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Since early times, Chinese understood basic arithmetic (which dominated far eastern history), algebra, equations, and negative numbers with counting rods. [ citation needed ] Although the Chinese were more focused on arithmetic and advanced algebra for astronomical uses, they were also the first to develop negative numbers, algebraic geometry ...
In Japan, Seki Takakazu developed the rod numerals into symbolic notation for algebra and drastically improved Japanese mathematics. [13] After his period, the positional numeral system using Chinese numeral characters was developed, and the rod numerals were used only for the plus and minus signs .
The ancient Chinese were acquainted with astronomical cycles, geometrical implements like the rule, compass, and plumb-bob, and machines like the wheel and axle. The Chinese independently developed very large and negative numbers, decimals, a place value decimal system, a binary system, algebra, geometry, and
Fangcheng (sometimes written as fang-cheng or fang cheng) (Chinese: 方程; pinyin: fāngchéng) is the title of the eighth chapter of the Chinese mathematical classic Jiuzhang suanshu (The Nine Chapters on the Mathematical Art) composed by several generations of scholars who flourished during the period from the 10th to the 2nd century BC.
For instance, the prime ideals of a ring are analogous to prime numbers, and the Chinese remainder theorem can be generalized to ideals. There is a version of unique prime factorization for the ideals of a Dedekind domain (a type of ring important in number theory ).
In less formal terms, the group consists of words in the generators and their inverses, subject only to canceling a generator with an adjacent occurrence of its inverse. If G is any group, and S is a generating subset of G, then every element of G is also of the above form; but in general, these products will not uniquely describe an element of G.
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The ZX-calculus is a rigorous graphical language for reasoning about linear maps between qubits, which are represented as string diagrams called ZX-diagrams.A ZX-diagram consists of a set of generators called spiders that represent specific tensors.