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Title: Analyses related to cubic and quintic polynomial equations.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0008
Format: Set of related objects

Title: Analysis associated with reduced quintic polynomial equation.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0022
Format: Set of related objects

Title: Analysis of a particular quintic polynomial equation.
Abstract/Description: 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).
Identifier: FSUDirac_12_1e_0009
Format: Set of related objects

Title: Analysis of cubic, quartic, and quintic expansions.
Abstract/Description: 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.
Identifier: FSUDirac_12_1d_0027
Format: Set of related objects

Title: Analysis related to solving reduced cubic polynomial equation.
Abstract/Description: Writing sums of terms a through d raised to fractional powers; ω and i also used; solving reduced cubic equation.
Identifier: FSUDirac_12_3_1_0015
Format: Set of related objects

Title: Comparison of coefficients for different summation expansions.
Abstract/Description: Comparison of coefficients of different summation expansions in three variables.
Identifier: FSUDirac_12_1d_0005
Format: Set of related objects

Title: Comparison of coefficients in different expansions.
Abstract/Description: 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?)
Identifier: FSUDirac_12_1d_0011_polyeq, fsu:186636
Format: Set of related objects

Title: Comparison of terms in expansion (fourth degree).
Abstract/Description: Comparison of terms in expansion of different combinations of products (usually to fourth degree); Expansions of squares of summations.
Identifier: FSUDirac_12_1a_0009
Format: Set of related objects

Title: Composition of various degreed expressions.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0001
Format: Set of related objects

Title: Construction of quintic expressions.
Abstract/Description: Construction of quintic expressions; Comparison of an expression raised to different degrees.
Identifier: FSUDirac_12_1a_0005
Format: Set of related objects

Title: Cubic equation investigation (also includes listing of permutations of five elements).
Abstract/Description: 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
Identifier: FSUDirac_12_1a_0021
Format: Set of related objects

Title: Expansions and factoring of terms in multiple variables.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0011
Format: Set of related objects

Title: Expansions and summations of fifth-degree term, with substitution.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0018
Format: Set of related objects

Title: Expansions and summations of fifth-degree term, with substitution and comparison of coefficients.
Abstract/Description: 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).
Identifier: FSUDirac_12_1e_0019
Format: Set of related objects

Title: Expansions of products of quartic polynomial expressions.
Abstract/Description: Expansions of products of given quartic expressions involving a, b, c and assignment of values to different expansions.
Identifier: FSUDirac_12_1d_0024
Format: Set of related objects

Title: Expansions of terms in third-, fourth-, and fifth-degree polynomials.
Abstract/Description: Expansions and summations of terms from a quintic polynomial.
Identifier: FSUDirac_12_1e_0014
Format: Set of related objects

Title: Expansions of various powers, with comparison of coefficients.
Abstract/Description: 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).
Identifier: FSUDirac_12_1e_0015
Format: Set of related objects

Title: Expansions related to quartic polynomial equation.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0007
Format: Set of related objects

Title: Expansions related to quintic polynomial equation.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0005
Format: Set of related objects

Title: Expressions and equations of various degree, including third- and fourth-degree equations.
Abstract/Description: 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.
Identifier: FSUDirac_12_1a_0007
Format: Set of related objects

Title: Expressions and equations of varying degree.
Abstract/Description: Labeling expressions in a, b, c, w with α-δ; Listing permutations of four elements 1-4 with repetition; Assigning values (5 and -5) to summation expressions with different coefficients.
Identifier: FSUDirac_12_1b_0002
Format: Set of related objects

Title: Factoring cubic polynomials.
Abstract/Description: Sketches of triangle with angle bisectors (?); factoring particular cubic polynomials (page smudged, difficult to read).
Identifier: FSUDirac_12_1d_0015
Format: Set of related objects

Title: Fifth-degree polynomial equations.
Abstract/Description: Expansion of x^5 for x = y + z and attempt to rewrite expanded expression in terms of q, r, p, s; expanding general quintic expressions.
Identifier: FSUDirac_12_1e_0013
Format: Set of related objects

