home *** CD-ROM | disk | FTP | other *** search
Text File | 1989-02-10 | 76.2 KB | 2,594 lines | [ TEXT/OMEG]
(*^ ::[paletteColors = 128; fontset = title, "New York", 18, L2, center, bold, nohscroll; fontset = subtitle, "New York", 14, L2, center, bold, nohscroll; fontset = subsubtitle, "New York", 12, L2, center, bold, nohscroll; fontset = section, "New York", 14, L2, bold, nohscroll, grayBox; fontset = subsection, "New York", 12, L2, bold, nohscroll, blackBox; fontset = subsubsection, "New York", 10, L2, bold, nohscroll, whiteBox; fontset = text, "New York", 10, L2, nohscroll; fontset = smalltext, "New York", 10, L2, nohscroll; fontset = input, "Courier", 12, L2, bold, B65535, nowordwrap; fontset = output, "Courier", 12, L2, R65535, B65535, nowordwrap; fontset = message, "Courier", 12, L2, R65535, nowordwrap; fontset = print, "Courier", 12, L2, nowordwrap; fontset = info, "Courier", 12, L2, nowordwrap; fontset = postscript, "Courier", 12, L2, nowordwrap; fontset = name, "Geneva", 10, L2, italic, B65535, nohscroll; fontset = header, "New York", 10, L2, nohscroll; fontset = footer, "New York", 12, L2, center, nohscroll; fontset = help, "Geneva", 10, L2, nohscroll; fontset = clipboard, "New York", 12, L2; fontset = completions, "New York", 12, L2; fontset = network, "Courier", 10, L2, nowordwrap; fontset = graphlabel, "Courier", 12, L2; fontset = special1, "New York", 12, L2; fontset = special2, "New York", 12, L2, center; fontset = special3, "New York", 12, L2, right; fontset = special4, "New York", 12, L2; fontset = special5, "New York", 12, L2;] :[inactive; startGroup; font = title; ] A Sampling of Mathematica™ ;[s] 4:0,2;14,1;25,2;27,0;28,-1; 4:1,23,17,New York,1,18,0,0,0;1,21,17,New York,3,18,65535,0,0;2,23,17,New York,1,18,65535,0,0;0,21,17,New York,0,18,65535,0,0; :[inactive; font = text; ] This file is a Mathematica Notebook that gives some examples of what Mathematica can do. ;[s] 6:0,0;15,1;26,0;69,1;80,0;90,0;91,-1; 2:4,14,10,New York,0,10,0,0,0;2,12,10,New York,2,10,0,0,0; :[inactive; font = text; ] For information on how to read this Notebook, see the file Read This First! ;[s] 3:0,0;59,1;75,0;76,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,1,10,0,0,0; :[inactive; font = text; ] This file is loosely based on Chapter 0 of The Mathematica Book: "Mathematica: A System for Doing Mathematics by Computer", by Stephen Wolfram. This book was published by Addison-Wesley in 1988, and is available at most bookstores. ;[s] 6:0,0;47,1;58,0;66,1;77,0;232,0;233,-1; 2:4,14,10,New York,0,10,0,0,0;2,12,10,New York,2,10,0,0,0; :[inactive; font = text; ] For information on how to obtain copies of Mathematica itself, see the section "Buying Mathematica" in the file Read This First! ;[s] 7:0,0;43,1;54,0;88,1;99,0;113,2;129,0;130,-1; 3:4,14,10,New York,0,10,0,0,0;2,12,10,New York,2,10,0,0,0;1,12,10,New York,1,10,0,0,0; :[inactive; startGroup; Cclosed; font = section; ] Numerical Calculations ;[s] 2:0,1;22,0;23,-1; 2:1,19,14,New York,1,14,0,0,0;1,19,14,New York,1,14,65535,0,0; :[inactive; font = text; ] You can use Mathematica as an enhanced scientific calculator. Let's start with a simple example. ;[s] 6:0,0;12,1;23,0;81,2;82,0;98,0;99,-1; 3:4,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0;1,14,10,New York,0,10,65535,0,65535; :[startGroup; font = input; ] 45 + 78 ;[s] 2:0,1;7,0;8,-1; 2:1,14,10,Courier,1,12,0,0,65535;1,14,10,Courier,1,12,0,0,65535; :[inactive; output; endGroup; font = output; ] 123 ;[o] 123 :[inactive; font = text; ] The first line here is what you type into Mathematica. The second line is the result Mathematica gives. If you are reading this Notebook on a color system, the input is blue and the output purple. ;[s] 5:0,0;42,1;53,0;86,1;97,0;200,-1; 2:3,14,10,New York,0,10,0,0,0;2,12,10,New York,2,10,0,0,0; :[inactive; font = text; ] Now let's try something more difficult. :[startGroup; font = input; ] 3^100 :[inactive; output; endGroup; font = output; ] 515377520732011331036461129765621272702107522001 ;[o] 515377520732011331036461129765621272702107522001 :[inactive; font = text; ] Unlike a calculator, Mathematica gives an exact answer for 3 raised to the power 100. ;[s] 3:0,0;21,1;32,0;87,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[inactive; font = text; ] Now let's really test out Mathematica. Here is 3 raised to the power 1000. ;[s] 3:0,0;26,2;37,0;76,-1; 3:2,14,10,New York,0,10,0,0,0;0,12,10,New York,3,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] 3^1000 :[inactive; output; endGroup; font = output; ] 13220708194808066368904552597521443659654220327521481676649\ 2036822682859734670489954077831385060806196390977769687258\ 2355950954582100618911865342725257953674027620225198320803\ 8780147742289648412743904001175886180411289478156230944380\ 6156617305408667449050617812548034440554705439703889581746\ 5368254916136220830268563778582290228416398307887896918556\ 4040848989376093732421718463599386955167650189405881090604\ 2608967143886410281435038564874716583201061436613217310276\ 8902855220001 ;[o] 13220708194808066368904552597521443659654220327521481676649\ 2036822682859734670489954077831385060806196390977769687258\ 2355950954582100618911865342725257953674027620225198320803\ 8780147742289648412743904001175886180411289478156230944380\ 6156617305408667449050617812548034440554705439703889581746\ 5368254916136220830268563778582290228416398307887896918556\ 4040848989376093732421718463599386955167650189405881090604\ 2608967143886410281435038564874716583201061436613217310276\ 8902855220001 :[inactive; font = text; ] This took about half a second on a Macintosh II. :[inactive; font = text; ] Here's the result in the form you might get on a calculator. :[startGroup; font = input; ] N[%] :[inactive; output; endGroup; font = output; ] "1.32207"*10^"477" ;[o] 477 1.32207 10 :[inactive; font = text; ] Here is the value of pi to two hundred decimal places. ;[s] 3:0,0;25,2;54,0;55,-1; 5:2,14,10,New York,0,10,0,0,0;0,12,10,Chicago,1,10,0,0,0;1,14,10,New York,0,10,0,0,0;0,11,9,Symbol,1,10,0,0,0;0,15,12,Symbol,1,14,0,0,0; :[startGroup; font = input; ] N[Pi, 200] :[inactive; output; endGroup; font = output; ] 3.141592653589793238462643383279502884197169399375105820974\ 9445923078164062862089986280348253421170679821480865132823\ 0664709384460955058223172535940812848111745028410270193852\ 1105559644622948954930382 ;[o] 3.141592653589793238462643383279502884197169399375105820974\ 9445923078164062862089986280348253421170679821480865132823\ 0664709384460955058223172535940812848111745028410270193852\ 1105559644622948954930382 :[inactive; font = text; ] Mathematica knows about a big collection of mathematical functions — most of those you would find in any book of mathematical tables. ;[s] 3:0,1;11,0;134,0;135,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] BesselJ[5, 34.6] :[inactive; output; endGroup; font = output; ] 0.0511826 ;[o] 0.0511826 :[startGroup; font = input; ] Log[4.5 + 2I] :[inactive; output; endGroup; font = output; ] 1.59421 + 0.418224*I ;[o] 1.59421 + 0.418224 I :[startGroup; font = input; ] Zeta[1/2 + 14.3 I] :[inactive; output; endGroup; endGroup; font = output; ] -0.0119878 + 0.132231*I ;[o] -0.0119878 + 0.132231 I :[inactive; startGroup; Cclosed; font = section; ] Algebraic Calculations ;[s] 2:0,1;22,0;23,-1; 2:1,19,14,New York,1,14,0,0,0;1,19,14,New York,1,14,65535,0,0; :[inactive; font = text; ] One of the most important features of Mathematica is its ability to deal with mathematical formulas in algebraic form. ;[s] 3:0,0;38,1;49,0;120,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] (1 + x)^3 :[inactive; output; endGroup; font = output; ] (1 + x)^3 ;[o] 3 (1 + x) :[inactive; font = text; ] This is what Mathematica does if you type in a simple algebraic expression. You can expand out the expression like this: ;[s] 3:0,0;13,1;24,0;121,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] Expand[%] :[inactive; output; endGroup; font = output; ] 1 + 3*x + 3*x^2 + x^3 ;[o] 2 3 1 + 3 x + 3 x + x :[inactive; font = text; ] Mathematica gives an explicit formula for the result. You can factor this result to get back to what you started from. % always stands for the last result that Mathematica gave you. ;[s] 6:0,1;11,0;119,2;120,0;160,1;171,0;182,-1; 3:3,14,10,New York,0,10,0,0,0;2,12,10,New York,2,10,0,0,0;1,11,9,Courier,0,10,0,0,0; :[startGroup; font = input; ] Factor[%] :[inactive; output; endGroup; font = output; ] (1 + x)^3 ;[o] 3 (1 + x) :[inactive; font = text; ] Now let's try a more complicated example. :[startGroup; font = input; ] (1 + 2x + 5y)^7 :[inactive; output; endGroup; font = output; ] (1 + 2*x + 5*y)^7 ;[o] 7 (1 + 2 x + 5 y) :[startGroup; font = input; ] Expand[%] :[inactive; output; endGroup; font = output; ] 1 + 14*x + 84*x^2 + 280*x^3 + 560*x^4 + 672*x^5 + 448*x^6 + 128*x^7 + 35*y + 420*x*y + 2100*x^2*y + 5600*x^3*y + 8400*x^4*y + 6720*x^5*y + 2240*x^6*y + 525*y^2 + 5250*x*y^2 + 21000*x^2*y^2 + 42000*x^3*y^2 + 42000*x^4*y^2 + 16800*x^5*y^2 + 4375*y^3 + 35000*x*y^3 + 105000*x^2*y^3 + 140000*x^3*y^3 + 70000*x^4*y^3 + 21875*y^4 + 131250*x*y^4 + 262500*x^2*y^4 + 175000*x^3*y^4 + 65625*y^5 + 262500*x*y^5 + 262500*x^2*y^5 + 109375*y^6 + 218750*x*y^6 + 78125*y^7 ;[o] 2 3 4 5 6 1 + 14 x + 84 x + 280 x + 560 x + 672 x + 448 x + 7 2 3 128 x + 35 y + 420 x y + 2100 x y + 5600 x y + 4 5 6 2 2 8400 x y + 6720 x y + 2240 x y + 525 y + 5250 x y + 2 2 3 2 4 2 5 2 21000 x y + 42000 x y + 42000 x y + 16800 x y + 3 3 2 3 3 3 4375 y + 35000 x y + 105000 x y + 140000 x y + 4 3 4 4 2 4 70000 x y + 21875 y + 131250 x y + 262500 x y + 3 4 5 5 2 5 175000 x y + 65625 y + 262500 x y + 262500 x y + 6 6 7 109375 y + 218750 x y + 78125 y :[startGroup; font = input; ] Factor[%] :[inactive; output; endGroup; font = output; ] (1 + 2*x + 5*y)^7 ;[o] 7 (1 + 2 x + 5 y) :[inactive; startGroup; Cclosed; font = subsection; ] Calculus :[inactive; font = text; ] You can use Mathematica to do calculus. Here's a simple integral. ;[s] 3:0,0;12,1;23,0;66,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] Integrate[x^n, x] :[inactive; output; endGroup; font = output; ] x^(1 + n)/(1 + n) ;[o] 1 + n x ------ 1 + n :[inactive; font = text; ] Here's a more complicated example. :[startGroup; font = input; ] Integrate[x/(x^3-1), x] :[inactive; output; endGroup; font = output; ] (3^(1/2)*ArcTan[(1 + 2*x)/3^(1/2)])/3 + Log[1 - x]/3 - Log[1 + x + x^2]/6 ;[o] 1 + 2 x Sqrt[3] ArcTan[-------] 2 Sqrt[3] Log[1 - x] Log[1 + x + x ] ----------------------- + ---------- - --------------- 3 3 6 :[inactive; font = text; ] Now let's try differentiating again. :[startGroup; font = input; ] D[%, x] :[inactive; output; endGroup; font = output; ] -1/(3*(1 - x)) + 2/(3*(1 + (1 + 2*x)^2/3)) - (1 + 2*x)/(6*(1 + x + x^2)) ;[o] -1 2 1 + 2 x --------- + ------------------ - -------------- 3 (1 - x) 2 2 (1 + 2 x) 6 (1 + x + x ) 3 (1 + ----------) 3 :[inactive; font = text; ] This gives the expression in a different algebraic form. We can get back our original form using Simplify. ;[s] 3:0,0;97,2;105,0;107,-1; 3:2,14,10,New York,0,10,0,0,0;0,11,9,Courier,0,10,0,0,0;1,11,9,Courier,1,10,0,0,0; :[startGroup; font = input; ] Simplify[%] :[inactive; output; endGroup; endGroup; font = output; ] x/(-1 + x^3) ;[o] x ------- 3 -1 + x :[inactive; startGroup; Cclosed; font = subsection; ] Solving Equations :[inactive; font = text; ] This is how you solve a quadratic equation in Mathematica. ;[s] 3:0,0;46,1;57,0;59,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] Solve[x^2 + 2 a x + 1 == 0, x] :[inactive; output; endGroup; font = output; ] {{x -> (-2*a + (-4 + 4*a^2)^(1/2))/2}, {x -> (-2*a - (-4 + 4*a^2)^(1/2))/2}} ;[o] 2 -2 a + Sqrt[-4 + 4 a ] {{x -> ----------------------}, 2 2 -2 a - Sqrt[-4 + 4 a ] {x -> ----------------------}} 2 :[inactive; font = text; ] Here's a more complicated example. :[startGroup; font = input; ] Solve[x^5 + 3x + 1 == 0, x] :[inactive; output; endGroup; font = output; ] {ToRules[Roots[3*x + x^5 == -1, x]]} ;[o] 5 {ToRules[Roots[3 x + x == -1, x]]} :[inactive; font = text; ] It is a fact of mathematics that there is no way to get an exact formula for the solutions of a quintic equation like this. You can nevertheless ask Mathematica to give you numerical results. You get the five complex number roots to the equation. ;[s] 3:0,0;150,1;161,0;249,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] N[%] :[inactive; output; endGroup; endGroup; endGroup; font = output; ] {{x -> -0.839072 - 0.943852*I}, {x -> -0.839072 + 0.943852*I}, {x -> -0.331989}, {x -> 1.00507 - 0.937259*I}, {x -> 1.00507 + 0.937259*I}} ;[o] {{x -> -0.839072 - 0.943852 I}, {x -> -0.839072 + 0.943852 I}, {x -> -0.331989}, {x -> 1.00507 - 0.937259 I}, {x -> 1.00507 + 0.937259 I}} :[inactive; startGroup; Cclosed; font = section; ] Graphics ;[s] 2:0,1;8,0;9,-1; 2:1,19,14,New York,1,14,0,0,0;1,19,14,New York,1,14,65535,0,0; :[startGroup; font = input; ] Plot[Sin[x], {x, 0, 2Pi}] :[inactive; PostScript; output; endGroup; pictureLeft = 61; pictureWidth = 282; pictureHeight = 174; preserveAspect; font = postscript; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.02381 0.15158 0.30902 0.2943 [ [(1.)] 0.17539 0.29652 0 1 Msboxa [(2.)] 0.32696 0.29652 0 1 Msboxa [(3.)] 0.47854 0.29652 0 1 Msboxa [(4.)] 0.63011 0.29652 0 1 Msboxa [(5.)] 0.78169 0.29652 0 1 Msboxa [(6.)] 0.93327 0.29652 0 1 Msboxa [(-1.)] 0.01131 0.01472 1 0 Msboxa [(-0.5)] 0.01131 0.16187 1 0 Msboxa [(0.5)] 0.01131 0.45617 1 0 Msboxa [(1.)] 0.01131 0.60332 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave 0.002 setlinewidth 0 0.30902 moveto 1 0.30902 lineto stroke 0.17539 0.30277 moveto 0.17539 0.31527 lineto stroke [(1.)] 0.17539 0.29652 0 1 Mshowa 0.32696 0.30277 moveto 0.32696 0.31527 lineto stroke [(2.)] 0.32696 0.29652 0 1 Mshowa 0.47854 0.30277 moveto 0.47854 0.31527 lineto stroke [(3.)] 0.47854 0.29652 0 1 Mshowa 0.63011 0.30277 moveto 0.63011 0.31527 lineto stroke [(4.)] 