International Baccalaureate Organization (IBO)
Alexander Pushkin School Perm Russian Federation
Municipal Autonomic Educational Institution
"Alexander Pushkin secondary primary school № 9
with in-depth study of subjects physics and mathematics”
Personal project
Creation of a site for helping students in mathematics
and information technology
The author - Sergey Tsaplin student MYP 5
student of 9G grade
Supervisor - Vyazmina Olga Nikolaevna
The teacher of algebra and geometry
Content
1. Title page…...................................................................................... 1
2. Content…………………………………………………………….. 2
3. Introduction………….…………………………………………….. 3
4. The main part ................................................................................... 5
5. Conclusion…………………………………………………………10
6. Bibliography……………………………………………………….12
7. Addition…………………………………………………………….13
Introduction
Topic: creation a site to help students in learning mathematics and IT.
Purpose: To create a site that will help students in computer science and
mathematics. The site will also have a program that implement some algorithms in
mathematics, for example, a program that draws the graphs of functions and some
algorithms in IT. For the user it should be very easy to download any program
from my site.
For whom? This site will be helpful for many people. In it will be interested
students who want to check their answers in math, for example, if students were
given a task to build several graphs of functions, they can use the program from
my site that draws these charts to see their results. The site will be useful for
programmers because it is much easier to use an algorithm that is already written,
than write it by your self. In any program you can choose language: English or
Russian. This makes possible to use my programs not only in Russia but also in
other countries. Building a graph of the function – is a very popular topic for
students. Statistics in Yandex (http://wordstat.yandex.ru) shows that each month
more than 30,000 people are searching for such programs.
Product. Product will be a site written on «Wordpress».The site will contain the
algorithms for programmists with explanation, in which cases, and what algorithm
to use. Also, there will be some useful programs in mathematics. The product has
been tested by Professor of "Mathematical modeling of systems and
processes", candidate of technical sciences of PNIPU (PSTU) Nyashina N.D.
Why I have chosen this topic? I have chosen this topic because in the 9th grade,
we where given a lot of hard work to do on maths lessons, and I thought that not
every student is able to cope with them, and it will be much easier if there would
be some programs to help you in maths. After a long searching in the Internet, I
haven’t found any site that would contain lot of these programs, so I decided to
create it. Also I decided that the site will contain algorithms for IT, since some
times you need some new algorithms that you don’t know for your program and
having all of them on one site will greatly help many programmers and reduse the
time of writing the code. I decided to create a site using «Wordpress», because I
was advised this program by my dad, who created his personal website
http://tsaplin.ru/ with using it. I liked it very much. After I learned how to work in
this program, I realized that it would be very easy and quick to make my site with
use of it, so my site is also written with the help of «Wordpress».
Methods and techniques. Oral interviews. I interviewed many of my friends and
classmates, and as a result I understood what types of tasks cause a lot of problems,
and what features for programming they would like to have. To address these types
of tasks were written program and where added functions for writing programs.
Comparing. After reviewing many similar programs on the Internet, with their
flaws and positive traits I had thought out scheme of work and the interface of each
program.
The area of interaction – Community and service. My website is made to help
people involve their knowledge in mathematics and computer science.
For creating a project was made following plan:
1.Collection of information and analysis.
2. Product Creation
2.1. Creating a shell of the site
2.2. Evaluation of similar programs from the Internet
2.3. Planning each program
2.4. Creating programs
2.5. Creating functions for programming
2.6. Placing programs on the site
2.7. Placing the site on the Internet
3. Testing the project.
3.1. Changing and editing the site and programs in accordance with feedback on
them.
4. Creation of the written work in English and Russian languages
5. Preparing the presentation
6. Protection of the project
Description of the process
Poll
After polling my friends and classmates, I realized what programs would be
helpful to pupils and students. So I decided to create programs to draw graphs of
functions and working with scales of notation, namely, to transfer a number from
one scale of notation to another and do simple arithmetic operations (addition,
subtraction, multiplication and division) with numbers written in the same
notation.
Creating a shell of a site
I created a site with a shell program Denwer. Denver - a set of Web
development. The name translates as DNVR - Gentleman's suite of web
developer. With this program I made my computer a server for my site. The
program
has
been
downloaded
from
the
official
site
http://www.denwer.ru. Installation and operation of the program is very clear and
understandable. I really like this program.After creating a shell website I needed to
learn the system «Wordpress», with which I will continue to fill the site. This
helped me to my dad. Also, I often turned to the site http://codex.wordpress.org/ is
the official site, with easy and convenient to operate. It gave me a lot of useful
information.
Evaluation of similar programs from the Internet
I had found 5 sites on the Internet which where building the graphs online:
http://school35.ucoz.ru/grapher/grapher_e.htm,
http://um-razum.ru/graph/,
http://www.kontrolnaya-rabota .ru
/
s
/
grafik
/
xy
/,
http://matesha.ru/schedule_function.php, http://www.reshalki.ru/yasam/graph.htm.
Program on sites http://school35.ucoz.ru/grapher/grapher_e.htm, http://umrazum.ru/graph/ and http://www.reshalki.ru/yasam/graph.htm were absolutely
identical . These programs work bad with the modules, don’t always build the
correct graph of the module containing the variable, there were no features both
integer and fractional parts of numbers.
The program from the site http://www.kontrolnaya-rabota.ru/s/grafik/xy/
contains all the same flaws as the previous three. On this site can not be selected
for plotting scale on the axis Y (vertical axis), which can greatly interfere with the
perception of some graphs. I do not like this program by the fact that, after drawing
the graph of a regular site goes to another page, and to construct the following
graph, it is necessary to return to the previous, and it is too long and
uncomfortable.
