Results 1  10
of
2,171
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
Abstract

Cited by 520 (1 self)
 Add to MetaCart
wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials. Ancdlary fast algorithms for calculating resultants
The secret lives of polynomial identities
, 2011
"... The secret lives of polynomial identities“An idea which can be used only once is a trick. If you can use it more than once it becomes a method. ” – George Pólya and Gábor ..."
Abstract
 Add to MetaCart
The secret lives of polynomial identities“An idea which can be used only once is a trick. If you can use it more than once it becomes a method. ” – George Pólya and Gábor
Progress on Polynomial Identity Testing
"... Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress on this ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress
Polynomial Identities of Banach Algebras
, 2015
"... In this paper we consider PIalgebras A over the real and complex numbers and address the question of whether it is possible to find a normed PIalgebra B with the same polynomial identities as A, and moreover, whether there is some Banach PIalgebra with this property. Our main theorem provides an ..."
Abstract
 Add to MetaCart
In this paper we consider PIalgebras A over the real and complex numbers and address the question of whether it is possible to find a normed PIalgebra B with the same polynomial identities as A, and moreover, whether there is some Banach PIalgebra with this property. Our main theorem provides
Interprocedurally Analyzing Polynomial Identities
"... Abstract. Since programming languages are Turing complete, it is impossibleto decide for all programs whether a given nontrivial semantic property is valid or not. The wayout chosen by abstract interpretation is to provide approximatemethods which may fail to certify a program property on some pro ..."
Abstract
 Add to MetaCart
programs. Precision of the analysis can be measured by providing classes of programs for whichthe analysis is complete, i.e., decides the property in question. Here, we consider analyses of polynomial identities between integer variables such as x1 * x2 2x3 = 0. We describe current approaches and clarify
ALGEBRAS, DIALGEBRAS, AND POLYNOMIAL IDENTITIES
 SERDICA MATH. J. 38 (2012), 91–136
, 2012
"... This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for conver ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm
Interprocedurally analyzing polynomial identities
 IN PROC. OF STACS 2006
, 2006
"... Since programming languages are Turing complete, it is impossible to decide for all programs whether a given nontrivial semantic property is valid or not. The wayout chosen by abstract interpretation is to provide approximate methods which may fail to certify a program property on some programs. ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
. Precision of the analysis can be measured by providing classes of programs for which the analysis is complete, i.e., decides the property in question. Here, we consider analyses of polynomial identities between integer variables such as x1 · x2 − 2x3 = 0. We describe current approaches and clarify
Polynomial identities, indices, and . . .
, 1995
"... We prove polynomial identities for the N = 1 superconformal model SM(2, 4ν) which generalize and extend the known Fermi/Bose character identities. Our proof uses the qtrinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursio ..."
Abstract
 Add to MetaCart
We prove polynomial identities for the N = 1 superconformal model SM(2, 4ν) which generalize and extend the known Fermi/Bose character identities. Our proof uses the qtrinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing
ALGEBRAS WITH POLYNOMIAL IDENTITIES AND BERGMAN POLYNOMIALS ∗
"... Abstract. The talk is an introduction to the theory of algebras with polynomial identities. It stresses on matrix algebras and polynomial identities for them. The notion of Bergman polynomials is introduced. Such types of polynomials are investigated being identities for algebras with symplectic i ..."
Abstract
 Add to MetaCart
Abstract. The talk is an introduction to the theory of algebras with polynomial identities. It stresses on matrix algebras and polynomial identities for them. The notion of Bergman polynomials is introduced. Such types of polynomials are investigated being identities for algebras with symplectic
Polynomial identities of the Rogers–Ramanujan type
, 1994
"... Presented are polynomial identities which imply generalizations of Euler and Rogers–Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical onetoone correspondence between th ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
Presented are polynomial identities which imply generalizations of Euler and Rogers–Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical onetoone correspondence between
Results 1  10
of
2,171