1620.sagews

x=var('x')
y=function('y',x)
G=var('G')
k=var('k')
DE=diff(y,x)-k*y*(G-y)
desolve(DE,[y,x])
var('D,G,z')
eq=z/(G-z)==exp(D)*exp(k*G*x)
show(eq)
#solve(eq,z)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{z}{G - z} = e^{\left(G k x + D\right)}

f = lambda x: G*e^(G*k*x + D)/(e^(G*k*x + D) + 1)

show(f(x))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{G e^{\left(G k x + D\right)}}{e^{\left(G k x + D\right)} + 1}

@interact
def test(G = slider(0,20,1,default = 6), k = slider(0,1,0.1,default = 0.1),xa=slider(0,10,1,default=0),ya=slider(0,10,1,default=1)):
    D=-G*k*xa + log(ya/(G - ya))
    var('y')
    html('$y'+"'="+latex(k*y*(G-y)))
    html('$y='+latex(G*e^(G*k*x + D)/(e^(G*k*x + D) + 1)))
    gf=plot(G*e^(G*k*x + D)/(e^(G*k*x + D) + 1),(x,0,5),gridlines=True)
    show(gf)

G  k  xa  ya  [removed] [removed] [removed] [removed]

latex?

File: /usr/local/sage2/local/lib/python2.6/site-packages/sage/misc/latex.py

Type: <type ‘instance’>

Definition: latex(x)

Docstring:

Enter, e.g.,

%latex
The equation $y^2 = x^3 + x$ defines an elliptic curve.
We have $2006 = \sage{factor(2006)}$.

in an input cell in the notebook to get a typeset version. Use %latex_debug to get debugging output.

Use latex(...) to typeset a Sage object.

Use %slide instead to typeset slides.

Warning

You must have dvipng (or dvips and convert) installed on your operating system, or this command won’t work.

%latex_debug

WARNING: Output truncated!

full_output.txt

cd "/tmp/sagenbws/temp/boxen/28949/dir_0"&& sage-native-execute latex \\nonstopmode \\input{sage13.tex} && cd "/tmp/sagenbws/temp/boxen/28949/dir_0"&& sage-native-execute dvipng --picky -q -T tight -D 130 sage13.dvi -o sage13.png This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, croatian, ukrainian, russian, bulgarian, czech, slovak, danish, dut ch, finnish, basque, french, german, ngerman, ibycus, greek, monogreek, ancient greek, hungarian, italian, latin, mongolian, norsk, icelandic, interlingua, tur kish, coptic, romanian, welsh, serbian, slovenian, estonian, esperanto, upperso rbian, indonesian, polish, portuguese, spanish, catalan, galician, swedish, loa ded. (./sage13.tex (/usr/share/texmf-texlive/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size10.clo)) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty (/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty)) (/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty (/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty) (/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty (/usr/share/texmf-texlive/tex/latex/graphics/trig.sty) (/etc/texmf/tex/latex/config/graphics.cfg) (/usr/share/texmf-texlive/tex/latex/graphics/dvips.def))) (/usr/share/texmf-texlive/tex/latex/pstricks/pstricks.sty (/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.tex `PSTricks' v1.15 <2006/12/22> (tvz) (/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.con)) (/usr/share/texmf/tex/latex/xcolor/xcolor.sty (/etc/texmf/tex/latex/config/color.cfg))) (/usr/share/texmf-texlive/tex/latex/base/inputenc.sty (/usr/share/texmf-texlive/tex/latex/base/utf8.def (/usr/share/texmf-texlive/tex/latex/base/t1enc.dfu) (/usr/share/texmf-texlive/tex/latex/base/ot1enc.dfu) (/usr/share/texmf-texlive/tex/latex/base/omsenc.dfu))) (/usr/share/texmf-texlive/tex/latex/base/fontenc.sty (/usr/share/texmf-texlive/tex/latex/base/t1enc.def)) No file sage13.aux. (./sage13.aux) ) No pages of output. Transcript written on sage13.log. This is dvipng 1.9 Copyright 2002-2006 Jan-Ake Larsson sage13.dvi: No such file or directory 'dvipng' failed; trying 'convert' instead... cd "/tmp/sagenbws/temp/boxen/28949/dir_0" && sage-native-execute dvips sage13.dvi && sage-native-execute convert -density 140x140 -trim sage13.ps sage13.png This is dvips(k) 5.96.1 Copyright 2007 Radical Eye Software (www.radicaleye.com) dvips: ! DVI file can't be opened. An error occurred. This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2010.9.1) 11 SEP 2010 01:53 entering extended mode %&-line parsing enabled. **\nonstopmode \input{sage13.tex} (./sage13.tex (/usr/share/texmf-texlive/tex/latex/base/article.cls ... (/usr/share/texmf-texlive/tex/latex/base/omsenc.dfu File: omsenc.dfu 2006/03/30 v1.1i UTF-8 support for inputenc defining Unicode char U+00A7 (decimal 167) defining Unicode char U+00B6 (decimal 182) defining Unicode char U+00B7 (decimal 183) defining Unicode char U+2020 (decimal 8224) defining Unicode char U+2021 (decimal 8225) defining Unicode char U+2022 (decimal 8226) ) Now handling font encoding OMX ... ... no UTF-8 mapping file for font encoding OMX Now handling font encoding U ... ... no UTF-8 mapping file for font encoding U defining Unicode char U+00A9 (decimal 169) defining Unicode char U+00AA (decimal 170) defining Unicode char U+00AE (decimal 174) defining Unicode char U+00BA (decimal 186) defining Unicode char U+02C6 (decimal 710) defining Unicode char U+02DC (decimal 732) defining Unicode char U+200C (decimal 8204) defining Unicode char U+2026 (decimal 8230) defining Unicode char U+2122 (decimal 8482) defining Unicode char U+2423 (decimal 9251) )) (/usr/share/texmf-texlive/tex/latex/base/fontenc.sty Package: fontenc 2005/09/27 v1.99g Standard LaTeX package (/usr/share/texmf-texlive/tex/latex/base/t1enc.def File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file LaTeX Font Info: Redeclaring font encoding T1 on input line 43. )) No file sage13.aux. \openout1 = `sage13.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 30. LaTeX Font Info: ... okay on input line 30. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 30. LaTeX Font Info: ... okay on input line 30. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 30. LaTeX Font Info: ... okay on input line 30. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 30. LaTeX Font Info: ... okay on input line 30. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 30. LaTeX Font Info: ... okay on input line 30. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 30. LaTeX Font Info: ... okay on input line 30. (./sage13.aux) ) Here is how much of TeX's memory you used: 3137 strings out of 94102 33719 string characters out of 1165834 101046 words of memory out of 1500000 6423 multiletter control sequences out of 10000+50000 4403 words of font info for 15 fonts, out of 1200000 for 2000 637 hyphenation exceptions out of 8191 31i,1n,37p,284b,38s stack positions out of 5000i,500n,6000p,200000b,5000s No pages of output. None