Tag
Discriminant
8 resources tagged “Discriminant” across the knowledge library.
8 items
Article7 Aug 2026Binary Quadratic Forms and the Ideal CorrespondenceThe dictionary between binary quadratic forms and ideals of a quadratic order, and why the form language is computationally preferable.2 min readRead MoreArticle7 Aug 2026Discriminants and Integral BasesThe discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.2 min readRead MoreArticle7 Aug 2026Galois Groups of Cubic and Quartic FieldsComplete determination of Galois groups in degrees three and four, where the discriminant and one cubic resolvent decide everything.2 min readRead MoreArticle7 Aug 2026Quadratic Field Discriminants and Integral BasesDiscriminants and integral bases of quadratic fields, given by closed formulas with no computation required.2 min readRead MoreArticle7 Aug 2026Resultants and DiscriminantsThe resultant as a criterion for common roots, the discriminant as a test for repeated roots, and how both are computed in practice.2 min readRead MoreArticle7 Aug 2026Solving Quadratic CongruencesReducing a general quadratic congruence to a square root extraction, and handling the degenerate cases the reduction assumes away.2 min readRead MoreArticle7 Aug 2026Weierstrass Equations and InvariantsGeneral and short Weierstrass forms, the discriminant and j-invariant, and the transformations relating equivalent models.2 min readRead MoreGuide6 Aug 2026The Subresultant Algorithm, Resultants and DiscriminantsThe subresultant polynomial remainder sequence, the resultant as a determinant and as a product over roots, the discriminant, and their use in elimination and in number field arithmetic.5 min readRead More