0.63011 0.29652 0 1 Mshowa 0.78169 0.30277 moveto 0.78169 0.31527 lineto stroke [(5.)] 0.78169 0.29652 0 1 Mshowa 0.93327 0.30277 moveto 0.93327 0.31527 lineto stroke [(6.)] 0.93327 0.29652 0 1 Mshowa 0.02381 0 moveto 0.02381 0.61803 lineto stroke 0.01756 0.01472 moveto 0.03006 0.01472 lineto stroke [(-1.)] 0.01131 0.01472 1 0 Mshowa 0.01756 0.16187 moveto 0.03006 0.16187 lineto stroke [(-0.5)] 0.01131 0.16187 1 0 Mshowa 0.01756 0.45617 moveto 0.03006 0.45617 lineto stroke [(0.5)] 0.01131 0.45617 1 0 Mshowa 0.01756 0.60332 moveto 0.03006 0.60332 lineto stroke [(1.)] 0.01131 0.60332 1 0 Mshowa grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath gsave 0 setgray gsave 0.004 setlinewidth 0.02381 0.30902 moveto 0.06349 0.38519 lineto 0.10317 0.45617 lineto 0.14286 0.51712 lineto 0.1627 0.5425 lineto 0.18254 0.56389 lineto 0.20238 0.58092 lineto 0.2123 0.5877 lineto 0.22222 0.59329 lineto 0.23214 0.59766 lineto 0.2371 0.59939 lineto 0.24206 0.6008 lineto 0.24702 0.6019 lineto 0.2495 0.60233 lineto 0.25198 0.60269 lineto 0.25446 0.60296 lineto 0.2557 0.60307 lineto 0.25694 0.60316 lineto 0.25818 0.60323 lineto 0.25942 0.60328 lineto 0.26066 0.60331 lineto 0.2619 0.60332 lineto 0.26314 0.60331 lineto 0.26438 0.60328 lineto 0.26563 0.60323 lineto 0.26687 0.60316 lineto 0.26935 0.60296 lineto 0.27183 0.60269 lineto 0.27431 0.60233 lineto 0.27679 0.6019 lineto 0.28175 0.6008 lineto 0.28671 0.59939 lineto 0.29167 0.59766 lineto 0.30159 0.59329 lineto 0.32143 0.58092 lineto 0.34127 0.56389 lineto 0.38095 0.51712 lineto 0.42063 0.45617 lineto 0.46032 0.38519 lineto 0.5 0.30902 lineto 0.53968 0.23285 lineto 0.57937 0.16187 lineto 0.61905 0.10091 lineto 0.63889 0.07553 lineto 0.65873 0.05414 lineto 0.67857 0.03712 lineto 0.68849 0.03033 lineto 0.69841 0.02474 lineto 0.70833 0.02037 lineto 0.71329 0.01865 lineto Mistroke 0.71825 0.01723 lineto 0.72321 0.01613 lineto 0.72569 0.0157 lineto 0.72817 0.01535 lineto 0.73065 0.01507 lineto 0.73189 0.01496 lineto 0.73313 0.01487 lineto 0.73438 0.0148 lineto 0.73562 0.01475 lineto 0.73686 0.01472 lineto 0.7381 0.01472 lineto 0.73934 0.01472 lineto 0.74058 0.01475 lineto 0.74182 0.0148 lineto 0.74306 0.01487 lineto 0.74554 0.01507 lineto 0.74802 0.01535 lineto 0.7505 0.0157 lineto 0.75298 0.01613 lineto 0.75794 0.01723 lineto 0.7629 0.01865 lineto 0.76786 0.02037 lineto 0.77778 0.02474 lineto 0.79762 0.03712 lineto 0.81746 0.05414 lineto 0.85714 0.10091 lineto 0.89683 0.16187 lineto 0.93651 0.23285 lineto 0.97619 0.30902 lineto Mfstroke grestore grestore % End of Graphics MathPictureEnd :[inactive; font = text; ] Here is a simple Mathematica plot. ;[s] 4:0,0;17,1;28,0;35,0;36,-1; 2:3,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[inactive; font = text; ] Now for some three-dimensional graphics. :[startGroup; font = input; ] Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}] :[inactive; PostScript; output; endGroup; pictureLeft = 61; pictureWidth = 282; pictureHeight = 282; preserveAspect; font = postscript; ] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart % Scaling calculations 0.02381 0.95238 0.02381 0.95238 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 moveto 1 0 lineto 1 1 lineto 0 1 lineto closepath clip newpath %%Object: SurfaceGraphics 0 setgray gsave 0.002 setlinewidth 0.06558 0.32026 moveto 0.39347 0.6265 lineto stroke 0.06558 0.32026 moveto 0.03248 0.52913 lineto stroke 0.38687 0.8155 moveto 0.03248 0.52913 lineto stroke 0.38687 0.8155 moveto 0.39347 0.6265 lineto stroke 0.64594 0.09301 moveto 