The program from the site http://matesha.ru/schedule_function.php also
contains all the flaws, that the first three, but the program does not have the
constants - numbers e and π, which are often needed for plotting, such as f (x) = e ^
x. It is unclear what functions are in the program, and how they should be used.
Thus, my program should contain besides the basic functions and features as
the integer and fractional parts of numbers. The program should be understandable
to use and must contain a statement to the users of the program did not raise
questions about its operation and that they know all its functions and how to work
with them. Also, in all the programs I have not viewed the visual effect of the
construction schedule. My program will build the schedule gradually.
I have found six sites, online programs, like my second program:
http://math.semestr.ru/inf/index.php,
http://eict.ru/calsystem.html,
http://allcalc.ru/node/418,
http://life-prog.ru/servis.php?id=1,
http://numsys.ru/calculator,
http://live.mephist.ru/show/calc/help/ numeralsystems.
The site http://life-prog.ru/servis.php?id=1 does good translation from one
scale of notation to another, but it is not possible to do arithmetic operations on
numbers.
The site http://math.semestr.ru/inf/index.php allows you to convert fractional
numbers in other number systems, but it only works with binary, octal, decimal
and hexadecimal number system.
The site http://allcalc.ru/node/418 can translate numbers only from the
decimal number system in a number system with base 2, 8 or 16, or vice versa.
On the web sites http://live.mephist.ru/show/calc/help/numeral-systems
http://eict.ru/calsystem.html you can do the translation, and arithmetic.
Web site http://numsys.ru/calculator allows arithmetic operations on long
numbers (up to 50 characters).
Thus, my program should be able to handle very large numbers (up to 1000
characters) and should be able to translate numbers from one system to another,
and to do simple operations on numbers written in any number system.
Planning the programs
The main component of the program, building the graph of the function is a
procedure that by the function f (x) and the value of x will show its value. After
user selects the extreme value of the variable X under consideration, the program
will break the interval from minimum to maximum values at several points of
equal parts, considers the value of the function at each point, to build all the points
on the graph and connect them in series.
In the program, working with the scales of notation, will be the two main
routines. One would be to transfer the number in the usual decimal notation. For
storing very large numbers in the decimal system will set up special structures. The
second sub-program will convert the resulting transformations after the number
written in decimal notation, the desired number system.
Creating the programs
I was advised to write my programs use PascalABC.net. This programming
environment is very similar to the Delphi 7, which is known to me, so I decided to
study it. On the Internet has been found a site with tutorials on this program:
http://sunschool.math.rsu.ru/pabc/. It was a presentation showing all the
differences PascalABC.net from Delphi 7, and that I needed. The presentations
were made by one of the authors of the programm - S.S.Mihalkovich. So I was
sure that I learned all the important differences between these two programs and
signed off on this search for sites with tutorials.
I had two options - write a program in Delphi 7 or PascalABC.net. Each of
these programs have their pros and cons.
In Delphi, faster and more convenient to create a program interface, Delphi
quickly.It makes for a second hundred million operations, and PascalABC.net only
a million, that is, PascalABC.net a hundred times slower, which will affect, for
example, the accuracy of the graph, as for one and the same time, we can build a
hundred times smaller than the points for a schedule.Delphi has worse graphics,
and it often flies in the presence of small missteps, than I do, this program is not
like that. In PascalABC.net easier to write code, since there are many built-in
algorithms that do not exist in Delphi, which reduces the code.
After long reflection, having weighed all the pros and cons of each program,
I decided to write their programs in Delphi 7.
The interface to the program was created with the help of the book written
by C.Bobrovskiy – “Delphi 7 training course.” This book has a wonderful
description of all parts of the interface. Also, there are examples of correct and
clear instructions for their use.
The site http://www.delphi-manual.ru/drawing.php has descriptions and
examples of functions which draws the lines, dots and circles in Delphi 7. The site
had a lot of examples, which allowed me to learn all the possibilities. The
functions described on this site have been used in my work. I was pleased with the
site.
While working on the programs I needed to establish the exact time. At
different sites has been described many solutions to this problem, but the method
described on the site http://forum.3dnews.ru/archive/index.php/t-57874.html allow
time to consider the program with high accuracy, so I chose it.
Create functions for programming
Also I posted on my website various features for programming. They were
taken from various sites, for example, http://codeforces.ru - is a site of online
competitions in IT, After regular olympiad you can watch the decision of its
members.From this site were taken out many functions. They are certainly right
and work smoothly, as taken from the solution of the problem which has received a
full score, that is absolutely right decision.
Some functions have been taken from the site http://ejudge.179.ru - this is
the site of the Summer Computer School, where I was this summer. On this
website have been saved a lot of my programs that were written by me and tested
in this school.
Also, several functions have been written and tested by me, such as
programs written by me on IT lessons at our school. They were tested on the
system
testing
and
stored
on
the
site
of
our
school
http://www.school9.perm.ru/gate/tester/.
Placement programs on the site
The program «Wordpress», allows you to put on your website files up to 2
megabytes.My programs weigh less, thus placing them on my website wasn’t hard.
Placing the site on the Internet
The site was placed under the name http://sergei.tsaplin.ru, as it is placed
under the domain of my family - tsaplin.ru. In my opinion, create a new domain
name is meaningless, as for the use of the domain you have to pay money, but for
the use of the domain tsaplin.ru you don’t need to pay.
