Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Recipe for Symbolic Geometric Computing: Long Geometric Product,
  BREEFS and Clifford Factorization   In symbolic computing, a major bottleneck is middle expression swell.
Symbolic geometric computing based on invariant algebras can alleviate this
difficulty. For example, the size of projective geometric computing based on
bracket algebra can often be restrained to two terms, using final polynomials,
area method, Cayley expansion, etc. This is the "binomial" feature of
projective geometric computing in the language of bracket algebra.
  In this paper we report a stunning discovery in Euclidean geometric
computing: the term preservation phenomenon. Input an expression in the
language of Null Bracket Algebra (NBA), by the recipe we are to propose in this
paper, the computing procedure can often be controlled to within the same
number of terms as the input, through to the end. In particular, the
conclusions of most Euclidean geometric theorems can be expressed by monomials
in NBA, and the expression size in the proving procedure can often be
controlled to within one term! Euclidean geometric computing can now be
announced as having a "monomial" feature in the language of NBA.
  The recipe is composed of three parts: use long geometric product to
represent and compute multiplicatively, use "BREEFS" to control the expression
size locally, and use Clifford factorization for term reduction and transition
from algebra to geometry.
  By the time this paper is being written, the recipe has been tested by 70+
examples from \cite{chou}, among which 30+ have monomial proofs. Among those
outside the scope, the famous Miquel's five-circle theorem \cite{chou2}, whose
analytic proof is straightforward but very difficult symbolic computing, is
discovered to have a 3-termed elegant proof with the recipe.

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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol