dollars是什么意思

This article is about a software package. For other uses, see Gap (disambiguation).

百度 我想，可能是秋老师觉得自己并不是明星艺人，知名度不高，所以就想多做一些，赢得点好感！不过，各位明星艺人们倒是做的不是很对了，似乎是将秋老师所做的种种当成了理所应当，于是就有了下面这样的事情发生！有一次，李静带着一群人出去玩了，并且交代秋老师，6点钟回来要准时开饭！秋老师也一口答应了，但是下午呢，秋老师看着时间还早，与何穗一起将工作做完了，就和游客一起出去爬山了！在这期间，李静还打电话回来顶住秋老师一定要准备好饭菜，是程晓玥接的电话，她明明知道秋老师不再，但还是一口答应了下来，搞不懂这是什么逻辑！等到李静等人回来的时候，见到秋老师不再，瞬间李静就炸了，非常生气的样子！等到秋老师回来之后，发现自己玩的太高兴，忘记了时间，也是一脸的愧疚！秋老师道歉的态度也是非常的诚恳，先是和戴军老师道歉，随后又和何穗道歉，态度也是相当的诚恳，但却被何穗一脸不耐烦的推开了！最后，秋老师去给李静道歉，整个过程，李静都没有给秋老师任何的好脸色，最终还是别的人家给秋老师求情，李静才勉为其难的原谅了秋老师！其实，我很不懂，为什么秋老师要为大家道歉，本来做饭就不是一个人的事情啊！我想，很多看过节目的人都会很气愤，明星艺人就可以高人一等的对素人秋老师颐指气使了么？可能真的是因为秋老师是一个素人吧！不出意外的是，在节目播出之后，李静自然是成为了网友群起攻之的对象，而何穗也没有被网友拉下！依照何穗的微博，我能想到的只有这件事了，毕竟那时候何穗也是被人指责过于势力了！但综艺节目么，不要天当真了，通过后期剪辑，可以制造出各种各样的效果，如今旧事被重提，看来何穗真的是被冤枉了！秋老师在微博中也为何穗辩解过，还称赞何穗是非常会照顾人的知心大姐姐，但不晓得何穗为什么不自己去澄清，反而是要背负这这样的骂名！所以，对待综艺节目，我们要辩证的去看待，毕竟为了收视率，后期是什么都能做的出来的！本文来自凤凰号，仅代表凤凰号自媒体观点。

GAP
Developer(s)	University of St Andrews RWTH Aachen TU Braunschweig Colorado State University TU Kaiserslautern
Initial release	1988
Stable release	4.14.0 / 5 December 2024 (5 December 2024)
Repository	github.com/gap-system/gap
Written in	C
Operating system	Cross-platform
Type	Computer algebra system
License	GNU General Public License
Website	www.gap-system.org

GAP (Groups, Algorithms and Programming) is an open source computer algebra system for computational discrete algebra with particular emphasis on computational group theory.

History

GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westf?lische Technische Hochschule Aachen, Germany from 1986 to 1997. After the retirement of Joachim Neubüser from the chair of LDFM, the development and maintenance of GAP was coordinated by the School of Mathematical and Computational Sciences at the University of St Andrews, Scotland. In the summer of 2005 coordination was transferred to an equal partnership of four 'GAP Centres', located at the University of St Andrews, RWTH Aachen, Technische Universit?t Braunschweig, and Colorado State University at Fort Collins; in April 2020, a fifth GAP Centre located at the TU Kaiserslautern was added.

Features

GAP contains a procedural programming language and a large collection of functions to create and manipulate various mathematical objects. It supports integers and rational numbers of arbitrary size, memory permitting. Finite groups can be defined as groups of permutations and it is also possible to define finitely presented groups by specifying generators and relations. Several databases of important finite groups are included. GAP also allows to work with matrices and with finite fields (which are represented using Conway polynomials). Rings, modules and Lie algebras are also supported.

