Maxima (software)

**Maxima** (/ˈmæksɪmə/) kunshin software ne don yin lissafin algebra na kwamfuta a cikin lissafi da kimiyyar kwamfuta.   An rubuta shi a cikin Common Lisp kuma yana gudana a duk dandamali na POSIX kamar macOS, Unix, BSD, da Linux, da kuma ƙarƙashin Microsoft Windows da Android. Software ne na kyauta wanda aka saki a ƙarƙashin sharuddan GNU General Public License (GPL).

## Tarihi
Maxima ya dogara ne akan sigar 1982 na Macsyma, wanda aka haɓaka a MIT tare da tallafi daga Ma'aikatar Makamashi ta Amurka da sauran hukumomin gwamnati. Bill Schelter ya ci gaba da amfani da sigar Macsyma daga 1982 har zuwa rasuwarsa a 2001. A shekarar 1998, Schelter ya sami izini daga Ma'aikatar Makamashi don fitar da sigarsa a ƙarƙashin GPL. Wannan sigar, wacce yanzu ake kira Maxima, ƙungiyar masu amfani da masu haɓakawa ce ke kula da ita. Maxima ba ta haɗa da duk wani gyare-gyare da haɓakawa da aka yi wa sigar kasuwanci ta Macsyma a lokacin 1982-1999 ba. Kodayake aikin babban aikin ya kasance iri ɗaya, lambar da ta dogara da waɗannan haɓakawa na iya yin aiki ba akan Maxima ba, kuma kurakurai da aka gyara a Macsyma na iya kasancewa har yanzu suna nan a Maxima, kuma akasin haka. Maxima ya shiga cikin Google Summer of Code a 2019 a ƙarƙashin Cibiyar Haɗin Kan Neuroinformatics ta Duniya.

## Lissafi na alama
Kamar yawancin tsarin algebra na kwamfuta, Maxima tana tallafawa hanyoyi daban-daban na sake tsara maganganun algebra masu alama, kamar factorization na polynomial, lissafin polynomial mafi girma na rabawa, faɗaɗawa, rabuwa zuwa sassan gaske da na tunani, da kuma canza ayyukan trigonometric zuwa exponential da akasin haka. Yana da hanyoyi daban-daban don sauƙaƙe maganganun algebra da suka haɗa da ayyukan trigonometric, tushen, da ayyukan exponential. Yana iya ƙididdige alamun antiderivatives ("indefinite intelligent intelligent intelligent"), takamaiman haɗin kai, da iyakoki. Yana iya samo faɗaɗa jerin tsare-tsare masu tsari da kuma sharuɗɗan jerin Taylor-Maclaurin-Laurent. Yana iya yin matrix manipulations tare da shigarwar alama.

Maxima tsarin manufa ne na gaba ɗaya, kuma lissafi na musamman kamar Factorization na manyan lambobi, sarrafa manyan polynomials, da dai sauransu wani lokacin ana yin su da kyau a cikin tsarin na musamman.

### Lissafin lambobi
Maxima ta ƙware a cikin ayyukan alama, amma kuma tana ba da ƙwarewar lambobi  kamar ƙididdiga ƙididdiga, lambar da ke da ma'ana, da lambobin da ke iyo kawai, an iyakance su da ƙuntatawa na sarari da lokaci.

### Shirye-shiryen
Maxima ya haɗa da cikakken harshe na shirye-shirye tare da haɗin kai kamar ALGOL amma Lisp-like semantics. An rubuta shi a cikin Common Lisp kuma ana iya samun damar yin amfani da shi ta hanyar shirye-shirye da faɗaɗa, kamar yadda za'a iya kiran Lisp na asali daga Maxima. Yana amfani da gnuplot don zanawa.

Don lissafi ta amfani da ma'anar ruwa da tsararru sosai, Maxima yana da masu fassara daga harshen Maxima zuwa wasu harsunan shirye-shirye (musamman Fortran), wanda zai iya aiwatar da kyau.