0.89589 0.47534 lineto stroke 0.64594 0.09301 moveto 0.65863 0.31163 lineto stroke 0.92319 0.67509 moveto 0.65863 0.31163 lineto stroke 0.92319 0.67509 moveto 0.89589 0.47534 lineto stroke 0.06558 0.32026 moveto 0.03248 0.52913 lineto stroke 0.06558 0.32026 moveto 0.64594 0.09301 lineto stroke 0.65863 0.31163 moveto 0.64594 0.09301 lineto stroke 0.65863 0.31163 moveto 0.03248 0.52913 lineto stroke 0.39347 0.6265 moveto 0.38687 0.8155 lineto stroke 0.39347 0.6265 moveto 0.89589 0.47534 lineto stroke 0.92319 0.67509 moveto 0.89589 0.47534 lineto stroke 0.92319 0.67509 moveto 0.38687 0.8155 lineto stroke 0.06558 0.32026 moveto 0.64594 0.09301 lineto stroke 0.06558 0.32026 moveto 0.39347 0.6265 lineto stroke 0.89589 0.47534 moveto 0.39347 0.6265 lineto stroke 0.89589 0.47534 moveto 0.64594 0.09301 lineto stroke 0.03248 0.52913 moveto 0.65863 0.31163 lineto stroke 0.03248 0.52913 moveto 0.38687 0.8155 lineto stroke 0.92319 0.67509 moveto 0.38687 0.8155 lineto stroke 0.92319 0.67509 moveto 0.65863 0.31163 lineto stroke grestore 0.49975 setgray 0.0015 setlinewidth 0.37007 0.70047 0.39027 0.7181 0.4226 0.76375 0.40243 0.74276 Metetra 0.71417 setgray 0.40243 0.74276 0.4226 0.76375 0.45688 0.78857 0.43676 0.76824 Metetra 0.85443 setgray 0.43676 0.76824 0.45688 0.78857 0.49252 0.77696 0.47266 0.76305 Metetra 0.87201 setgray 0.47266 0.76305 0.49252 0.77696 0.5283 0.72948 0.5091 0.72503 Metetra 0.76083 setgray 0.5091 0.72503 0.5283 0.72948 0.56336 0.6626 0.54511 0.66484 Metetra 0.55935 setgray 0.54511 0.66484 0.56336 0.6626 0.59773 0.59974 0.58037 0.60079 Metetra 0.33725 setgray 0.58037 0.60079 0.59773 0.59974 0.63244 0.56082 0.61543 0.551 Metetra 0.17136 setgray 0.61543 0.551 0.63244 0.56082 0.66891 0.55603 0.65143 0.52779 Metetra 0.11905 setgray 0.65143 0.52779 0.66891 0.55603 0.70832 0.58368 0.68962 0.53501 Metetra 0.19841 setgray 0.68962 0.53501 0.70832 0.58368 0.75084 0.63038 0.7308 0.56751 Metetra 0.382 setgray 0.7308 0.56751 0.75084 0.63038 0.79516 0.67396 0.77481 0.61176 Metetra 0.60632 setgray 0.77481 0.61176 0.79516 0.67396 0.83868 0.6911 0.82019 0.64873 Metetra 0.79377 setgray 0.82019 0.64873 0.83868 0.6911 0.87879 0.66869 0.86456 0.66011 Metetra 0.87953 setgray 0.86456 0.66011 0.87879 0.66869 0.9145 0.61155 0.90563 0.63651 Metetra 0.49975 setgray 0.34934 0.68237 0.37007 0.70047 0.40243 0.74276 0.38177 0.72115 Metetra 0.69946 setgray 0.38177 0.72115 0.40243 0.74276 0.43676 0.76824 0.41614 0.74662 Metetra 0.84006 setgray 0.41614 0.74662 0.43676 0.76824 0.47266 0.76305 0.45223 0.74691 Metetra 0.87991 setgray 0.45223 0.74691 0.47266 0.76305 0.5091 0.72503 0.48919 0.71816 Metetra 0.80723 setgray 0.48919 0.71816 0.5091 0.72503 0.54511 0.66484 0.52609 0.66639 Metetra 0.64353 setgray 0.52609 0.66639 0.54511 0.66484 0.58037 0.60079 0.56235 0.60485 Metetra 0.43727 setgray 0.56235 0.60485 0.58037 0.60079 0.61543 0.551 0.59811 0.54878 Metetra 0.2495 setgray 0.59811 0.54878 0.61543 0.551 0.65143 0.52779 0.63411 0.51072 Metetra 0.1358 setgray 0.63411 0.51072 0.65143 0.52779 0.68962 0.53501 0.67146 0.49774 Metetra 0.12985 setgray 0.67146 0.49774 0.68962 0.53501 0.7308 0.56751 0.71119 0.51046 Metetra 0.23338 setgray 0.71119 0.51046 0.7308 0.56751 0.77481 0.61176 0.75387 0.54291 Metetra 0.41577 setgray 0.75387 0.54291 0.77481 0.61176 0.82019 0.64873 0.79919 0.58323 Metetra 0.62302 setgray 0.79919 0.58323 0.82019 0.64873 0.86456 0.66011 0.84578 0.61598 Metetra 0.79377 setgray 0.84578 0.61598 0.86456 0.66011 0.90563 0.63651 0.89152 0.62656 