Distribution

GAP and its sources, including packages (sets of user contributed programs), data library (including a list of small groups) and the manual, are distributed freely, subject to "copyleft" conditions. GAP runs on any Unix system, under Windows, and on Mac systems. The standard distribution requires about 300 MB (about 400 MB if all the packages are loaded).

The user contributed packages are an important feature of the system, adding a great deal of functionality. GAP offers package authors the opportunity to submit these packages for a process of peer review, hopefully improving the quality of the final packages, and providing recognition akin to an academic publication for their authors. As of March 2021, there are 151 packages distributed with GAP, of which approximately 71 have been through this process.

An interface is available for using the SINGULAR computer algebra system from within GAP. GAP is also included in the mathematical software system SageMath.

Sample session

Permutation group

gap> G:=SmallGroup(8,1); # Set G to be the 1st group (in GAP catalogue) of order 8.
<pc group of size 8 with 3 generators>
gap> i:=IsomorphismPermGroup(G); # Find an isomorphism from G to a group of permutations.
<action isomorphism>
gap> Image(i,G); # Generators for the image of G under i - written as products of disjoint cyclic permutations.
Group([ (1,5,3,7,2,6,4,8), (1,3,2,4)(5,7,6,8), (1,2)(3,4)(5,6)(7,8) ])
gap> Elements(Image(i,G)); # All the elements of im G.
[ (), (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,4,2,3)(5,8,6,7),
  (1,5,3,7,2,6,4,8), (1,6,3,8,2,5,4,7), (1,7,4,5,2,8,3,6), (1,8,4,6,2,7,3,5) ]

Euclidean ring

gap> # test consistency of EuclideanDegree, EuclideanQuotient, EuclideanRemainder,
gap> # and QuotientRemainder for some ring and elements of it
gap> checkEuclideanRing :=
> function(R, colls...)
>   local coll1, coll2, a, b, deg_b, deg_r, q, r, qr;
>   if Length(colls) >= 1 then coll1:=colls[1];
>   elif Size(R) <= 100 then coll1 := R;
>   else coll1 := List([1..100],i->Random(R));
>   fi;
>   if Length(colls) >= 2 then coll2:=colls[2];
>   elif Size(R) <= 100 then coll2 := R;
>   else coll2 := List([1..100],i->Random(R));
>   fi;
>   for b in coll1 do
>     if IsZero(b) then continue; fi;
>     deg_b := EuclideanDegree(R, b);
>     for a in coll2 do
>       q := EuclideanQuotient(R, a, b); Assert(0, q in R);
>       r := EuclideanRemainder(R, a, b); Assert(0, r in R);
>       if a <> q*b + r then Error("a <> q*b + r for ", [R,a,b]); fi;
>       deg_r := EuclideanDegree(R, r);
>       if not IsZero(r) and deg_r >= deg_b then Error("Euclidean degree did not decrease for ",[R,a,b]); fi;
>       qr := QuotientRemainder(R, a, b);
>       if qr <> [q, r] then Error("QuotientRemainder inconsistent for ", [R,a,b]); fi;
>     od;
>   od;
>   return true;
> end;;

gap> # rings in characteristic 0
gap> checkEuclideanRing(Integers,[-100..100],[-100..100]);
true
gap> checkEuclideanRing(Rationals);
true
gap> checkEuclideanRing(GaussianIntegers);
true
gap> checkEuclideanRing(GaussianRationals);
true

gap> # finite fields
gap> ForAll(Filtered([2..50], IsPrimePowerInt), q->checkEuclideanRing(GF(q)));
true

gap> # ZmodnZ
gap> ForAll([1..50], m -> checkEuclideanRing(Integers mod m));
true
gap> checkEuclideanRing(Integers mod ((2*3*5)^2));
true
gap> checkEuclideanRing(Integers mod ((2*3*5)^3));
true
gap> checkEuclideanRing(Integers mod ((2*3*5*7)^2));
true
gap> checkEuclideanRing(Integers mod ((2*3*5*7)^3));
true

See also

• Comparison of computer algebra systems

External links

• Official website
• Gap-system on GitHub