The first video was about the basic concept of algebra, exponential notation, and conversion between text and algebraic; the second went over the basic definition of powers, like terms and unlike terms; the third one was to do with the understanding of monomials
and polynomials, arranging in ascending or descending order of powers and addition and subtraction of polynomials; the fourth one is about the multiplication and division of monomials
, and the fifth one, also the last one was concerned with multiplication of polynomials.
q] generated by the ordered monomials
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are all the Cartan roots of [B.
Indeed, all polynomials are linear combinations of such monomials
with constant coefficients.
Thus, a new technique is introduced in this paper, which enables exact integration of monomials
of the form [x.
For the definition and properties of the Taylor monomials
The polynomials have to be ordered along a term order, meaning that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the monomials
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] satisfy a term order: 1 [?
A well known basis for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] consists of the descent monomials
A Grobner basis for I is a basis for I that depends on how we order monomials
The numerical calculation of the ratio between the numerator and denominator appearing in the expression of the coefficients of monomials
(13) rapidly tends to infinity as a function of q and m, while in reality the fraction tends to a finite value.
Intended for graduate students, the last chapter of the monograph touches on Koszul algebras, sortable sets of monomials
, the Rees ring of generalized Hibi ideals, determinental ideals, and binomial edge ideals.
In particular additive, quadratic, cubic and quartic functions are monomials
of degree one, two, three and four respectively.
This partition function only counts the dimension of the space of monomials
in [lambda] with degree of homogeneity p as the coefficient of [t.