From 8aeb86c75c525887119655f72a5f2ef5d68b0940 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Thu, 31 Mar 2022 16:38:55 +0200 Subject: Old work --- n10.wl | 10 + new_schofield.nb | 10888 +++++------------------------------------------------ s11-2.wl | 10 + schofield.py | 23 +- 4 files changed, 892 insertions(+), 10039 deletions(-) create mode 100644 n10.wl create mode 100644 s11-2.wl diff --git a/n10.wl b/n10.wl new file mode 100644 index 0000000..247fc42 --- /dev/null +++ b/n10.wl @@ -0,0 +1,10 @@ +(* Created with the Wolfram Language : www.wolfram.com *) +{41.5274892840305, {\[Theta]c -> 1.3815995225475306, + \[Theta]0 -> 0.19651193079603455, AH -> -2.5551253172888564, + A[1] -> 1.737677593541619, A[2] -> 0.6073072088307674, + gC[1] -> -0.3667051267605768, gC[2] -> -0.006993124776468467, + A[3] -> -0.2932002003072459, gC[3] -> 0.05281453358067984, + gC[4] -> -0.01981435048670272, A[4] -> 0.07310324475817341, + gC[5] -> 0.003490414297911533, gC[6] -> -0.0003499436527837343, + A[5] -> -0.007264248876828084, gC[7] -> 0.00001808613660184903, + gC[8] -> -9.089351672518404*^-7}} diff --git a/new_schofield.nb b/new_schofield.nb index 1c49fd2..a6d4c36 100644 --- a/new_schofield.nb +++ b/new_schofield.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 2421482, 43638] -NotebookOptionsPosition[ 2397461, 43263] -NotebookOutlinePosition[ 2397856, 43279] -CellTagsIndexPosition[ 2397813, 43276] +NotebookDataLength[ 1861428, 34460] +NotebookOptionsPosition[ 1837886, 34089] +NotebookOutlinePosition[ 1838285, 34105] +CellTagsIndexPosition[ 1838242, 34102] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -168,9 +168,9 @@ Cell[BoxData[ 2^Rational[5, 6] Schofield`\[Theta]0^Rational[5, 6], 0, 0, 0, 0, (Schofield`\[Theta] + Complex[0, -1] Schofield`\[Theta]0)^ Rational[-5, 6] (Complex[0, 1] Schofield`\[Theta] + Schofield`\[Theta]0)^ - Rational[5, 6], Complex[0, - Rational[-5, 6]] 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+{1370.3010684561127, {\[Theta]c -> 1.3910372586447357, + \[Theta]0 -> 0.19656274355982506, AH -> -2.5430070509937934, + A[1] -> 1.72003157406972, A[2] -> 0.5919956154568292, + gC[1] -> -0.3581984134361347, gC[2] -> -0.0008279978792175252, + A[3] -> -0.28645050025521357, gC[3] -> 0.052775222902559024, + gC[4] -> -0.020203799501789483, A[4] -> 0.07392503484513055, + gC[5] -> 0.003410853564504481, gC[6] -> -0.00021113319124048676, + A[5] -> -0.0072554264252400035, gC[7] -> -0.00002625143929826904, + gC[8] -> 3.719711744852983*^-6, A[6] -> -0.00002209555890920773}} diff --git a/schofield.py b/schofield.py index 96fe68a..0894a42 100644 --- a/schofield.py +++ b/schofield.py @@ -1,5 +1,5 @@ -from sympy import * -from mpmath import glaisher, pi +from sympy import Rational, Symbol, Ei, diff +from mpmath import glaisher, pi, exp, factorial β = Rational(1/8) δ = 15 @@ -9,19 +9,29 @@ from mpmath import glaisher, pi s = 2**Rational(1, 12) * exp(-β) * glaisher**Rational(3, 2) + def f(B, θc, θ): - return (θc * Ei(-1 / (B * θc)) * exp(1 / (B * θc)) + (θ - θc) * Ei(1/(B * (θ - θc))) * exp(-1/(B * (θ - θc)))) / pi + return (θc * Ei(-1 / (B * θc)) * exp(1 / (B * θc)) + + (θ - θc) * Ei(1/(B * (θ - θc))) * exp(-1/(B * (θ - θc)))) / pi + def FH(θ0, θ): return (θ**2 + θ0**2)**σ - (θ0**2)**σ + +def FA(As, θ): + return sum([A * θ**(2 * i + 2) for i, A in enumerate(As)]) + + def FR(AL, AH, As, B, θc, θ0, θ): - return AL * f(B, θc, -θ) + AH * FH(θ0, θ) + sum([A * θ**(2 * i + 2) for i,A in enumerate(As)]) + return AL * f(B, θc, -θ) + AH * FH(θ0, θ) + FA(As, θ) + def F(AL, AH, As, B, θc, θ0, θ): return FR(AL, AH, As, B, θc, θ0, θ) + AL * f(B, θc, θ) -def dfc(AL, B, m): + +def dfc(AL, B, θc, m): if m == 0: return AL * θc * Ei(-1 / (B * θc)) * exp(1 / (B * θc)) / pi elif m == 1: @@ -29,6 +39,7 @@ def dfc(AL, B, m): else: return AL * factorial(m) * factorial(m - 2) * B**(m-1) / pi + def dFc(AL, AH, As, B, θc, θ0, m): θ = Symbol['θ'] - return dfc(AL, B, m) + diff(FR(AL, AH, As, B, θc, θ0, θ), θ).subs(θ, θc) + return dfc(AL, B, m) + diff(FR(AL, AH, As, B, θc, θ0, θ), θ).subs(θ, θc) -- cgit v1.2.3-54-g00ecf