Title: FSUDirac_12_1a_0002.
Abstract/Description: Expansions of expressions involving a,b,c,d,e, and various powers of w all to the fifth power (hard to read); Listing permutations of combinations of two elements chosen from five of form a^2 b; Work with logarithmic equations/integration (possibly physics related).
Identifier: FSUDirac_12_1a_0002
Format: Set of related objects

Title: General quintic polynomial equation and fifth roots of unity.
Abstract/Description: Evaluation of different algebraic expressions involving imaginary fifth roots of unity raised to the fifth (perhaps in attempt to solve certain class of quintic polynomial equations).
Identifier: FSUDirac_12_1d_0016
Format: Set of related objects

Title: Investigating solutions of cubic and quartic equations.
Abstract/Description: Analysis of quartic polynomial with all coefficients of 1 and attempted substitutions to find solution; similar analysis of cubic polynomial with all coefficients of 1.
Identifier: FSUDirac_12_1d_0006
Format: Set of related objects

Title: Investigating solutions of polynomial equations.
Abstract/Description: Possible attempt to equate α to a root of a polynomial (square root involved)
Identifier: FSUDirac_12_1a_0004
Format: Set of related objects

Title: List of roots of unity for a given quartic polynomial equation.
Abstract/Description: Listing of roots of possible quartic equation (as continued from FSUDirac_12_1d_0021); writing combinations of general a, b, c, d with different powers of general w (continued on FSUDirac_12_1d_0027); raising above combinations to the fifth power and setting them equal to terms A1 through D1 for substitution.
Identifier: FSUDirac_12_1d_0023
Format: Set of related objects

Title: Manipulation of third-, fourth-, and fifth-degree polynomial equations.
Abstract/Description: Combinations of quartic polynomials; expansion of general five-term expression raised to the fifth power; possible attempt to find solutions of cubic equation (hard to read).
Identifier: FSUDirac_12_1d_0022
Format: Set of related objects

Title: Multiplication of expressions involving cube roots.
Abstract/Description: Multiplication/Expansion of products of expressions involving cube roots (possible roots for cubic polynomials?)
Identifier: FSUDirac_12_1a_0012
Format: Set of related objects

Title: Non-standard solution for a quadratic equation.
Abstract/Description: Solutions to quadratic polynomials and equations
Identifier: FSUDirac_12_1a_0008
Format: Set of related objects

Title: Of interest: general solution of reduced cubic equation.
Abstract/Description: Equating quintic polynomials of certain coefficients to summations of expressions; general solution for cubic without x^2 term (see FSUDirac_12_1a_0003 and FSUDirac_12_1a_0011); simplification of trigonometric functions with integral multiples of arguments (e.g. cos3θ, etc.).
Identifier: FSUDirac_12_1d_0002
Format: Set of related objects

Title: Quintic equation investigation.
Abstract/Description: Analysis of coefficients in quintic polynomials with no x^4 term; Combinations of equations of three variables and involving imaginary numbers.
Identifier: FSUDirac_12_1a_0010
Format: Set of related objects

Title: Quintic expansions, with comparison of coefficients.
Abstract/Description: 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.
Identifier: FSUDirac_12_1e_0017
Format: Set of related objects

Title: Random quadratic equation.
Abstract/Description: Apparent beginning of analysis of algebraic expressions; possible beginning of attempt to find relations between a0-2 and b0-2.
Identifier: FSUDirac_12_1d_0029
Format: Image (JPEG2000)

Title: Solution of general cubic and quartic equations.
Creator: Dirac, P. A. M. (Paul Adrien Maurice)
Abstract/Description: Solutions of two types of cubic equations (reduced and general); Solutions of two types of quartic equations (reduced and general).
Identifier: FSUDirac_12_1d_0004_parent
Format: Set of related objects