## Hanyar sadarwa

Hanyoyin masu amfani daban-daban (GUIs) don Maxima sune:

* wxMaxima  yana da ingancin hoto na gaba ta amfani da tsarin wxWidgets. wxMaxima yana ba da tsarin tantanin halitta mai kama da littafin lissafi na Mathematica kamar yadda aka nuna a cikin adadi a dama. Za'a iya adana tarurruka a cikin wxMaxima a cikin tsarin fayil daban-daban don amfani daga baya.
* Akwai ƙwayoyin don Project Jupyter, mai sassauƙa, GUI mai salon littafin rubutu da aka rubuta a Python.
* R="./Cantor_(mathematics_software)" id="mwWw" rel="mw:WikiLink" title="Cantor (mathematics software)">Cantor, ta amfani da Qt, na iya hulɗa tare da Maxima (tare da SageMath, R, da KAlgebra) 
* Ana iya amfani da shirye-shiryen editan lissafi na GNU TeXmacs da LyX don samar da GUI mai ma'amala don Maxima, kamar yadda SageMath zai iya. Sauran zaɓuɓɓuka sun haɗa da ƙarshen gaba na Imaxima, da kuma yanayin hulɗa na Emacs da XEmacs wanda Imaxima ke kunnawa.
* CLIM  shine ƙarshen gaba na CLIM.

## Misalan lambar Maxima

### Ayyuka na asali

#### Arithmetic na daidaito

```maxima
bfloat(sqrt(2)), fpprec=40;
```

```maxima
f(x):=x^3$
f(4);
```
64
```maxima
expand((a-b)^3);
```
-b^3+3 ab^2-3a^2b+a^3

#### Dalili

```maxima
factor(x^2-1);
```
(x-1)(x+1)

### Warware daidaitattun
x^2+a \ x + 1=0
```maxima
solve(x^2 + a*x + 1, x);
```
[x=-\Biggl(\frac{\sqrt{a^2-4}+a}{2}\Biggr),x=\frac{\sqrt{a^2-4}-a}{2}]

### Warware ma'auni da lambobi
\cos x = x
```maxima
find_root(cos(x) = x, x, 0, 1);
```
0.7390851332151607
```maxima
bf_find_root(cos(x) = x, x, 0, 1), fpprec = 50;
```
7.3908513321516064165531208767387340401341175890076 \cdot 10^{-1}

### Cikakken ƙayyadaddun
\int x^2+\cos x\ d x
```maxima
integrate(x^2 + cos(x), x);
```
\sin x + \frac{x^3}{3}

### Cikakken ƙididdiga
\int_{0}^{1}\frac{1}{x^3+1}\, dx
```maxima
integrate(1/(x^3 + 1), x, 0, 1), ratsimp;
```
\frac{\sqrt3 \log2+\pi}{3^{\frac{3}{2}}}

### Ƙididdigar ƙididdiga
\int_{0}^{2} \sin(\sin (x)) \, dx
```maxima
quad_qags(sin(sin(x)), x, 0, 2)[1];
```
1.247056058244003

### Rashin daidaituwa
{d^3 \over d x^3} \cos^2 x
```maxima
diff(cos(x)^2, x, 3);
```
8 \cos{x}\sin{x}

### Ƙayyadadden
\lim_{x \to \infty} \frac{1+\sinh{x}}{e^{x}}
```maxima
limit((1+sinh(x))/exp(x), x, inf);
```
\frac{1}{2}
```maxima
primes(10, 20);
```
[11,13,17,19]
```maxima
fib(10);
```
55

\sum_{x=1}^\infty \frac{1}{x^2} 
```maxima
sum(1/x^2, x, 1, inf), simpsum;
```
\frac{\pi^2}{6}

### Yaduwar jerin

```maxima
taylor(sin(x), x, 0, 9);
```
x-\frac{x^3}{6}+\frac{x^5}{120}-\frac{x^7}{5040}+\frac{x^9}{362880}
```maxima
niceindices(powerseries(cos(x), x, 0));
```
\sum_{i=0}^\infty \frac{(-1)^ix^{2i}}{(2i)!}

### Ayyuka na musamman

```maxima
bessel_j(0, 4.5);
```
-0.3205425089851214
```maxima
airy_ai(1.5);
```


## Dubi kuma
 

* Kwatanta tsarin algebra na kwamfuta
* SageMath, software na lissafi kyauta wanda ke karɓar ɗakunan karatu da yawa daga Maxima

## Bayanan da aka ambata

## Ƙarin karantawa

*