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Discriminants of symmetric polynomials.

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Title: Discriminants of symmetric polynomials.
Authors: Perminov, N. S.1,2 (AUTHOR) qm.kzn@ya.ru, Shakirov, S. R.3 (AUTHOR) shakirov.work@gmail.com
Source: Theoretical & Mathematical Physics. May2026, Vol. 227 Issue 2, p753-774. 22p.
Subjects: Homogeneous polynomials, Symmetric functions, Polynomials, Mathematical formulas, Mathematical invariants, Symbolic computation
Abstract: A homogeneous polynomial of degree in variables possesses a discriminant , which vanishes if and only if the system of equations has nontrivial solutions. We provide an explicit formula for the discriminants of symmetric (under permutations of) homogeneous polynomials of degree in variables. This formula is highly effective from a computational perspective: symbolic computer calculations using this formula take seconds even for. We work out the cases , , and in detail. We also consider the case of completely antisymmetric polynomials. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
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  Data: Discriminants of symmetric polynomials.
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  Data: <searchLink fieldCode="DE" term="%22Homogeneous+polynomials%22">Homogeneous polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetric+functions%22">Symmetric functions</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+invariants%22">Mathematical invariants</searchLink><br /><searchLink fieldCode="DE" term="%22Symbolic+computation%22">Symbolic computation</searchLink>
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  Data: A homogeneous polynomial of degree in variables possesses a discriminant , which vanishes if and only if the system of equations has nontrivial solutions. We provide an explicit formula for the discriminants of symmetric (under permutations of) homogeneous polynomials of degree in variables. This formula is highly effective from a computational perspective: symbolic computer calculations using this formula take seconds even for. We work out the cases , , and in detail. We also consider the case of completely antisymmetric polynomials. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1134/S0040577926050028
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      – Code: eng
        Text: English
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    Subjects:
      – SubjectFull: Homogeneous polynomials
        Type: general
      – SubjectFull: Symmetric functions
        Type: general
      – SubjectFull: Polynomials
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      – SubjectFull: Mathematical formulas
        Type: general
      – SubjectFull: Mathematical invariants
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      – SubjectFull: Symbolic computation
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              Text: May2026
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