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Primitive roots of unity and cyclotomic polynomials
 Journal of Formalized Mathematics
"... Summary. We present a formalization of roots of unity, define cyclotomic polynomials and demonstrate the relationship between cyclotomic polynomials and unital polynomials. ..."
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Summary. We present a formalization of roots of unity, define cyclotomic polynomials and demonstrate the relationship between cyclotomic polynomials and unital polynomials.
Yatsuka Nakamura
"... Summary. Concepts of the inner product and conjugate of matrix of complex numbers are defined here. Operations such as addition, subtraction, scalar multiplication and inner product are introduced using correspondent definitions of the conjugate of a matrix of a complex field. Many equations for suc ..."
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Summary. Concepts of the inner product and conjugate of matrix of complex numbers are defined here. Operations such as addition, subtraction, scalar multiplication and inner product are introduced using correspondent definitions of the conjugate of a matrix of a complex field. Many equations for such operations consist like a case of the conjugate of matrix of a field and some operations on the set of sum of complex numbers are introduced.
unknown title
"... Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in ..."
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Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in terms of their complex coefficients are also presented [5].
DOI: 10.2478/v100370090012z Solution of Cubic and Quartic Equations
"... Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in ..."
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Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in terms of their complex coefficients are also presented [5].
unknown title
"... Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in ..."
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Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in terms of their complex coefficients are also presented [5].
unknown title
"... Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in ..."
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Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in terms of their complex coefficients are also presented [5].
unknown title
"... Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in ..."
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Summary. In this article, the principal nth root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the DescartesEuler solution of quartic equations in terms of their complex coefficients are also presented [5].