gnuplot + TeX

Install

<TeX install>

TeXworks-win-setup-0.6.2-201704300708-git_7ecce17.exe

 

<Ghostscript install>

gs921w32full-gpl.exe

 -> https://www.ghostscript.com/download/gsdnld.html

 

<scilab install>

scilab-5.5.2_x64.exe (previous version)

 -> http://www.scilab.org/

 

<KETpic setting>

ketpicsciL5_1_6c.zip

 -> http://ketpic.com/?page_id=56

  (KeTpic for Scilab/old/ketpicsciL5_1_6c.zip)

 

<gnuplot install>

 -> http://www.gnuplot.info/

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Necessary condition

y = f(x) ∧ y = g(x) ⇒ 2y = f(x) + g(x)

 

 

Example:

y = x² ∧ y = -x² + 1  ⇒ y = 1/2

 

cf.

[i]

y = f(x) ∧ y = g(x) ⇔ 2y = f(x) + g(x) ∧ 0 = f(x) - g(x)

 

[ii]

f(x,y) = 0 ∧ f(y,x) = 0 ⇔  f(x,y) + f(y,x) = 0 ∧ f(x,y) - f(y,x) = 0

 

[iii]

f(x,y)=0 ∧ g(x,y)=0 ⇒ ∃k ( f(x,y) + kg(x,y)=0 )

 

[iv]

f(x,y)=0 ∧ g(x,y)=0 ⇔ ∀k ( f(x,y) + kg(x,y)=0 )

 

[v]

y=ax²+bx+c ∧ y=px²+qx+r ⇒ (p-a)y=(pb-aq)x+(pc-ar)

 

[vi]

x²+y²+ax+by+c=0 ∧ x²+y²+px+qy+r=0 ⇒ (a-p)x+(b-q)y+(c-r)=0

Geometry translation

Every point of the shape must move:

  • the same distance
  • in the same direction.

 

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