Testing the site
The site was launched, and all users can send their feedback to my e-mail,
shown on the site. On February 16 at 10:00 pm were received 3 reviews for my site
and programs. All of them are in the adding to the project.
Changing the product.
In one of the reviews said about the software interface, and it was described
how to make it better and more intuitive for users of my programs. The
background was made white, as in the two reviews was mentioned that the gray
background makes the program an old-fashioned and ugly. After the changes it has
become more clear how to work in the program, there was a statement on the use
of various functions of the program. Changing the interface can be seen in the
following figures.
In the process, I showed my site to my classmates. Gregory Shartsev have
found a few mistakes in my product, for example, the program did not build the
graph of the square root of the module X. Because of this, I had found some errors
in the code of my program, and it was perfected.
The picture (see Annex 1) shows the old and ugly interface and improper
construction of the graph of f (x) = 1 / (x ^ 2). It also strikes a lot of space to the
right of the graph and it is unclear what to do with some of the cells (see Annex 2).
It is also convenient that all the parameters of the function are pressed on the upper
edge and elongated in one line. It is also unclear where the boundaries of the
graph. In general, all this makes the program inconvenient to use and ugly. With
this program convenient to work with.
The following picture (see Annex 3), there is a clear interface and the proper
construction of the graph. One can see the boundaries of schedule. There is no
extra space, and everything is clear for use. With such a program is very
convenient to operate. Introduced animation plotting gives a certain "flavor" of my
program and distinguishes it from others. Also instruction appeared.
Conclusion
In general, a product of my project (the site for those who are engaged in
mathematics and computer science) turned out as I had planned. I was pleased with
his project. The site is laid out on the Internet under the name
http://sergei.tsaplin.ru.
I have created a program that draws graphics functions. It contains all of the
previously scheduled function. The program is very useful. I myself have used it
for a work in algebra. It was possible to reduce the weight of both programs. They
weigh less than a megabyte, which allows you to quickly download. Also I got rid
of the installation program, that is to start using my program you just download
them and do not need to run any load. This makes the program more useful.
It also turned out to create a program that works with the degrees of notation,
which performs arithmetic operations with numbers in any base and converts the
number in any radix. It turned out to make it possible to use the programs in
English. To use this program you need just to download it. This program also
weighs not very much, and it will download quickly.
Successfully created a function for programming. Almost all of them are
written in several programming languages, mostly Pascal, C + + and Java - the
most popular programming languages. Due to the abundance of built structures in
C + +, many of the functions are written very shortly.
But there were things that I could not do, for example, in the program, which
draws graphs of functions, an error appears - the program connects to the point of
the graph, which should not be connected (see Annex 4). This happened due to the
fact that the program builds a graph of the points, and very difficult to determine
whether to join the regular line of two points - is there a gap chart or not. This will
probably be removed soon and the site will be a new program.
In another program I failed to make it work with long integers as difficult to
work with very long numbers and perform arithmetic operations with them. The
program will be fixed soon. This operation will be placed on my website along
with other functions.
The site lacks some features in Java, since don’t know it all programs are
taken from the Internet or website http://codeforces.ru. Some of the features I have
not found.
In the future, I plan to add new programs to the site to assist in the teaching of
mathematics, update old ones. Maybe there will some entertainment to make the
site more interesting.
I selected the interaction region contains two key questions - How can I help
others? and what can I do for people? In my project I'm helping others to study
mathematics and computer science.
In the course of the project I have improved my knowledge in the creation of
presentations and work with a text editor. I improved my knowledge in
mathematics and computer science, learned how to build applications, how to carry
out various surveys to gather feedback and analyze information.
In the end I want to thank people who helped me in writing of the project,
namely my dad - Tsaplin Vitaliy Alekseevich, who introduced me to «Wordpress»,
helped to deal with the site and post it on the Internet. Because of his advice on the
interface of programs, they look more beautiful and clear. I also want to thank my
classmate - Gregory Shartsevu for that at the time of writing programs, he advised
me how to improve my programs. Because of this in my programs there are no
mistakes, and they are working properly. Also Gregory wrote a great review about
my
program,
which
draws
graphs
of
functions.
Bibliography
http://wordstat.yandex.ru
2) http://codex.wordpress.org/
3) http://wordpress.org/download/
4) http://www.delphi-manual.ru/drawing.php
5) S. Bobrovskiy. Delphi7.training course. 2008.
6) http://forum.3dnews.ru/archive/index.php/t-57874.html
7) http://ejudge.179.ru
8) http://codeforces.ru
9) http://www.school9.perm.ru/gate/tester/
10) http://www.denwer.ru
1)
Addition
1.
2.
3.
4.
Texts of the programs:
Program that works whit the scales of notation.
