Algebra

Original unencrypted text from wikipedia () [9]:

Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written in Arabic by the Persian[1] mathematician, astronomer, astrologer and geographer, Muhammad bin Muhammad bin Mūsā al-Khwārizmī titled Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations.

Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.

Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.

Report for Test: Algebra
 

Best Match Shift: 2
 

Percent Word Match: 88.33397
 

Total Calculation Time: 1366.813

 (22 minutes 46 seconds)

Original Input for Test: Algebra
 

CNIGDTCKUCDTCPEJQHOCVJGOCVKEUEQPEGTPKPIVJGUVWFAQHUVTWEVWTG,TGNC VKQPCPFSWCPVKVA.VJGPCOGKUFGTKXGFHTQOVJGVTGCVKUGYTKVVGPKPCTCDKE DAVJGRGTUKCP[1]OCVJGOCVKEKCP,CUVTQPQOGT,CUVTQNQIGTCPFIGQITCRJGT,OWJ COOCFDKPOWJCOOCFDKPONULCN-MJYLTKBOBVKVNGFMKVCDCN-LCDTYC-N-OWSC DCNC(OGCPKPI"VJGEQORGPFKQWUDQQMQPECNEWNCVKQPDAEQORNGVKQPCPFD CNCPEKPI"),YJKEJRTQXKFGFUAODQNKEQRGTCVKQPUHQTVJGUAUVGOCVKEUQNWVK QPQHNKPGCTCPFSWCFTCVKEGSWCVKQPU.VQIGVJGTYKVJIGQOGVTA,CPCNAUKU,EQ ODKPCVQTKEU,CPFPWODGTVJGQTA,CNIGDTCKUQPGQHVJGOCKPDTCPEJGUQHOCVJ GOCVKEU.GNGOGPVCTACNIGDTCKUQHVGPRCTVQHVJGEWTTKEWNWOKPUGEQPFCT AGFWECVKQPCPFRTQXKFGUCPKPVTQFWEVKQPVQVJGDCUKEKFGCUQHCNIGDTC,K PENWFKPIGHHGEVUQHCFFKPICPFOWNVKRNAKPIPWODGTU,VJGEQPEGRVQHXCTKCD NGU,FGHKPKVKQPQHRQNAPQOKCNU,CNQPIYKVJHCEVQTKBCVKQPCPFFGVGTOKPKPI VJGKTTQQVU.CNIGDTCKUOWEJDTQCFGTVJCPGNGOGPVCTACNIGDTCCPFECPDGIGPG TCNKBGF.KPCFFKVKQPVQYQTMKPIFKTGEVNAYKVJPWODGTU,CNIGDTCEQXGTUYQTM KPIYKVJUAODQNU,XCTKCDNGU,CPFUGVGNGOGPVU.CFFKVKQPCPFOWNVKRNKECVK QPCTGXKGYGFCUIGPGTCNQRGTCVKQPU,CPFVJGKTRTGEKUGFGHKPKVKQPUNGCFV QUVTWEVWTGUUWEJCUITQWRU,TKPIUCPFHKGNFU.

Decoded Text for Test: Algebra
 

ALGEBRAISABRANCHOFMATHEMATICSCONCERNINGTHESTUDYOFSTRUCTURE,RELATI ONANDQUANTITY.THENAMEISDERIVEDFROMTHETREATISEWRITTENINARABICBYTHEPER SIAN[1]MATHEMATICIAN,ASTRONOMER,ASTROLOGERANDGEOGRAPHER,MUHAMMADBI NMUHAMMADBINMLSJAL-KHWJRIZMZTITLEDKITABAL-JABRWA-L-MUQABALA(MEANING"T HECOMPENDIOUSBOOKONCALCULATIONBYCOMPLETIONANDBALANCING"),WHICHPROV IDEDSYMBOLICOPERATIONSFORTHESYSTEMATICSOLUTIONOFLINEARANDQUADRATICE QUATIONS.TOGETHERWITHGEOMETRY,ANALYSIS,COMBINATORICS,ANDNUMBERTHEORY ,ALGEBRAISONEOFTHEMAINBRANCHESOFMATHEMATICS.ELEMENTARYALGEBRAISOFT ENPARTOFTHECURRICULUMINSECONDARYEDUCATIONANDPROVIDESANINTRODUCTIO NTOTHEBASICIDEASOFALGEBRA,INCLUDINGEFFECTSOFADDINGANDMULTIPLYINGNUM BERS,THECONCEPTOFVARIABLES,DEFINITIONOFPOLYNOMIALS,ALONGWITHFACTORIZA TIONANDDETERMININGTHEIRROOTS.ALGEBRAISMUCHBROADERTHANELEMENTARYALG EBRAANDCANBEGENERALIZED.INADDITIONTOWORKINGDIRECTLYWITHNUMBERS,ALGE BRACOVERSWORKINGWITHSYMBOLS,VARIABLES,ANDSETELEMENTS.ADDITIONANDMU LTIPLICATIONAREVIEWEDASGENERALOPERATIONS,ANDTHEIRPRECISEDEFINITIONSLEA DTOSTRUCTURESSUCHASGROUPS,RINGSANDFIELDS.

