Fundamentals of creating the algebra science and algorithms

FUNDAMENTALS OF CREATING THE ALGEBRA
SCIENCE AND ALGORITHMS

M.M.Aripov¹, R.N.Normatov², I.M.Siddikov³, U.Oripova⁴

^1,2,3Associate Professor of the Department «Mathematics informatics»
of the Kokand State Pedagogical Institute named after Mukimi
⁴Student of the Tashkent State Legal University
As far as we know, the founder of algebra and algorithms sciences is Al Khorezmi. In his world famous book "Kitab al-jabrwa al-muqabala" algorithms for solving 6 different types’ problems are presented. The most common algorithm in practice is the socio-economic algorithm. The book bequest section sets out 60 tasks related to inheritance distribution [4]. When you become familiar with these problems, you will see that the algorithm problems that were once considered difficult are described only in words, without any mathematical symbols. Because at that time (IX century) signs +, -, /, = and other mathematical operations, even decimal fractions, were not known.
It is currently impossible to imagine algebra without symbols, but there was a time when of some of these symbols introduction into the mathematics world was a big breakthrough. Al-Kalasadi is best known for his writings on mathematics. The most significant of these was Tafsir fi-l-ilm al-hisab (Commentary on the arithmetic science). It is important to understand that Kalasadi's special contribution was not that he was the first to introduce new symbols or develop a notation system in algebra, but that he was the first to do both at the same time. He used the symbol ∫ as an equal sign (=), the Arabic equivalent of m for square values such as x2 (arabic mal') and the Arabic equivalent of K for cubic values such as x3 (Arabic ka'b). Kalasadi also standardized the Arabic terms use “wa” for addition, “illa” for subtraction, “fi” for multiplication, and “ala” for division. He was also the first to separate the numerator and a fraction denominator using a line [10].
“Kitab al-jabrwa al-muqabala” was translated from Arabic into Latin by Robert Chester in 1145 as Liber Algebra eet Almucabola, and this work became known to European mathematicians as algebra for short.
In the first half of the twelfth century, Al-Khwarizmi's book "Indian Account" entered Europe. The translator, whose name has not come down to us, calls it "Algorithmide Numberro Indorum", so the Latinized name of our compatriot is included in the title of the book.
Verses 11, 12 and 176 of An-Nisa Suras in Qur'an are the basis for solving the issues given in the section on the wills of Al-Khwarizmi book, Kitab al-Jabrwa-al-mukabala. These verses, along with the hadiths on this topic, form the faroiz science basis (faroiz is the science of distributing inheritance). The Quran was the basis for many sciences formation. For example, tafsir, tajwid, fiqh, faroiz and others.
In a hadith narrated by Imam Ibn Majoyiz Abu Hurayrah, the Prophet (peace and blessings of Allaah be upon him) said: “Teach faroiz and teach it to people. He is half of science. He will be forgotten. This is the first thing that will be taken from my ummah".
According to faroise, a testator can bequeath up to his third property to a stranger. Imam Bukhari has the following hadiths about this. On behalf of Amir ibn Saad, it is narrated that his father said:
The Prophet (peace and blessings of Allaah be upon him) came to me. I said: "O Messenger of Allah, pray to Allah, may He not bring me back." He said: "Perhaps Allah will resurrect you and benefit people thanks to you". “I wanted to make a will. I only have one daughter. Should I bequeath halfI said. He said, "Half a lot." Thus, people bequeathed one third, and this was permissible for them.
In a hadith narrated by Ibn Abbas, the Prophet (peace and blessings of Allaah be upon him) said: « Give the heirs your share in accordance with Shariah, and the rest will go to the next male relative of the deceased".
Dr. Zaglul Najjar cites an interesting case related to the Islamic heritage science law (pharoiz), which he was told about by a professor, an Egyptian lawyer, an acquaintance who teaches at a US university. « There was an atheist at the round table on legal issues. He started to say the wrong things about Islam. To make it a good lesson, I asked him: "Do you know how many volumes on inheritance distribution in the United States?" “More than eight volumes,” he replied. «Do you believe in the greatness of Islam when I tell you there are about ten rows of inheritance rights in Islam? “It can't be,” he replied. I wrote the verses about the inheritance on a piece of paper and gave it to him. A few days later he confessed to me. "The human mind cannot comprehend all kinship relations, as in the Koran, and it cannot divide the inheritance justly!" And he converted to Islam. Verses on inheritance were the only reason why he converted to Islam [5].
Below are the verses from Surah al-Nisa about the division of inheritance:
The almost creator given the following commandment for your sons and daughters. A male person receives as inheritance as much as it is for two women. If the dead only have daughters (more than two), they totally receive two thirds of the total heritage. If one daughter is remaining, she receives half of the inheritance. The father and mother of the dead are fitting one sixh inheritance each. Such distribution should be provided if the heirer has a child remain. However, if his has no children and no brothers, the mother gets one third inheritance. Such distribution of shares is possible only after the property of the dead has been payed out of the property of the dead and the testament is fulfilled (4:11).
Men are relied one second what is remained by wives. Such distribution is characteristic for a situation when a man and a woman do not have a child together. If there is a child, then a man is responsible for a fourth of wife's inheritance. Such distribution is possible only after the debts and the testament have been payed. Wives receive a fourth of husband's inheritance if the family doesn't have a child. However if there is a child in the family, then the wife has one eight property that remains after the man's death. Such distribution of property is possible only after the debts have been payed and the testament is fulfilled. If the dead didn't remain it’s in the form of children and parents, then his brothers and sisters get one sixth from the remaining heritage. Such distribution of property is possible only after the debts and the testament of the dead have payed. This is all commanded to you by the god creator who knows everything (4:12).