unit it1;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, StdCtrls, ExtCtrls, Menus;
const kol = 14;
//const l = 1;
const lng: array[1..2, 1..kol] of string = (('Выполнить арифметические действия', 'Перевод в другую
систему счисления', 'Посчитать', 'Запомнить',
'Система счисления', 'Число', '+,-,*,/', 'Выберите действие',
'Достать из памяти', 'Очистить ячейку памяти', 'Число не соответствует системе счисления','Нет
свободной ячейки памяти',
'Ячейка памяти пуста','Вы выбрали русский язык'),
('Do arithmetic', 'Transfer to another scale of notation', 'Count', 'Remember',
'Scale of notation', 'Number', '+,-,*,/', 'Select the action', 'Get from memory', 'Clear memory cell',
'Number don''t feet in the scale of notation','No empty memory cell','Memory cell is empty','You
choosed english language'));
type
TForm1 = class(TForm)
Label2: TLabel;
Button1: TButton;
Label3: TLabel;
Label4: TLabel;
Button2: TButton;
Button3: TButton;
Button4: TButton;
Edit1: TEdit;
Label5: TLabel;
Edit2: TEdit;
Label6: TLabel;
Edit3: TEdit;
Edit4: TEdit;
Label7: TLabel;
Label8: TLabel;
Button5: TButton;
Button6: TButton;
Label9: TLabel;
RadioButton1: TRadioButton;
RadioButton2: TRadioButton;
RadioGroup1: TRadioGroup;
Button7: TButton;
MainMenu1: TMainMenu;
File1: TMenuItem;
Exit1: TMenuItem;
Label1: TLabel;
//procedure CheckBox1Click(Sender: TObject);
//procedure CheckBox2Click(Sender: TObject);
procedure CheckBox3Click(Sender: TObject);
//procedure CheckBox4Click(Sender: TObject);
procedure Button5Click(Sender: TObject);
procedure RadioButton1Click(Sender: TObject);
procedure RadioButton2Click(Sender: TObject);
procedure RadioGroup1Click(Sender: TObject);
procedure Button6Click(Sender: TObject);
procedure Button1Click(Sender: TObject);
procedure Button2Click(Sender: TObject);
procedure Button3Click(Sender: TObject);
procedure Button4Click(Sender: TObject);
procedure Button7Click(Sender: TObject);
procedure Exit1Click(Sender: TObject);
//procedure Button7Click(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
var
Form1: TForm1;
l, i, activity: longint;
st1, st2: int64;
u1, u2, rg1: boolean;
st, h: string;
cod: integer;
implementation
function max(var a, b: integer): integer;
begin
if a > b then max := a else max := b;
end;
Procedure PutBig(var a: string);
begin
for i := 1 to length(a) do
if a[i] in ['a'..'z'] then
a[i] := chr(ord(a[i]) + ord('A') - ord('a'));
end;
Function chekSys(a: string; s: int64): boolean;
var fail: boolean;
begin
fail := false;
while length(a) > 0 do
begin
if (a[length(a)] >= '0') and (a[length(a)] <= '9') and (a[length(a)] >= chr(ord('0') + s)) then fail := true else
if (a[length(a)] >= chr(ord('A') + s - 10)) then fail := true;
delete(a, length(a), 1);
end;
chekSys := fail;
end;
Function Tto10(var a: string; s1: int64): int64;
var k, p, h: int64; i, j: longint;
begin
k := 0;
p := 1;
while length(a) > 0 do
begin
if (a[length(a)] <= '9') then
h := ord(a[length(a)]) - ord('0') else h := ord(a[length(a)]) - ord('A') + 10;
k := p * h + k;
p := p * s1;
delete(a, length(a), 1);
end;
Tto10 := k;
end;
Function Tfrom10(var a, s: int64): string;
var k, h, p: int64; st: string;
begin
p := s;
st := '';
while a > 0 do
begin
h := a mod p;
if h <= 9 then st := chr(ord('0') + h) + st else st := chr(ord('A') + h - 10) + st;
a := a div p;
end;
Tfrom10 := st;
end;
Function trans(var a: string; s1, s2: int64): string;
var k, p, q: int64; b: int64;
begin
b := Tto10(a, s1);
trans := Tfrom10(b, s2);
end;
{$R *.dfm}
procedure TForm1.CheckBox3Click(Sender: TObject);
begin
L := 1;
Label2.Caption := lng[l, 8];
Form1.Label5.Caption := '';
Form1.Label6.Caption := '';
Form1.Label7.Caption := '';
Form1.Label8.Caption := '';
Button5.Caption := lng[l, 3];
Button6.Caption := lng[l, 4];
Button1.Caption := lng[l, 9];
Button2.Caption := lng[l, 9];
Button3.Caption := lng[l, 10];
Button4.Caption := lng[l, 10];
Label3.Caption := '';
Label9.Caption := '';
Label4.Caption := '';
Edit1.Text := '';
Edit2.Text := '';
Edit3.Text := '';
Edit4.Text := '';
Form1.RadioButton1.Caption := lng[l, 2];
Form1.RadioButton2.Caption := lng[l, 1];
