In mathematics, a formal sum, formal series, or formal linear combination may be:
In group theory, an element of a free abelian group, a sum of finitely many elements from a given basis set multiplied by integer coefficients.
In linear algebra, an element of a vector space, a sum of finitely many elements from a given basis set multiplied by real, complex, or other numerical coefficients.
In the study of series (mathematics), a sum of an infinite sequence of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum converges.
In the study of power series, a sum of infinitely many monomials with distinct positive integer exponents, again considered as an abstract object regardless of convergence.
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mathematics, a formalsum, formal series, or formal linear combination may be: In group theory, an element of a free abelian group, a sum of finitely many...
In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual...
equivalent ways. These include formalsums over B {\displaystyle B} , which are expressions of the form ∑ a i b i {\textstyle \sum a_{i}b_{i}} where each a...
quasitriangular" in that there exists an infinite formalsum which plays the role of an R-matrix. This infinite formalsum is expressible in terms of generators ei...
the standard n-simplex to a topological space, and composing them into formalsums, called singular chains. The boundary operation – mapping each n-dimensional...
is to think of a 0-th homology class not as a formalsum of connected components, but as such a formalsum where the coefficients add up to zero. In the...
_{E_{y}}\,\sum _{j=0}^{\infty }a_{j}:=\sum _{i=0}^{\infty }{\frac {1}{(1+y)^{i+1}}}\sum _{j=0}^{i}{\binom {i}{j}}y^{j+1}a_{j}.} If all the formalsums actually...
formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules called a formal grammar...
Sumer (/ˈsuːmər/) is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during...
standard domain D in Rk, usually a cube or a simplex. A k-chain is a formalsum of smooth embeddings D → M. That is, it is a collection of smooth embeddings...
h, or in other words the formalsum of its zeroes and poles counted with multiplicity; and a function applied to a formalsum means the product (with multiplicities...
\Gamma } (an ordered group) is the set of formal expressions of the form f = ∑ e ∈ Γ c e T e {\displaystyle f=\sum _{e\in \Gamma }c_{e}T^{e}} with c e ∈ K...
convenient to denote the function a in R[N] as the formalsum: ∑ n ∈ N a n X n {\displaystyle \sum _{n\in N}a_{n}X^{n}} and then the formulas for addition...
mathematics, a formal distribution is an infinite sum of powers of a formal variable, usually denoted z {\displaystyle z} in the theory of formal distributions...
addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials...
= − 1. {\displaystyle \sum _{n=0}^{\infty }2^{n}=-1.} Substituting q=2 into the proof of the first equation, yields a formal calculation that produces...
In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative...
maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within...
module as a formalsum of simple modules. Over semisimple rings, this is no loss as every module is a semisimple module and so a direct sum of simple modules...
given by a formalsum over Feynman diagrams. The exponential formula shows that ln ( Z ) {\displaystyle \ln(Z)} can be written as a sum over connected...
referred as formal concentrations, it could explain the origin of the adjective formal in the expression formal potential.[citation needed] The formal potential...
simplicial complex. A simplicial k-chain is a finite formalsum ∑ i = 1 N c i σ i , {\displaystyle \sum _{i=1}^{N}c_{i}\sigma _{i},\,} where each ci is an...
simplicial complex. A simplicial k-chain is a finite formalsum ∑ i = 1 N c i σ i , {\displaystyle \sum _{i=1}^{N}c_{i}\sigma _{i},\,} where each ci is an...
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