Sharedwww / talks / circles / example_two_comp.texOpen in CoCalc
Author: William A. Stein
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\documentclass[12pt]{article}
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\usepackage{pstricks}
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\pagestyle{empty}
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\textwidth=1.2\textwidth
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\hoffset=-.7in
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\textheight=1.2\textheight
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\voffset=-.9in
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\begin{document}
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{\LARGE$$y^2 = x^3 - x$$}
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\begin{center}
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\psset{unit=.75in}%,xunit=.5in, yunit=.5in}
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\pspicture(-2,-5)(5,5)
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\psgrid[gridcolor=gray]
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\pscircle*[linecolor=red](-1,0){0.1}\rput(-1.5,0.2){$(-1,0)$}
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\pscircle*[linecolor=red](1,0){0.1}\rput(1.5,0.2){$(1,0
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)$}
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\psline[linewidth=0.03]{->}(-2,0)(5,0)\rput(5.2,0){$x$}
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\psline[linewidth=0.03]{->}(0,-5)(0,5)\rput(0,5.2){$y$}
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\pscurve[linecolor=blue]
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(3.0000,4.8989)
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(2.9500,4.7668)
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(2.9000,4.6356)
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(2.8500,4.5054)
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(2.8000,4.3763)
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(2.7500,4.2481)
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(2.7000,4.1210)
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(2.6500,3.9949)
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(2.6000,3.8698)
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(2.5500,3.7458)
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(2.5000,3.6228)
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(2.4500,3.5008)
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(2.4000,3.3799)
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(2.3500,3.2600)
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(2.3000,3.1411)
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(2.2500,3.0233)
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(2.2000,2.9065)
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(2.1500,2.7907)
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(2.1000,2.6760)
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(2.0500,2.5622)
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(2.0000,2.4494)
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(1.9500,2.3377)
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(1.9000,2.2268)
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(1.8500,2.1169)
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(1.8000,2.0079)
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(1.7500,1.8998)
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(1.7000,1.7924)
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(1.6500,1.6858)
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(1.6000,1.5798)
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(1.5500,1.4744)
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(1.5000,1.3693)
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(1.4500,1.2643)
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(1.4000,1.1593)
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(1.3500,1.0537)
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(1.3000,0.94710)
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(1.2500,0.83852)
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(1.2000,0.72663)
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(1.1500,0.60899)
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(1.1000,0.48062)
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(1.0500,0.32806)
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(1.0000,0)
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(1.0000,0)
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(1.0500,-0.32806)
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(1.1000,-0.48062)
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(1.1500,-0.60899)
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(1.2000,-0.72663)
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(1.2500,-0.83852)
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(1.3000,-0.94710)
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(1.3500,-1.0537)
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(1.4000,-1.1593)
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(1.4500,-1.2643)
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(1.5000,-1.3693)
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(1.5500,-1.4744)
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(1.6000,-1.5798)
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(1.6500,-1.6858)
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(1.7000,-1.7924)
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(1.7500,-1.8998)
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(1.8000,-2.0079)
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(1.8500,-2.1169)
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(1.9000,-2.2268)
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(1.9500,-2.3377)
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(2.0000,-2.4494)
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(2.0500,-2.5622)
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(2.1000,-2.6760)
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(2.1500,-2.7907)
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(2.2000,-2.9065)
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(2.2500,-3.0233)
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(2.3000,-3.1411)
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(2.3500,-3.2600)
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(2.4000,-3.3799)
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(2.4500,-3.5008)
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(2.5000,-3.6228)
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(2.5500,-3.7458)
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(2.6000,-3.8698)
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(2.6500,-3.9949)
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(2.7000,-4.1210)
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(2.7500,-4.2481)
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(2.8000,-4.3763)
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(2.8500,-4.5054)
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(2.9000,-4.6356)
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(2.9500,-4.7668)
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(3.0000,-4.8989)
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\psccurve[linecolor=blue]
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(-0.050000,0.22332)
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(-0.10000,0.31464)
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(-0.15000,0.38291)
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(-0.20000,0.43817)
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(-0.25000,0.48412)
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(-0.30000,0.52249)
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(-0.35000,0.55418)
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(-0.40000,0.57965)
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(-0.45000,0.59906)
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(-0.50000,0.61237)
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(-0.55000,0.61937)
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(-0.60000,0.61967)
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(-0.65000,0.61267)
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(-0.70000,0.59749)
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(-0.75000,0.57282)
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(-0.80000,0.53665)
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(-0.85000,0.48567)
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(-0.90000,0.41352)
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(-0.95000,0.30434)
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(-1.0000,0)
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(-1.0000,0)
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(-0.95000,-0.30434)
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(-0.90000,-0.41352)
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(-0.85000,-0.48567)
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(-0.80000,-0.53665)
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(-0.75000,-0.57282)
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(-0.70000,-0.59749)
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(-0.65000,-0.61268)
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(-0.60000,-0.61967)
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(-0.55000,-0.61937)
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(-0.50000,-0.61237)
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(-0.45000,-0.59906)
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(-0.40000,-0.57965)
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(-0.35000,-0.55419)
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(-0.30000,-0.52249)
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(-0.25000,-0.48412)
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(-0.20000,-0.43817)
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(-0.15000,-0.38291)
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(-0.10000,-0.31464)
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(-0.050000,-0.22332)
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\endpspicture
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\vspace{.5in}
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Add $(-1,0)$ and $(1,0)$ together!
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\end{center}
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\end{document}
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