Form1.RadioGroup1.Items.Add('Ðóññêèé');
Form1.RadioGroup1.Items.Add('English');
Form1.Canvas.Rectangle(5, 75, 510, 37);
end;
procedure TForm1.Button5Click(Sender: TObject);
var s1: string;
ste1, ste2: integer;
begin
s1 := Edit1.text;
PutBig(s1);
ste1 := strtoint(Edit2.Text);
ste2 := strtoint(Edit3.Text);
if ChekSys(s1, max(ste1, ste2)) then
Label9.Caption := lng[l, 11] else
if activity = 1 then
begin
val(Edit4.Text, st1, cod);
Label9.Caption := '';
st := Edit1.Text;
h := Edit3.Text;
if (cheksys(st, st1) = false) or (cheksys(h, st1) = false)
then Label9.Caption := lng[l,11] else
begin
st := Edit1.Text;
h := Edit3.Text;
if Edit2.Text = '+' then st2 := TTo10(st,st1) + TTo10(h, st1);
if Edit2.Text = '-' then begin st2 := TTo10(st,st1) + TTo10(h, st1);
if st2 < 0 then Label9.Caption := '-'; st2 := -st2; end;
if Edit2.Text = '/' then st2 := round(Tto10(st,st1) / Tto10(h,st1));
if Edit2.Text = '*' then st2 := TTo10(st,st1) * TTo10(h, st1);
Label9.Caption := Tfrom10(st2, st1);
end;
end
else
begin
st := Edit1.Text;
val(Edit2.Text, st1, cod);
val(Edit3.Text, st2, cod);
st := trans(st, st1, st2);
Label9.Caption := st;
end;
end;
procedure TForm1.RadioButton1Click(Sender: TObject);
begin
if l = 0 then l := 1;
Form1.Label5.Caption := lng[l, 6];
Form1.Label6.Caption := lng[l, 5] + ' 1';
Form1.Label7.Caption := lng[l, 5] + ' 2';
Form1.Label8.Caption := '';
activity := 0;
Form1.Edit4.Text := '-';
end;
procedure TForm1.RadioButton2Click(Sender: TObject);
begin
if l = 0 then l := 1;
Form1.Label5.Caption := lng[l, 6] + ' 1';
Form1.Label6.Caption := lng[l, 7];
Form1.Label7.Caption := lng[l, 6] + ' 2';
Form1.Label8.Caption := lng[l, 5];
Form1.Edit4.Text := '';
activity := 1;
end;
procedure TForm1.RadioGroup1Click(Sender: TObject);
begin
if Form1.RadioGroup1.ItemIndex = 0 then
begin
L := 1;
Button5.Caption := lng[l, 3];
Button6.Caption := lng[l, 4];
Button1.Caption := lng[l, 9];
Button2.Caption := lng[l, 9];
Button3.Caption := lng[l, 10];
Button4.Caption := lng[l, 10];
Label3.Caption := '';
Label4.Caption := '';
Edit1.Text := '';
Edit2.Text := '';
Edit3.Text := '';
Edit4.Text := '';
Label9.Caption := '';
Form1.RadioButton1.Caption := lng[l, 2];
Form1.RadioButton2.Caption := lng[l, 1];
Form1.Canvas.Rectangle(5, 75, 510, 37);
activity := 2;
Form1.Label9.Caption := lng[l, 14];
Form1.Label2.Caption := lng[l, 8];
end;
if Form1.RadioGroup1.ItemIndex = 1 then
begin
L := 2;
Label2.Caption := lng[l, 8];
Button5.Caption := lng[l, 3];
Button6.Caption := lng[l, 4];
Button1.Caption := lng[l, 9];
Button2.Caption := lng[l, 9];
Button3.Caption := lng[l, 10];
Button4.Caption := lng[l, 10];
Label3.Caption := '';
Label9.Caption := '';
Label4.Caption := '';
Edit1.Text := '';
Edit2.Text := '';
Edit3.Text := '';
Edit4.Text := '';
Form1.RadioButton1.Caption := lng[l, 2];
Form1.RadioButton2.Caption := lng[l, 1];
// Form1.RadioGroup1.InsertComponent(RadioButton1);
Form1.Canvas.Rectangle(5, 75, 510, 37);
activity := 2;
Form1.Label9.Caption := lng[l, 14];
Form1.Label2.Caption := lng[l, 8];
end;
end;
procedure TForm1.Button6Click(Sender: TObject);
begin
st := Form1.Label9.Caption;
if (u1) and (u2) then
begin
Form1.Label9.Caption := lng[l, 12];
end
else
if not u1 then begin label3.Caption := st; u1 := true; end else
if not u2 then begin label4.Caption := st; u2 := true; end;
end;
procedure TForm1.Button1Click(Sender: TObject);
begin
if not u1 then Form1.Label9.Caption := lng[l, 13] else
Edit1.Text := Label3.Caption;
end;
procedure TForm1.Button2Click(Sender: TObject);
begin
if not u2 then Form1.Label9.Caption := lng[l, 13] else
Edit1.Text := Label4.Caption;
end;
procedure TForm1.Button3Click(Sender: TObject);
begin
u1 := false;
Label3.Caption := '';
end;
procedure TForm1.Button4Click(Sender: TObject);
begin
u2 := false;
Label4.Caption := '';
end;
procedure TForm1.Button7Click(Sender: TObject);
begin
L := 1;
RadioGroup1.Caption := '';
if not rg1 then begin
Form1.RadioGroup1.Items.Add('Ðóññêèé');
Form1.RadioGroup1.Items.Add('English');
rg1 := true;
end;
Form1.Canvas.Rectangle(5, 75, 510, 37);
end;
procedure TForm1.Exit1Click(Sender: TObject);
begin
halt;
end;
end.
Graphic builder:
unit graphic_builder;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, StdCtrls, Math;
const
eps = 0.00000001;
const
dotes = 8000;
type
Temas = array[1..10000] of extended;
type
Tdmas = array[1..10000] of integer;
type
Wh = record
str: string;
oth: Temas;
end;
type
Wfail = record
x: extended;
fail: boolean;
end;
type
TForm1 = class(TForm)
Edit1: TEdit;
Label1: TLabel;
Edit2: TEdit;
Label2: TLabel;
Edit3: TEdit;
Edit4: TEdit;
Label3: TLabel;
Label4: TLabel;
CheckBox1: TCheckBox;
Edit5: TEdit;
Button1: TButton;
Label6: TLabel;
Label7: TLabel;
ListBox1: TListBox;
Label5: TLabel;
Label8: TLabel;
Label9: TLabel;
Label10: TLabel;
Button2: TButton;
procedure Button1Click(Sender: TObject);
procedure Button2Click(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
var
Form1: TForm1;
hait_of_form, hait, wid: longint;
implementation
procedure set_constants;
begin
hait_of_form := 800;
wid := 690;
hait := 690;
end;
procedure draw_osi;
var
x, y, m: longint;
h, xmin1, ymin1, xmin, ymin, xmax, ymax: longint;
size: longint;
s: string;
begin
Form1.Canvas.MoveTo(3, hait_of_form - 3);
Form1.Canvas.LineTo(712, hait_of_form - 3);
Form1.Canvas.LineTo(712, hait_of_form - 11 - hait);
Form1.Canvas.LineTo(3, hait_of_form - 11 - hait);
Form1.Canvas.LineTo(3, hait_of_form - 3);
Form1.Canvas.MoveTo(5, hait_of_form - 5);
Form1.Canvas.LineTo(710, hait_of_form - 5);
Form1.Canvas.LineTo(710, hait_of_form - 9 - hait);
Form1.Canvas.LineTo(5, hait_of_form - 9 - hait);
Form1.Canvas.LineTo(5, hait_of_form - 5);
xmin := strtoint(Form1.Edit1.text);
xmax := strtoint(Form1.Edit2.text);
ymin := strtoint(Form1.Edit3.text);
ymax := strtoint(Form1.Edit4.text);
if xmin * xmax < 0 then
begin
xmin1 := -xmin;
x := round(wid * xmin1 / (xmin1 + xmax));
Form1.Canvas.MoveTo(x + 10, hait_of_form - 10);
Form1.Canvas.LineTo(x + 10, Hait_of_form - hait);
Form1.Canvas.LineTo(x + 8, hait_of_form - hait + 6);
Form1.Canvas.LineTo(x + 12, Hait_of_form - hait + 6);
Form1.Canvas.LineTo(x + 10, Hait_of_form - hait);
end;
if ymin * ymax < 0 then
begin
ymin1 := -ymin;
y := round(hait_of_form - hait * ymin1 / (ymin1 + ymax));
Form1.Canvas.MoveTo(10, y);
Form1.Canvas.LineTo(wid, y);
Form1.Canvas.LineTo(wid - 6, y + 2);
Form1.Canvas.LineTo(wid - 6, y - 2);
Form1.Canvas.LineTo(wid, y);
end;
Form1.Canvas.TextOut(x - 5, hait_of_form - hait - 5, 'Y');
Form1.Canvas.TextOut(wid - 5, y + 8, 'X');
Form1.Canvas.TextOut(x - 5, y + 8, '0');
size := 1;
m := x + round(wid / (xmax - xmin) * size);
str(size, s);
Form1.Canvas.TextOut(m + 5, y + 8, s);
Form1.Canvas.MoveTo(m + 10, y + 3);
Form1.Canvas.LineTo(m + 10, y - 3);
size := 1;
m := y - round(hait / (ymax - ymin) * size);
Form1.Canvas.TextOut(x - 5, m, s);
Form1.Canvas.MoveTo(x + 13, m);
Form1.Canvas.LineTo(x + 7, m);
end;
function tan(x: extended): extended;
begin
tan := sin(x) / cos(x);
end;
function find_close(var s: string; num: integer): integer;
var
i, k: integer;
begin
k := 1;
i := num;
while k <> 0 do
begin
inc(i);
if s[i] = '(' then inc(k);
if s[i] = ')' then dec(k);
end;
find_close := i;
end;
function end_of_sin(var s: string; n: integer): integer;
var
i: integer;
begin
if s[n + 3] = '2' then end_of_sin := find_close(s, n + 4) else
end_of_sin := find_close(s, n + 3);
end;
procedure prepare(var s: string);
var
l, r, i: integer;
begin
for i := 1 to length(s) do
begin
if s[i] in ['s', 'c', 't'] then
begin
r := end_of_sin(s, i);
if s[i + 3] = '2' then l := 4 else l := 3;
delete(s, i + 1, l);
if (l = 3) and (s[i] = 's') then begin s[i] := '@'; s[r - l] := '#'; end;
if (l = 3) and (s[i] = 'c') then begin s[i] := '$'; s[r - l] := '%'; end;
if (l = 3) and (s[i] = 't') then begin s[i] := '&'; s[r - l] := '?'; end;
if (l = 4) and (s[i] = 's') then begin s[i] := '"'; s[r - l] := ';'; end;
if (l = 4) and (s[i] = 'c') then begin s[i] := ':'; s[r - l] := '\'; end;
if (l = 4) and (s[i] = 't') then begin s[i] := '`'; s[r - l] := '~'; end;
end;
if s[i] = '|' then
if (i = 1) or
(s[i - 1] in ['+', '-', '*', '/', '^', '!', '<', '[', '{', '(', '@', '$', '&', '"', ':', '`'])
then
s[i] := '!';
end;
end;
function sk(ch: char): boolean;
begin
if ch in ['<', '>', '(', ')', '[', ']', '{', '}', '|', '!', '@', '#', '$', '%', '&', '?', '"', ';', ':', '\', '`', '~'] then
sk := true else sk := false;
end;
function count_in_skoba(var sk: char; n: extended): extended;