Spaced Text for Test: Algebra
 

ALGEBRA IS BRANCH OF MATHEMATICS CONCERNING THE STUDY OF STRUCTURE RELATION AND QUANTITY THEN AM IS DERIVED FROM THE TREATISE WRITTEN IN BY THE PER AN MATHEMATICIAN ASTRONOMER AS LOG ERA GRAPH HAM MAD BIN HAM MAD BIN ML TITLED KIT JAB QA MEANING THE PEND US BOOK ON CALCULATION BY COMPLETION AND BALANCING WHICH PROVIDED SYMBOLIC OPERATIONS FORTH SYSTEMATICS ION OF LINEAR AND QUADRATIC EQUATIONS TOGETHER WITH GEOMETRY ANALYSIS COMBINATORICS AND NUMBER THEORY ALGEBRA IS ONE OFT HEM IN BRANCHES OF MATHEMATICS ELEMENTARY ALGEBRA IS OFTEN PART OFT HE CURRICULUM INS ON RYE CAT ION AND PROVIDES AN INTRODUCTION TO THE BASIC IDEAS OF ALGEBRA INCLUDING EFFECTS OF ADDING AND MULTIPLYING NUMBERS THE CONCEPT OF VARIABLES DEFINITION OF POLYNOMIALS ALONG WITH FACTOR AT ION AND DETERMINING THEIR ROOTS ALGEBRA IS MUCH BROADER THAN ELEMENTARY ALGEBRA AND CAN BEG ERA IN ADDITION TOW OR KING DIRECTLY WITH NUMBERS ALGEBRA COVERS WORKING WITH SYMBOLS VARIABLES ANDS ELEMENTS ADDITION AND MULTIPLICATION ARE VIEWED AS GENERAL OPERATIONS AND THEIR PRECISE DEFINITIONS LEAD TO STRUCTURES SUCH AS GROUPS RINGS AND FIELDS
 

Final Spaced Output for Test: Algebra
 

 ALGEBRA IS A BRANCH OF MATHEMATICS CONCERNING THE STUDY OF STRUCTURE , RELATION AND QUANTITY . THEN AM E IS DERIVED FROM THE TREATISE WRITTEN IN ARABIC BY THE PER SI AN [1] MATHEMATICIAN , ASTRONOMER , AS TRO LOG ERA NDGEO GRAPH ER,MU HAM MAD BIN MU HAM MAD BIN ML SJAL-KHWJRIZMZ TITLED KIT ABAL- JAB RWA-L-MU QA BALA( MEANING " THE COM PEND IO US BOOK ON CALCULATION BY COMPLETION AND BALANCING "), WHICH PROVIDED SYMBOLIC OPERATIONS FORTH E SYSTEMATICS OLUT ION OF LINEAR AND QUADRATIC EQUATIONS . TOGETHER WITH GEOMETRY , ANALYSIS , COMBINATORICS , AND NUMBER THEORY , ALGEBRA IS ONE OFT HEM A IN BRANCHES OF MATHEMATICS . ELEMENTARY ALGEBRA IS OFTEN PART OFT HE CURRICULUM INS EC ON DA RYE DU CAT ION AND PROVIDES AN INTRODUCTION TO THE BASIC IDEAS OF ALGEBRA , INCLUDING EFFECTS OF ADDING AND MULTIPLYING NUMBERS , THE CONCEPT OF VARIABLES , DEFINITION OF POLYNOMIALS , ALONG WITH FACTOR IZ AT ION AND DETERMINING THEIR ROOTS . ALGEBRA IS MUCH BROADER THAN ELEMENTARY ALGEBRA AND CAN BEG EN ERA LIZED. IN ADDITION TOW OR KING DIRECTLY WITH NUMBERS , ALGEBRA COVERS WORKING WITH SYMBOLS , VARIABLES , ANDS ET ELEMENTS . ADDITION AND MULTIPLICATION ARE VIEWED AS GENERAL OPERATIONS , AND THEIR PRECISE DEFINITIONS LEAD TO STRUCTURES SUCH AS GROUPS , RINGS AND FIELDS .