Metetra 0.49975 setgray 0.32804 0.66379 0.34934 0.68237 0.38177 0.72115 0.3606 0.69888 Metetra 0.68433 setgray 0.3606 0.69888 0.38177 0.72115 0.41614 0.74662 0.39502 0.72372 Metetra 0.82282 setgray 0.39502 0.72372 0.41614 0.74662 0.45223 0.74691 0.43123 0.72841 Metetra 0.88062 setgray 0.43123 0.72841 0.45223 0.74691 0.48919 0.71816 0.4686 0.70836 Metetra 0.84329 setgray 0.4686 0.70836 0.48919 0.71816 0.52609 0.66639 0.50627 0.66609 Metetra 0.72017 setgray 0.50627 0.66609 0.52609 0.66639 0.56235 0.60485 0.54355 0.61027 Metetra 0.54199 setgray 0.54355 0.61027 0.56235 0.60485 0.59811 0.54878 0.58024 0.55266 Metetra 0.35327 setgray 0.58024 0.55266 0.59811 0.54878 0.63411 0.51072 0.61672 0.5046 Metetra 0.20112 setgray 0.61672 0.5046 0.63411 0.51072 0.67146 0.49774 0.65376 0.47441 Metetra 0.12356 setgray 0.65376 0.47441 0.67146 0.49774 0.71119 0.51046 0.69237 0.46618 Metetra 0.13995 setgray 0.69237 0.46618 0.71119 0.51046 0.75387 0.54291 0.73341 0.47933 Metetra 0.2462 setgray 0.73341 0.47933 0.75387 0.54291 0.79919 0.58323 0.77732 0.50861 Metetra 0.41577 setgray 0.77732 0.50861 0.79919 0.58323 0.84578 0.61598 0.82382 0.54465 Metetra 0.60632 setgray 0.82382 0.54465 0.84578 0.61598 0.89152 0.62656 0.87179 0.57538 Metetra 0.49975 setgray 0.30617 0.6447 0.32804 0.66379 0.3606 0.69888 0.33889 0.67596 Metetra 0.66881 setgray 0.33889 0.67596 0.3606 0.69888 0.39502 0.72372 0.37339 0.69953 Metetra 0.80286 setgray 0.37339 0.69953 0.39502 0.72372 0.43123 0.72841 0.40968 0.70749 Metetra 0.8741 setgray 0.40968 0.70749 0.43123 0.72841 0.4686 0.70836 0.44733 0.69519 Metetra 0.86779 setgray 0.44733 0.69519 0.4686 0.70836 0.50627 0.66609 0.48562 0.66276 Metetra 0.78524 setgray 0.48562 0.66276 0.50627 0.66609 0.54355 0.61027 0.52386 0.61512 Metetra 0.64353 setgray 0.52386 0.61512 0.54355 0.61027 0.58024 0.55266 0.56164 0.56045 Metetra 0.47204 setgray 0.56164 0.56045 0.58024 0.55266 0.61672 0.5046 0.59897 0.50788 Metetra 0.30629 setgray 0.59897 0.50788 0.61672 0.5046 0.65376 0.47441 0.6363 0.46548 Metetra 0.18062 setgray 0.6363 0.46548 0.65376 0.47441 0.69237 0.46618 0.67438 0.43889 Metetra 0.12106 setgray 0.67438 0.43889 0.69237 0.46618 0.73341 0.47933 0.71407 0.43075 Metetra 0.13995 setgray 0.71407 0.43075 0.73341 0.47933 0.77732 0.50861 0.75612 0.44048 Metetra 0.23338 setgray 0.75612 0.44048 0.77732 0.50861 0.82382 0.54465 0.80095 0.46426 Metetra 0.382 setgray 0.80095 0.46426 0.82382 0.54465 0.87179 0.57538 0.84846 0.49537 Metetra 0.49975 setgray 0.2837 0.62508 0.30617 0.6447 0.33889 0.67596 0.31663 0.65236 Metetra 0.65294 setgray 0.31663 0.65236 0.33889 0.67596 0.37339 0.69953 0.35124 0.67407 Metetra 0.78034 setgray 0.35124 0.67407 0.37339 0.69953 0.40968 0.70749 0.3876 0.68412 Metetra 0.8605 setgray 0.3876 0.68412 0.40968 0.70749 0.44733 0.69519 0.42543 0.67828 Metetra 0.87991 setgray 0.42543 0.67828 0.44733 0.69519 0.48562 0.66276 0.46419 0.65533 Metetra 0.83532 setgray 0.46419 0.65533 0.48562 0.66276 0.52386 0.61512 0.50325 0.61737 Metetra 0.73423 setgray 0.50325 0.61737 0.52386 0.61512 0.56164 0.56045 0.54212 0.56935 Metetra 0.59365 setgray 0.54212 0.56935 0.56164 0.56045 0.59897 0.50788 0.58057 0.51775 Metetra 0.43727 setgray 0.58057 0.51775 0.59897 0.50788 0.6363 0.46548 0.6187 0.46929 Metetra 0.2914 setgray 0.6187 0.46929 0.6363 0.46548 0.67438 0.43889 0.65696 0.42968 Metetra 0.18062 setgray 0.65696 0.42968 0.67438 0.43889 0.71407 0.43075 0.696 0.403 Metetra 0.12356 setgray 0.696 0.403 0.71407 0.43075 0.75612 0.44048 0.73654 0.3913 