var
rez: extended;
begin
rez := 0;
if sk in ['<', '>'] then if n + eps > 0 then rez := sqrt(n) else rez := -1;
if sk in ['[', ']'] then rez := trunc(n);
if sk in ['{', '}'] then rez := n - trunc(n);
if sk in ['(', ')'] then rez := n;
if sk in ['|', '!'] then rez := abs(n);
if sk in ['@', '#'] then rez := sin(n);
if sk in ['$', '%'] then rez := cos(n);
if sk in ['&', '?'] then rez := tan(n);
if sk in ['"', ';'] then rez := sin(n) * sin(n);
if sk in [':', '\'] then rez := cos(n) * cos(n);
if sk in ['`', '~'] then rez := tan(n) * tan(n);
count_in_skoba := rez;
end;
function pr(ch: char): integer;
begin
if ch in ['+', '-'] then pr := 2 else
if ch in ['*', '/'] then pr := 3 else
if ch = '^' then pr := 4 else
if sk(ch) then pr := 1 else
pr := -1;
end;
function checkoz(var o, z: char): boolean;
begin
if ((o = '!') and (z = '|')) or ((o = '{') and (z = '}')) or ((o = '[') and (z = ']'))
or ((o = '(') and (z = ')')) or ((o = '<') and (z = '>')) or ((o = '@') and (z = '#'))
or ((o = '$') and (z = '%')) or ((o = '&') and (z = '?')) or ((o = '"') and (z = ';'))
or ((o = ':') and (z = '\')) or ((o = '`') and (z = '~')) then
checkoz := true else checkoz := false;
end;
function make_string(var s: string; l, r: integer): string;
var
k: string; i: integer;
begin
k := '';
for i := l to r do k := k + s[i];
make_string := k;
end;
function mins(var s: string; i: integer): boolean;
begin
if s[i] <> '-' then mins := false else
begin
if i = 1 then mins := true else
begin
if s[i - 1] = '(' then mins := true else mins := false;
end;
end;
end;
function make(var s: string; x: extended): Wh;
var
j, i, kol, cot: integer; q: string; w: extended;
n: Temas; k: string;
minus: longint;
begin
kol := 0;
k := '';
fillchar(n, sizeof(n), 0);
i := 1;
while i <= length(s) do
begin
if (pr(s[i]) > 0) or (s[i] in ['s', 'c', 't']) then
begin
if s[i] in ['s', 'c', 't'] then
begin
k := k + make_string(s, i, end_of_sin(s, i));
i := end_of_sin(s, i);
end
else
k := k + s[i];
end;
inc(i);
end;
i := 1;
kol := 0;
while i <= length(s) do
begin
q := 'z';
while pr(s[i]) > 0 do inc(i);
if s[i] in ['s', 'c', 't'] then begin i := end_of_sin(s, i); inc(kol); end;
minus := 1;//if mins(s, i - 1) then minus := -1 else minus := 1;
while (i <= length(s)) and ((pr(s[i]) < 0) or ((q[1] in ['s', 'c', 't']) and (not sk(s[i])))) do
begin
if q = 'z' then q := '';
q := q + s[i];
inc(i);
end;
val(q, w, cot);
if cot = 0 then begin inc(kol); n[kol] := w * minus; end;
if q = 'x' then begin inc(kol); n[kol] := x * minus; end;
if (q = 'pi') or (q = 'p') then begin inc(kol); n[kol] := pi * minus; end;
if q = 'e' then begin inc(kol); n[kol] := 2.71828182846 * minus; end;
inc(i);
if i <= length(s) then
end;
kol := 0;
{for i := 1 to length(k) do
begin
if not sk(k[i]) then inc(kol);
if k[i] = '-' then
begin
j := i + 1;
if pr(k[j]) = 2 then begin
k[i] := '+';
n[kol + 1] := -n[kol + 1]; end;
end;
end; }
kol := 0;
for i := 1 to length(k) do
begin
if not sk(k[i]) then inc(kol);
if k[i] = '/' then
begin
j := i + 1;
if pr(k[j]) = 3 then begin
k[i] := '*'; if n[kol + 1] <> 0 then
n[kol + 1] := 1 / n[kol + 1]; end;
end;
end;
make.str := k;
make.oth := n;
end;
function op(var s: string; n: integer): boolean;
begin
if s[n] in ['(', '{', '[', '<', '!', '@', '$', '&', '"', ':', '`'] then op := true
else op := false;
end;
function cl(var s: string; n: integer): boolean;
begin
if s[n] in [']', '}', ')', '>', '|', '#', '%', '?', ';', '\', '~'] then
cl := true else cl := false;
end;
function krut(var s: string; n: integer): boolean;
var
f, w: boolean;
begin
f := false; w := false;
if (n = 1) or ((not cl(s, n - 1)) and (pr(s[n]) >= pr(s[n - 1]))) then f := true;
if(n = length(s)) or ((not op(s, n + 1)) and (pr(s[n]) >= pr(s[n + 1]))) then w := true;
if (f) and (w) then krut := true else krut := false;
end;
function operation(var ch: char; a, b: extended; err: integer): WFail;
var
st: longint;
ans: WFail;
begin
if err = 0 then
begin
if ch = '+' then b := a + b;
if ch = '-' then b := a - b;
if ch = '*' then b := a * b;
if ch = '^' then
begin
if (a < 0) and (abs(b - round(b)) < eps) then
begin
st := round(b);
if st mod 2 = 0 then b := power(-a, b) else b := -power(-a, b);
end
else
if ((a = 0) and (b = 0)) or (a < 0) then err := 1 else
b := power(a, b);
end;
if ch = '/' then
if abs(b) < eps then err := 1
