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  2. Monomial order - Wikipedia

    en.wikipedia.org/wiki/Monomial_order

    Then the set M of the (monic) monomials in R is a basis of R, considered as a vector space over the field of the coefficients. Thus, any nonzero polynomial p in R has a unique expression = as a linear combination of monomials, where S is a finite subset of M and the c u are all nonzero

  3. Monomial - Wikipedia

    en.wikipedia.org/wiki/Monomial

    In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.Two definitions of a monomial may be encountered: A monomial, also called a power product or primitive monomial, [1] is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. [2]

  4. Gröbner basis - Wikipedia

    en.wikipedia.org/wiki/Gröbner_basis

    In particular, a one step lead-reduction of f produces a polynomial all of whose monomials are smaller than lm(f). Given a finite set G of polynomials, one says that f is reducible or lead-reducible by G if it is reducible or lead-reducible, respectively, by at least one element g of G.

  5. Partition function (number theory) - Wikipedia

    en.wikipedia.org/wiki/Partition_function_(number...

    This expands the product into a sum of monomials of the form for some sequence of coefficients , only finitely many of which can be non-zero. The exponent of the term is n = ∑ i a i {\textstyle n=\sum ia_{i}} , and this sum can be interpreted as a representation of n {\displaystyle n} as a partition into a i {\displaystyle a_{i}} copies of ...

  6. FOIL method - Wikipedia

    en.wikipedia.org/wiki/FOIL_method

    In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.

  7. Standard monomial theory - Wikipedia

    en.wikipedia.org/wiki/Standard_monomial_theory

    In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive algebraic group by giving an explicit basis of elements called standard monomials. Many of the results have been extended to Kac–Moody algebras and their groups.

  8. Dying To Be Free - The Huffington Post

    projects.huffingtonpost.com/projects/dying-to-be...

    “The history of 12-step came out of white, middle-class, Protestant people who want to be respectable,” said historian Nancy Campbell, a professor at Rensselaer Polytechnic Institute. “It offers a form of community and a form of belonging that is predicated upon you wanting to be normal, you wanting to be respectable, you wanting to have ...

  9. Separation of variables - Wikipedia

    en.wikipedia.org/wiki/Separation_of_variables

    Dividing the PDE through by () gives T f f = S g g {\displaystyle {\frac {Tf}{f}}={\frac {Sg}{g}}} The right hand side depends only on x {\displaystyle x} and the left hand side only on t {\displaystyle t} so both must be equal to a constant K {\displaystyle K} , which gives two ordinary differential equations

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