Say in answer to the explanation required by them: "the most explanation will present an explanation about those people who have no children or parents." if a person of a man who doesn't have children goes out of life, half of his inheritance will have to his sister. This is a distribution even if the sister has no children of own. If a dead man has two sisters, then they become the heirers of two thirds of his property. If his brother and sister left, the brother gets as much as two women. Really, the god explains everything, let you will not be delayed. The creator knows absolutely everything (4: 176) [1,5].
They say that a person who at the time of death has no children, grandchildren, parents or grandparents is called Kalola. The following criteria follow from the interpretation of the above verses.
1. The debts and wills of the deceased are first executed, and then the inheritance is distributed among the heirs.
2. For one son the share of two daughters corresponds.
3. If the deceased has more than two daughters and no sons, they inherit two-thirds.
4. If the deceased has one daughter and no son, she will have half the inheritance.
5. If the deceased has a daughter, son, one or more children, and at the same time the parents are alive, each parents has the right to one sixth of the inheritance. The rest of the inheritance is divided among the children in accordance with Sharia. If the deceased has only one son, he gets the rest. But if there is only one daughter, she gets half. The excess is added to the father - a close male relative.
6. If there is no child and the parents are heirs, one third to the mother. Two-thirds to father. In this case, there is no other heir besides the parents, that is, there is no child or wife left after death.
7. If the deceased has brothers, then one-sixth is left to the mother. In this case, the deceased will be followed by his parents and brothers and sisters. In it, even if brothers do not inherit themselves, the share of their mothers is reduced by one-sixth. If only one brother or sister remains, the mother's share is one third.
8. If a childless wife dies and her husband follows her, he receives half of the inheritance.
9. However, if the child is the son or daughter of the wife - no matter how many - and also the child of the previous husband, the husband will inherit a quarter.
10. If a childless husband dies and his wife follows him, she receives a quarter of the inheritance.
11. However, if the deceased husband has a son, daughter, half-brother, that is, a child from another wife, the wife receives one eighth of the inheritance.
12. If a person died in the form of "Kalola" and he is left with one brother whose mother is the same, and one sibling, each of them will receive one-sixth of the inheritance.
13. If the deceased has more than one brother with a common mother and more than one sibling, they will share a third of the inheritance.
14. If a man dies with Kalola and leaves an inheritance, but he has a sister and children, that sister receives half of the inheritance left by her brother.
15. If a man dies with Kalola and leaves an inheritance, but he has a sister and no children, that sister receives all (one share) of the inheritance left by her brother.
16. If the husband dies with Kalola and two sisters remain from him, they will receive two-thirds of the inheritance.
17. If a man dies with Kalola, leaving behind brothers and sisters, they inherit, according to the rule of one man, two female shares.
When we look at the above criteria, we inevitably think of the branching operator (IF) used in different algorithmic languages, because they repeat the word “if” many times.
Ayats 11, 12 and 176 of Surah an-Nisa refer to the following heirs: father, mother, husband, wife, son, daughter, brother, sister, granddaughter, grandmother, grandfather, brother or sister from the mother. The shares received comprise the following set: 1/8; 1/6; 1/4; 1/3; 1/2; 2/3; 1. It should be noted that there are seven different shares in this collection. We know that the number seven is a divine number. Seven days of the week, seven climates, seven wonders, seven colors in a rainbow, seven different sounds in a note (do, re, mi, fa, sol, la, si), seven generations. In the Quran, the phrase “seven heavens”, “the heavens creation” occurs seven times, the verses number in Surah al-Fatiha is seven, and so on.
Seven is the spiritual perfection number (the God seal or the covenant number). It comes from the Hebrew word "savah", meaning "to be fulfilled or satisfied, to have abundance." When Dr. Ivan Panin began reading the Scriptures in the original Hebrew, his mathematical mind soon noticed the striking meaning repetition not only of the number 7, but also of the multiples of seven. The repetition was so constant and frequent that the doctor concluded that this could not be a mere coincidence. To his utter amazement, he found that in each completed passage of the Hebrew and Greek originals, the number 7 revealed that many individual passages had between 70 and 100 features of the number 7. Each passage is linked to its neighbor thanks to the wonderful number 7, and this is true for each of the 66 books [7].
Now let's summarize the numbers involved in verses 11, 12, 176:
1 + 1 + 1 + 2 + 1 + 7 + 6 = 19, this number is also divine. The number 19 is also mentioned in many verses of the Quran: the number of verses in Surah al-Halak, which was first revealed, is 19, the number of words in each verse is 19, and this is the 19th Surah, the end of this chapter. The last Surah an-Nas, contains 19 words, and the number of letters in the first verse is 19. In accordance with the above considerations, the numbers 7 and 19 are considered the most basic divine numbers.
In the following example, we will describe the method for calculating the share of heirs.
Example1. A woman's husband dies. The heirs are father, mother, wife, son and daughter. Inheritance is distributed according to the above criteria as follows:
one-sixth of the inheritance to his father;
one sixth of the mother's inheritance;
one eighth of the inheritance to his wife;
The rest of the inheritance is distributed among the children, and one son is given the share of two daughters.
We accept the common inheritance as a unit in which the remainder of the inheritance - Q is found as follows:
Q = 1 - ( +
Based on the fact that one son corresponds to the share of two daughters, we consider children to be three girls. Then we divide by 3, to find the fraction equal to one girl,
To calculate the fraction equal to one son, we multiply by 2,

We summarize the shares of all heirs:

This means that the inheritance is divided into seventy-two parts, that is, to find the parts of the inheritance, you need to find the least common denominator (LCD) of the shares (fractions). The heirs and their respective proportions are shown in the table and diagram below.

№	Heirs	Share	In percentages
1.	Father	12/72	16,67
2.	Mother	12/72	16,67
3.	Wife	9/72	12,51
4.	A son	26/72	36.10
5.	Daughter	13/72	18,05

Now we will consider Example 2, which is more complex than Example 1, given in the section of the will "Al-djabr and al muqabaly" [2, p. 111-112].
Example 2: A deceased person has a mother, wife, two siblings and two sisters, and he bequeathed one-ninth of his property to another. The rule is that if you say that the inheritance is forty-eight, you have found it [amount]. You know that if you subtract one-ninth of all the goods, you get eight out of nine and the subtracted is one-eighth of the remaining. Add one-eighth to nine-eight and one-eighth of forty-eight, that's six, and your property is complete. Fifty-four is formed. Anyone to whom one of the nine is hung will receive six of them, that is, one-ninth of the total property. The remaining forty-eight were distributed among the heirs according to their share.
Al-Khwarizmi solves this example on the basis of verses 4.11 and 4.12 (criteria 5 and 11), i.e. he finds the number 48, which is part of the inheritance, by adding 1/6 of the mother's share and 1/8 of the wife's share (common denominator 48, with LND = 24, the example is solved in a simpler form). Below is the algorithm for calculating the inheritance of Al Khorezmi:
1.
2. 1 - ; (1) (2)
3. In equation (1) -1/9 we translate to the right with a plus sign and put expression (2) instead of 1/9. Al-Khwarizmi called this operation al-djabr.
1 =  
4. 48 + (48 х
5. 54 х
6. The remaining forty-eight are distributed among the heirs according to their share (Al-Kharazmi concludes the example here).
7. Since the proportion of two girls is equal to that of one boy, we assume that the number of sisters is six.
8. Mother will get one sixth of the inheritance
48 х
9. Wife will get one eighth of the inheritance
48 х
10. Rest 48 - 8 - 6 = 34.
11. The sisters will get 34 х
12. The brothers will get 2 х
Al-Khwarizmi used the method of replenishment (al jabr) given in points 3 and 4 to solve hereditary problems. We also developed a separate algorithm by summarizing points 3 and 4 to compose a program in the algorithmic language C ++ Builder 6.
As can be seen from the above examples, the calculation of problems by inheritance on a computer will require an algorithm for searching for LNDs. The search algorithm for LND is shown below:
1. Find the largest denominator infractions (we call it max).
2. If max is divisible by all denominators without a remainder, we find the LND and transfer control to 4.
3. Otherwise, we multiply max by z until it divides by all consecutive denominators, z = 1, 2, 3, …………………
4. LND
Abjad is also the basis for the emergence of the science of algebra.
Abjad is the following sequence of Arabic letters:

Alif

Ba

Jim

Dal

Ha

Vav

Za

Ha

Ta

Ya

Kaaf

Lam

Mim

Nun

أ

ب

ج

د

ﻩ

و

ﺯ

ﺡ

ﻁ

ﻱ

ﻙ

ﻝ

ﻡ

ﻥ

1

2

3

4

5

6

7

8

9

10

20

30

40

50

Sin

Yan

Fa

Sad

Kaf

Reysh

Shin

Ta

Sa

Ha

Zal

Dad

Za

Gayn

ﺱ

ﻉ

ﻑ

ص

ﻕ

ﺭ

ﺵ

ﺕ

ﺙ

ﺥ

ﺫ

ﺽ

ﻅ

ﻍ

60

70

80

90

100

200

300

400

500

600

700

800

900

1000

It was also used in the pre-Islamic period to encrypt events. The Quran clearly indicates some events that will occur in the future, and some are encoded in encrypted form. The Prophet (peace and blessings of Allaah be upon him) predicted the conquest of Istanbul by Muslim warriors 1,400 years ago. Much has been written about this in history books and in the works of Western and Eastern scholars. Many rulers have tried to fulfill this prophecy of the Prophet and accomplish this great conquest. But the goal was not achieved. By the will of fate, this conquest was made by Sultan Muhammad in 1453 AD. (857 hidjri.). This conquest is also mentioned in the Quran. This is due to the fact that in the 15th verse of Surah Saba the phrase “Ballatun Tayiba” (“Good Country”) corresponds to 857 hidjri (1453 AD) [8].

The (tribe) of Sabah had a sign in their settlement (indicating the might of Allah): two gardens - (one) on the right and (the other) on the left. (And exhortations came to them, who said): “Feed on the inheritance of your Lord and give thanks to Him! (After all, the place where you live is) - a good country [with a good climate and fertile soil], and (after all, Allah, only Whom should serve and worship) - The Forgiving Lord [forgives when they turn to Him with repentance] [9].

From this verse, select the phrase "Ballat un toyiba" ("Noble country") and put the corresponding code for abdaj over each letter.

Let's calculate the sum of the received numbers:

400 + 2 +10 + 9 + 400 + 4 + 30 + 2 = 857. This number can be seen as a sign of the conquest of Istanbul in 857 hidjiy (1453 AС).
Based on the above criteria and the search algorithm for the LND, a program was created in the algorithmic language C ++ Builder 6. This program was used to solve some problems in the testamentary section of the book of Al-Khwarizmi "Kitab al-jabr wa-l-muqabala" on a computer. In the course of studying the verses on the division of inheritance, it was discovered that they contain the hidden divine numbers 7 and 19. Abjad the same is the basis of the emergence of algebra. Based on the abjad, one can predict the date of future events that are hidden in the texts of the Quran. A specific example shows the decoding of the conquest date of Istanbul.
For centuries, inheritance issues have been resolved on the basis of the above verses. Al-Khwarizmi also wrote a section on wills in the Kitab al-jabrwa al-muqabala, based on the verses and hadiths of calculating inheritance, and in it he gave a solution to inheritance problems applied in practice.
Based on the above considerations, we can say that verses 11, 12 and 176 from Surah al-Nisa are the basis for creating the science of algebra and algorithms, and the great scientist Al Khorezmi used these verses to compose algorithms for solving problems by inheritance.
References

1. Sheikh Mohammed Sadik Mohammed Yusuf. Tafsiri Hilal, first volume, "HILOL-NASHR", Tashkent, 2013.

2. Muhammad ibn Ismail Bukhari. Gold chain. Sahih Bukhari st., 4th edition, "HILOL-NASHR", Tashkent, 2014.
3. Al Khorezmi. Al zhabr wa al mukobala, Tashkent, 1983.
4. V.V.Kabulov, A.V. Kabulov, A.T.Kenjabaev. Al-Harazmi is the founder of algorithmicization. Monograph.
5. www.islamdag.ru/vse-ob-islame/46853
Islamic inheritance law, Nurmukhammed Izudinov, July 26, 2017.
6. https://www.business-gazeta.ru Razila Kukushkina. Numbers are the Greatest Banner of the Most High.
7. M.D. Stewart. The Amazing Meaning of Numbers and Colors in Scripture Texts, Second Edition, Moscow, 2001.
8. Osman Nuriy Topbosh. A jug of water. "Fan", Tashkent 2007.
9. www.quran-online.ru
10.http://islamosfera.ru/velikij-matematik-kotoryj-obyasnil-pravila-algebry-cherez-poeziyu/?fbclid=IwAR0KMlkPZbR7902wmSLelLxiB0jw0UeZBIi4SYGepnkQyCdIQnP6UNTfhlQ. The great mathematician who explained the rules of algebra through poetry.02.07.2020.