else b := a / b;
end
else
b := 0;
ans.x := b;
if err = 1 then ans.fail := true else ans.fail := false;
operation := ans;
end;
procedure ydal(var k: string; u: Tdmas);
var
s: string; i: integer;
begin
s := '';
for i := 1 to length(k) do if u[i] <> 100500 then s := s + k[i];
k := s;
end;
function get_value(var s: string; x: extended): WFail;
var
n: Temas;
u, uk: Tdmas;
k, t: string;
y, q, kl, l, r, i, j, kol, err, op: integer;
rez, m: extended;
yd, fail: boolean;
wth: Wh;
b, ans: Wfail;
daleko: longint;
begin
err := 0;
prepare(s);
wth := make(s, x);
k := wth.str;
n := wth.oth;
i := 1;
kol := 0;
err := 0;
for i := 1 to length(k) do u[i] := 0;
fail := false;
while not fail do
begin
kol := 0;
fillchar(u, sizeof(u), 0);
fillchar(uk, sizeof(uk), 0);
op := 0;
i := 1;
while i <= length(k) do
begin
yd := false;
if not sk(k[i]) then inc(kol);
if (i <> 1) and (checkoz(k[i - 1], k[i])) then
begin
n[kol + 1] := count_in_skoba(k[i], n[kol + 1]);
if (k[i] in ['<', '>']) and (n[kol + 1] < 0) then err := 1;
delete(k, i - 1, 2); i := i - 2; yd := true;
end;
if (not yd) and (length(k) > 0) and (not sk(k[i])) and (krut(k, i)) then
begin
ans := operation(k[i], n[kol], n[kol + 1], err);
n[kol + 1] := ans.x;
if ans.fail then err := 1;
u[kol] := 1;
uk[i] := 100500;
inc(op);
if err = 1 then fail := true;
end;
inc(i);
end;
kl := 0;
i := 1; q := 1;
while q <= length(k) + 1 do
begin
while u[q] = 1 do inc(q);
n[i] := n[q];
inc(i);
inc(q);
end;
ydal(k, uk);
kol := 0;
for i := 1 to length(k) do
begin
if not sk(k[i]) then inc(kol);
if k[i] = '-' then
begin
j := i + 1;
if pr(k[j]) = 2 then begin
k[i] := '+';
n[kol + 1] := -n[kol + 1]; end;
end;
end;
kol := 0;
for i := 1 to length(k) do
begin
if not sk(k[i]) then inc(kol);
if k[i] = '/' then
begin
j := i + 1;
if pr(k[j]) = 3 then begin
k[i] := '*'; if n[kol + 1] = 0 then begin
fail := true; err := 1; break; end else
n[kol + 1] := 1 / n[kol + 1]; end;
end;
end;
if length(k) = 0 then fail := true;
end;
if err = 0 then fail := false;
if err = 1 then fail := true;
get_value.x := n[1];
get_value.fail := fail;
end;
procedure get_reed_of_minus(var s: string);
var
i: longint;
begin
i := 1;
while i <= length(s) do
begin
if (s[i] = '-') and ((i = 1) or (s[i - 1] = '(')) then
insert('0', s, i);
inc(i);
end;
end;
procedure final();
var
i, code: integer;
s: string;
xprz, yprz, yd, x0, ypr, ylast, xd, xpr, x, y, xl, xh, yl, yh: extended;
mid, ylst, ycan: Wfail;
prev: boolean;
begin
if Form1.CheckBox1.State = cbUnchecked then Form1.refresh;
s := Form1.Edit1.text;
val(s, xl, code);
s := Form1.Edit2.text;
val(s, xh, code);
s := Form1.Edit3.text;
val(s, yl, code);
s := Form1.Edit4.text;
val(s, yh, code);
s := Form1.Edit5.text;
get_reed_of_minus(s);
x := xl;
prev := false;
for i := 1 to dotes do
begin
x := x + ((xh - xl) / (dotes - 1));
ycan := get_value(s, x);
y := ycan.x;
if x > -15 then
x := x;
if (not ycan.fail) and (y - yl + eps > 0) and (yh - y + eps > 0) then
begin
xd := wid * ((x - xl) / (xh - xl));
yd := hait_of_form - hait * ((y - yl) / (yh - yl));
if prev then
begin
mid := get_value(s, (x + xpr) / 2);
if (not mid.fail) and ((mid.x - y) * (mid.x - ypr) < eps) then
begin
Form1.Canvas.MoveTo(round(xprz) + 10, round(yprz));
Form1.Canvas.LineTo(round(xd) + 10, round(yd));
end;
end;
prev := true;
xpr := x;
ypr := y;
xprz := xd;
yprz := yd;
end
else
prev := false;
end;
end;
{$R *.dfm}
procedure TForm1.Button1Click(Sender: TObject);
begin
set_constants;
final;
draw_osi;
end;
procedure TForm1.Button2Click(Sender: TObject);
begin
Form1.ListBox1.Items.Add('Тригонометрические функции записываются:');
Form1.ListBox1.Items.Add('sin(), cos(), tan(), sin2(), cos2(), tan2().');
Form1.ListBox1.Items.Add('Квадратный корень - <...>.');
Form1.ListBox1.Items.Add('Выражение, из которого извлекается');
Form1.ListBox1.Items.Add('квадратный корень должно быть');
Form1.ListBox1.Items.Add('записано в следующих скобках: < и >.');
Form1.ListBox1.Items.Add('Например, корень и х должен быть');
Form1.ListBox1.Items.Add('записан, как <x>.');
Form1.ListBox1.Items.Add('Программа умеет работать с функциями');
Form1.ListBox1.Items.Add('модуля - |x|, целой части - [x] и');
Form1.ListBox1.Items.Add('дробной части - {x}.');
Form1.ListBox1.Items.Add('Пожалуйста, записывайте функции правильно,');
form1.ListBox1.Items.Add('иначе вылезет ошибка.');
end;
end.