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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 ad. 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 oneterm expressions in terms of ad and of power five to constants eh and attempt to construct equations of specific forms in terms in eh. 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 αδ that are possibly roots; assignment of constant to represent quotients of form ab/c in terms of ad (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 AF to fiveterm expressions composed of elements ae. Assigning values αε to reducible fourterm expressions composed of elements ae. 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 AE

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 fifthdegree 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 fifthdegree 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 fifthdegree 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 ad 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 14.

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 fourthdegree equations.

Abstract/Description

Expressions involving square roots of algebraic expressions (possibly roots of equations); Listing different multiterm 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 αδ; Listing permutations of four elements 14 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

Fifthdegree 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 fifthdegree polynomial equations.

Abstract/Description

Combinations of quartic polynomials; expansion of general fiveterm 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

Nonstandard 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 a02 and b02.

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 ac 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 fourthdegree 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 ad

Identifier

FSUDirac_12_1a_0020

Format

Set of related objects


Title

Systems of fifthdegree equations, with only fifthdegree terms.

Abstract/Description

Similar quintic equations set to 0, possibly to solve system of equations; Labeling combinations of plus and minus ac with αδ; Listing permutations of five elements 04.

Identifier

FSUDirac_12_1b_0001

Format

Set of related objects


Title

Tenthdegree expressions.

Abstract/Description

Various tenthdegree 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 sixthdegree 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