani da su a cikin mahalli masu mu'amala, amma suna da wahalar sarrafa kansa ko faɗaɗa.
Ana iya amfani da shi ta hanyar mu'amala a Python ko shigo da shi cikin shirin Python ɗin ku. Hakanan yana da APIs don sauƙaƙe shi tare da abubuwan yau da kullun na ku.
Shigar da SymPy
Yi amfani da umarnin da ke ƙasa kawai don shigarwa a cikin mahallin ku.
Alamomin Alama
Bari mu fara da shi yanzu! Babban abinsa alama ce. A cikin SymPy, zaku iya ƙirƙirar alamar x ta rubuta:
Lambar da ke sama tana haifar da alamar x. Alamu a ciki ana nufin yin koyi da alamomin lissafi waɗanda ke wakiltar ƙimar da ba a san su ba.
A sakamakon haka, ana nuna lissafin mai zuwa a ƙasa:
Kamar yadda aka nuna a sama, alamar x tana aiki daidai da adadin da ba a sani ba. Idan kuna son yin alamomi da yawa, rubuta su kamar haka:
Kun ƙirƙiri alamomi biyu, y, da z, a lokaci guda a wannan yanayin. Ana iya ƙara waɗannan alamomin yanzu, ragi, ninka, da raba su kamar yadda ake so:
Ayyukan SymPy
1. tausayi () aiki
Hanyar sympify() tana canza magana ta sabani zuwa kalmar SymPy. Yana canza daidaitattun abubuwan Python, kamar lamba.
Zaɓuɓɓuka suna canzawa zuwa maganganunsu da lambobi, da sauransu.
2. evalf() aiki
Wannan aikin yana kimanta ƙayyadaddun furci na lambobi tare da madaidaicin madaidaicin bututun ruwa har zuwa lambobi 100.
Hakanan aikin yana karɓar abu na ƙamus tare da ƙimar lambobi don alamomi azaman hujjar kuɗi. Yi la'akari da jumla mai zuwa:
An saita daidaito-makikan iyo zuwa lambobi 15 ta tsohuwa. Koyaya, ana iya canza wannan zuwa kowace lamba tsakanin 1 zuwa 100.
Ana kimanta ma'auni mai zuwa zuwa madaidaicin lambobi 20.
3. Lambdify () aiki
Lambdify aiki ne da ke juyar da maganganunsa zuwa ayyukan Python. Hanyar evalf() ba ta da inganci yayin da ake kimanta magana a cikin kewayon ƙima.
Lambdify yana aiki daidai da aikin lambda, sai dai yana fassara sunayen SymPy zuwa sunayen ɗakin karatu na ƙididdiga, wanda gabaɗaya shine NumPy.
Ta hanyar tsoho, Lambdify ana amfani da shi zuwa daidaitaccen aikin laburare na lissafi.
Features
An jera kaɗan daga cikin mahimman abubuwan ɗakin karatu anan; akwai wasu da yawa da ba a haɗa su ba, amma kuna iya duba su nan.
1. Core Capabilities
- Mahimman ƙididdiga: +, -, *, /, da ** ana tallafawa (ikon)
- Fadada polynomial
- Ƙididdigar ƙididdiga, ma'ana, da kuma yawo tare da madaidaicin sabani
- Trigonometric, hyperbolic, da ayyuka masu fa'ida, Tushen, logarithms, cikakkiyar ƙima, daidaituwar yanayi, masana'anta da ayyukan gamma, ayyukan zeta, polynomials, da ayyuka na musamman
- Alamomin da ba sa musayarwa
- Samfuran da suka dace
2. Lissafi
- Haɗin kai: Wannan hanyar tana amfani da faɗaɗawar heuristic Risch-Norman
- Bambanci.
- Iyakance ayyuka
- Laurent Taylor's series
3. Polynomials
- Gröbner Foundations
- Rushewar ɓangarori
- Rarraba, gcd Sakamako misalai ne na asali na lissafi.
4. Combinatorics
- Maddamarwa
- Lambobin Grey da Prufer
- Haɗuwa, Rarraba, Rarraba
- Polyhedral, Rubik, Simmetric, da Sauran Rukunin Rubutu
5. Maths mai hankali
- Takaitattun bayanai
- Maganganu masu ma'ana
- Coefficients na binomial
- Lambar lambobi
Aikace-aikace
1. Ƙididdigar Gina
2. Computer Algebra Systems
Ba kamar sauran Tsarin Algebra na Kwamfuta ba, dole ne ka ayyana masu canji na alama da hannu ta amfani da aikin Alama ().
3. Lissafi
Ƙarfin tsarin ƙididdiga na alama don yin kowane nau'in ƙididdiga a alamance shine babban ƙarfinsa.
Yana iya sauƙaƙa kalamai, a alamance, ƙididdige abubuwan ban sha'awa, haɗaka, da iyakoki, warware daidaito, hulɗa tare da matrices, da yin ƙari mai yawa.
Don jin daɗin sha'awar ku, ga ɗanɗanon ikon alama.
Me kuma za ku iya yi tare da SymPy?
Maimakon yin zuzzurfan tunani game da ƙarin al'amura a cikin zurfafa, bari in samar muku da jerin albarkatun don taimaka muku haɓaka ƙwarewar ku:
- Matrices da Algebra Linear: Yana iya aiki tare da matrices kuma yayi ainihin ayyukan algebra na layi. Harshen yana kama da na NumPy's syntax. Duk da haka, akwai sanannun bambance-bambance. Don farawa, bincika matrices a cikin ɗakin karatu.
- Bayanin: Yana amfani da bishiyar magana, wanda shine tsarin tushen bishiya, don kiyaye maganganun maganganu. Kalli itatuwan magana idan kuna son ƙarin koyo game da ayyukansu na ciki.
- Abubuwan Haɓakawa da Haɗin kai: Zai iya cim ma mafi yawan abin da za ku koya a cikin aji na gabatarwa (ban da tunani). Kuna iya farawa da duba aikin mu bambanta in SymPy.
- Dangantaka da NumPy: NumPy da SymPy duka ɗakunan karatu ne masu alaƙa da lissafi. Suna, duk da haka, da gaske daban-daban! NumPy yana aiki tare da lambobi, yayin da yana aiki tare da maganganu na alama.
- Sauƙaƙe: Yana da isashen hankali don sauƙaƙe magana ta atomatik. Koyaya, idan kuna son ƙarin iko mai kyau akan wannan, duba ta saukakawa.
Kammalawa
SymPy babban ɗakin karatu ne don lissafi na alama.
Kuna iya amfani da shi don ƙirƙirar masu canji da ayyuka, da kuma ƙarawa da sauƙaƙa maganganun lissafi a alamance da warware ma'auni, rashin daidaito, har ma da tsarin ma'auni/masu ƙima.
Kuna iya rubuta ayyukan duka a cikin rubutun rubutun kuma kai tsaye a cikin tasha (ko Littafin rubutu na Jupyter) don samun saurin kima da ingantaccen hoto mai hoto na lissafin da aka yi.
Shin kuna shirye don bincika ƙarin SymPy? Bari mu sani a cikin sharhi.
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