Fundamental Theorem on Symmetric Polynomials and Discriminants

2012 ◽  
pp. 41-64
Keyword(s):  
Fundamental Theorem ◽  
Symmetric Polynomials

FURTHER REMARKS ON RATES OF STRETCH TENSORS

1991 ◽  
Vol 15 (2) ◽  
pp. 161-172 ◽  
Author(s):  
Guo Zhong-heng ◽  
Th. Lehmann ◽  
Liang Haoyun
Keyword(s):  
Representation Theory ◽  
Fundamental Theorem ◽  
Principal Axis ◽  
Special Technique ◽  
Symmetric Polynomials ◽  
Stretch Tensor

Using principal axis method, representation theory, fundamental theorem of symmetric polynomials and some special technique, the present paper obtains intrinsic expressions for rates of right and left stretch tensors and some new relations between these rates. The expression for the rate of the left stretch tensor is also new.

scholarly journals EVALUATION PROPERTIES OF SYMMETRIC POLYNOMIALS

2006 ◽  
Vol 16 (03) ◽  
pp. 505-523 ◽  
Author(s):  
PIERRICK GAUDRY ◽  
ÉRIC SCHOST ◽  
NICOLAS M. THIÉRY
Keyword(s):  
Fundamental Theorem ◽  
Symmetric Polynomials ◽  
Program Model ◽  
General Polynomial ◽  
Straight Line ◽  
Reynolds Operator ◽  
Elementary Symmetric Polynomials

By the fundamental theorem of symmetric polynomials, if P ∈ ℚ[X1,…,Xn] is symmetric, then it can be written P = Q(σ1,…,σn), where σ1,…,σn are the elementary symmetric polynomials in n variables, and Q is in ℚ[S1,…,Sn]. We investigate the complexity properties of this construction in the straight-line program model, showing that the complexity of evaluation of Q depends only on n and on the complexity of evaluation of P. Similar results are given for the decomposition of a general polynomial in a basis of ℚ[X1,…,Xn] seen as a module over the ring of symmetric polynomials, as well as for the computation of the Reynolds operator.

scholarly journals Milne’s volume function and vector symmetric polynomials

2009 ◽  
Vol 44 (5) ◽  
pp. 583-590 ◽  
Author(s):  
Emmanuel Briand ◽  
Mercedes Rosas
Keyword(s):  
Symmetric Polynomials ◽  
Volume Function

scholarly journals A symmetric Bloch–Okounkov theorem

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
Jan-Willem M. van Ittersum
Keyword(s):  
Symmetric Functions ◽  
Graded Algebra ◽  
Symmetric Polynomials ◽  
Generating Series

AbstractThe algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the q-bracket, is a quasimodular form. More generally, if a graded algebra A of functions on partitions has the property that the q-bracket of every element is a quasimodular form of the same weight, we call A a quasimodular algebra. We introduce a new quasimodular algebra $$\mathcal {T}$$ T consisting of symmetric polynomials in the part sizes and multiplicities.

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