Polynomial Equations Collection | DigiNole

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Permalink: https://diginole.lib.fsu.edu/islandora/object/fsu:diracpolyequations

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: Analyses related to cubic and quintic polynomial equations; Summary: Assigning values to expansions of quintic expressions in terms of a,b,c,d,e (similar to FSUDirac_12_1e_0001 and FSUDirac_12_1e_0006). Vieta’s formula. Writing quintic formula in terms of x,y,z,r, which are expressions in terms of a-d. Rewriting general cubic equation.

: Analysis associated with reduced quintic polynomial equation; Summary: Equating one-term expressions in terms of a-d and of power five to constants e-h and attempt to construct equations of specific forms in terms in e-h. Work with reduced quintic polynomial equation equal to zero.

: Analysis of a particular quintic polynomial equation; Summary: Quintic equation the same as on FSUDirac_12_1d_0027; attempt to find products of expressions α-δ that are possibly roots; assignment of constant to represent quotients of form ab/c in terms of a-d (linked to FSUDirac_12_1e_0023).

: Analysis of cubic, quartic, and quintic expansions; Summary: Continuation of combinations of general a, b, c, d with different powers of w (from FSUDirac_12_1d_0023); charts assigning values to different cubic, quartic, and quintic expansions equal to zero; writing general solution of cubic polynomial.

: Analysis related to solving reduced cubic polynomial equation; Summary: Writing sums of terms a through d raised to fractional powers; ω and i also used; solving reduced cubic equation.

: Comparison of coefficients for different summation expansions; Summary: Comparison of coefficients of different summation expansions in three variables.

: Comparison of coefficients in different expansions; Summary: Comparison of coefficients of terms in expansions of different summations/products of summations (like FSUDirac_12_1a_0011; FSUDirac_12_1d_0005); writing summations of products as quintic polynomials after substitution; comparison of coefficients of summated expressions up to degree 5 and assignment of values to each equation (e.g. 1, -5, 5. Possibly connected to Galois groups?)

: Comparison of terms in expansion (fourth degree); Summary: Comparison of terms in expansion of different combinations of products (usually to fourth degree); Expansions of squares of summations.

: Composition of various degreed expressions; Summary: Assigning values A-F to five-term expressions composed of elements a-e. Assigning values α-ε to reducible four-term expressions composed of elements a-e. Expansions of different powers (up to quintic) of expression x in terms of a and b.

: Construction of quintic expressions; Summary: Construction of quintic expressions; Comparison of an expression raised to different degrees.

: Cubic equation investigation (also includes listing of permutations of five elements); Summary: Analysis of cubic equation by substitutions using coefficients; Listing of permutations of five elements chosen from five; Drawing diagrams to represent combinations of five elements A-E

: Expansions and factoring of terms in multiple variables; Summary: Factoring of polynomial expressions in terms of a, b, c, d by using substitutions to e, f, g, h; expansions to different powers of expressions in terms of a, b, w; expansions of expressions a+b+c+d+e to different powers and assignment of values to different terms.

: Expansions and summations of fifth-degree term, with substitution; Summary: Assignment of values to different quintic summation expansions in terms of A,B,C,D (similar to FSUDirac_12_1d_0024). Comparison of coefficients of above expansions. Derivation of trigonometric equations from logarithmic equations. Rewriting equations in terms of O,P,Q,R in terms of a,b,r.

: Expansions and summations of fifth-degree term, with substitution and comparison of coefficients; Summary: Assignment of values to expansions of quintic summations of x and a in terms of a,b,c,d (similar to FSUDirac_12_1d_0024). Comparison of coefficients of above expansions. Assignment of values to expansions of summations of x,a,c (hard to read).

: Expansions of products of quartic polynomial expressions; Summary: Expansions of products of given quartic expressions involving a, b, c and assignment of values to different expansions.

: Expansions of terms in third-, fourth-, and fifth-degree polynomials; Summary: Expansions and summations of terms from a quintic polynomial.

: Expansions of various powers, with comparison of coefficients; Summary: Assignments of values to various expansions of different powers in terms of a, b, c, and sometimes d (similar to FSUDirac_12_1d_0027); chart comparing coefficients to different expansions in terms of a-d and with high powers (e.g. 30).

: Expansions related to quartic polynomial equation; Summary: Expansions of expressions in terms of x, y which are expressions in terms of a, b and comparison of coefficients; listing permutations of elements 1-4.

: Expansions related to quintic polynomial equation; Summary: Assigning values to quintic expansions in terms of a, b, c, d (similar to FSUDirac_12_1e_0001); forming equations out of results of above expansions.

: Expressions and equations of various degree, including third- and fourth-degree equations; Summary: Expressions involving square roots of algebraic expressions (possibly roots of equations); Listing different multi-term expressions using A1,A2,…,B1,B2,…,C1,C2,… Possibly solutions to certain cubics; Expansions of summations of quartic and quadratic expressions; Multiplication of summations; Work with cubic functions with specific coefficients.

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