Title: Solution of general quartic polynomial equation, using substitution.
Abstract/Description: Attempt to find general solution to quartic equations of a certain form using substitution.
Identifier: FSUDirac_12_1d_0018
Format: Image (JPEG2000)

Title: Solution of particular cubic polynomial equations.
Abstract/Description: Solving particular cubic equations; expanding cube roots of binomial arithmetic expressions; possible attempt to find general expansion of cube root of expression in terms of a-c and k; assigning values to lists of powers of a, b, c; algebra with f and f bar (page damaged).
Identifier: FSUDirac_12_1e_0003
Format: Set of related objects

Title: Solution of particular quartic polynomial equations, using substitution.
Abstract/Description: Attempt to find general solution to certain quartic polynomials using several subsequent substitutions (similar problems and form of expressions to FSUDirac_12_1d_0006).
Identifier: FSUDirac_12_1d_0019
Format: Set of related objects

Title: Solution of third- and fourth-degree equations.
Abstract/Description: Looking for general solution of cubic polynomial with no x2 term; Looking for general solution of quartic polynomial with given conditions.
Identifier: FSUDirac_12_1a_0003
Format: Set of related objects

Title: Solving a reduced quintic polynomial equation with substitution.
Abstract/Description: Attempt to find general solution to quintic polynomial with no x^4 term under certain conditions on coefficients.
Identifier: FSUDirac_12_1d_0008
Format: Set of related objects

Title: Solving polynomial equations with substitution.
Abstract/Description: Substitutions to help solve certain polynomials of degree 5 or possibly greater (hard to read).
Identifier: FSUDirac_12_1d_0007
Format: Image (JPEG2000)

Title: Substitutions in reduced quartic and quintic polynomial equations.
Abstract/Description: Using substitutions to simplify reduced quartic and quintic polynomials. Note: coefficients correspond to values assigned on FSUDirac_12_1d_0010 and FSUDirac_12_1d_0011 (i.e., 1, -4, 2, 4 and then 1, -5, 5, etc.)
Identifier: FSUDirac_12_1d_0012
Format: Set of related objects

Title: Substitutions to simplify polynomial equations.
Abstract/Description: Using substitutions to simplify polynomial equations; Connection to FSUDirac_12_1a_0003 – formula for general solution to cubic with no x^2 term used and expanded with different values; Comparison of coefficients of different expansions of products of summations.
Identifier: FSUDirac_12_1a_0011
Format: Set of related objects

Title: Summation expressions in four variables.
Abstract/Description: Assignment of variables to different summation expressions in four variables a-d
Identifier: FSUDirac_12_1a_0020
Format: Set of related objects

Title: Systems of fifth-degree equations, with only fifth-degree terms.
Abstract/Description: Similar quintic equations set to 0, possibly to solve system of equations; Labeling combinations of plus and minus a-c with α-δ; Listing permutations of five elements 0-4.
Identifier: FSUDirac_12_1b_0001
Format: Set of related objects

Title: Tenth-degree expressions.
Abstract/Description: Various tenth-degree expressions in five variables.
Identifier: FSUDirac_12_1a_0022
Format: Set of related objects

Title: Terms, coefficients, and equations.
Abstract/Description: Analysis of powers and sums of terms constructed in a, b, c, d, and e; Formation of equations.
Identifier: FSUDirac_12_1d_0001
Format: Set of related objects

Title: Third-, fourth-, and sixth-degree polynomial equations.
Abstract/Description: Constructing polynomial equation to the sixth power in terms of coefficients that are summations of terms containing a, b, c, d; Reduced cubic and quartic polynomial equations.
Identifier: FSUDirac_12_1d_0025
Format: Set of related objects

Title: Work on solutions to general cubic and quartic polynomial equations.
Abstract/Description: Investigating solutions of the general cubic polynomial equation; Investigating solutions of the general quartic polynomial equation; combinations of powers of w with a, b, c (possibly related to FSUDirac_12_1e_0013).
Identifier: FSUDirac_12_1e_0010
Format: Set of related objects

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