Metetra 0.12985 setgray 0.73654 0.3913 0.75612 0.44048 0.80095 0.46426 0.77928 0.39451 Metetra 0.19841 setgray 0.77928 0.39451 0.80095 0.46426 0.84846 0.49537 0.82468 0.41045 Metetra 0.49975 setgray 0.2606 0.60492 0.2837 0.62508 0.31663 0.65236 0.29381 0.62806 Metetra 0.63674 setgray 0.29381 0.62806 0.31663 0.65236 0.35124 0.67407 0.32857 0.64736 Metetra 0.75546 setgray 0.32857 0.64736 0.35124 0.67407 0.3876 0.68412 0.365 0.65831 Metetra 0.84006 setgray 0.365 0.65831 0.3876 0.68412 0.42543 0.67828 0.40293 0.65742 Metetra 0.87924 setgray 0.40293 0.65742 0.42543 0.67828 0.46419 0.65533 0.44201 0.64288 Metetra 0.86779 setgray 0.44201 0.64288 0.46419 0.65533 0.50325 0.61737 0.48172 0.61501 Metetra 0.80723 setgray 0.48172 0.61501 0.50325 0.61737 0.54212 0.56935 0.52158 0.57617 Metetra 0.70565 setgray 0.52158 0.57617 0.54212 0.56935 0.58057 0.51775 0.56124 0.53029 Metetra 0.57658 setgray 0.56124 0.53029 0.58057 0.51775 0.6187 0.46929 0.60055 0.48211 Metetra 0.43727 setgray 0.60055 0.48211 0.6187 0.46929 0.65696 0.42968 0.63965 0.43639 Metetra 0.30629 setgray 0.63965 0.43639 0.65696 0.42968 0.696 0.403 0.67889 0.39724 Metetra 0.20112 setgray 0.67889 0.39724 0.696 0.403 0.73654 0.3913 0.7188 0.3678 Metetra 0.1358 setgray 0.7188 0.3678 0.73654 0.3913 0.77928 0.39451 0.76 0.34992 Metetra 0.11905 setgray 0.76 0.34992 0.77928 0.39451 0.82468 0.41045 0.8031 0.34415 Metetra 0.49975 setgray 0.23685 0.58419 0.2606 0.60492 0.29381 0.62806 0.27039 0.60306 Metetra 0.62026 setgray 0.27039 0.60306 0.29381 0.62806 0.32857 0.64736 0.30537 0.61941 Metetra 0.72842 setgray 0.30537 0.61941 0.32857 0.64736 0.365 0.65831 0.34189 0.63011 Metetra 0.81317 setgray 0.34189 0.63011 0.365 0.65831 0.40293 0.65742 0.3799 0.63249 Metetra 0.86581 setgray 0.3799 0.63249 0.40293 0.65742 0.44201 0.64288 0.41917 0.62475 Metetra 0.88095 setgray 0.41917 0.62475 0.44201 0.64288 0.48172 0.61501 0.45933 0.60626 Metetra 0.85705 setgray 0.45933 0.60626 0.48172 0.61501 0.52158 0.57617 0.5 0.57767 Metetra 0.79655 setgray 0.5 0.57767 0.52158 0.57617 0.56124 0.53029 0.54079 0.54081 Metetra 0.70565 setgray 0.54079 0.54081 0.56124 0.53029 0.60055 0.48211 0.58144 0.49842 Metetra 0.59365 setgray 0.58144 0.49842 0.60055 0.48211 0.63965 0.43639 0.62185 0.4537 Metetra 0.47204 setgray 0.62185 0.4537 0.63965 0.43639 0.67889 0.39724 0.66209 0.40992 Metetra 0.35327 setgray 0.66209 0.40992 0.67889 0.39724 0.7188 0.3678 0.70242 0.37007 Metetra 0.2495 setgray 0.70242 0.37007 0.7188 0.3678 0.76 0.34992 0.74322 0.33658 Metetra 0.17136 setgray 0.74322 0.33658 0.76 0.34992 0.8031 0.34415 0.78499 0.31121 Metetra 0.49975 setgray 0.21241 0.56286 0.23685 0.58419 0.27039 0.60306 0.24636 0.57734 Metetra 0.60352 setgray 0.24636 0.57734 0.27039 0.60306 0.30537 0.61941 0.28162 0.59026 Metetra 0.69946 setgray 0.28162 0.59026 0.30537 0.61941 0.34189 0.63011 0.31829 0.59961 Metetra 0.78034 setgray 0.31829 0.59961 0.34189 0.63011 0.3799 0.63249 0.35637 0.60354 Metetra 0.84006 setgray 0.35637 0.60354 0.3799 0.63249 0.41917 0.62475 0.39575 0.60056 Metetra 0.8741 setgray 0.39575 0.60056 0.41917 0.62475 0.45933 0.60626 0.4362 0.58975 Metetra 0.87991 setgray 0.4362 0.58975 0.45933 0.60626 0.5 0.57767 0.47744 0.57088 Metetra 0.85705 setgray 0.47744 0.57088 0.5 0.57767 0.54079 0.54081 0.51917 0.5444 Metetra 0.80723 setgray 0.51917 0.5444 0.54079 0.54081 0.58144 0.49842 0.56109 0.51143 Metetra 0.73423 setgray 0.56109 0.51143 0.58144 0.49842 0.62185 0.4537 0.603 0.47361 Metetra 0.64353 setgray 0.603 0.47361 0.62185 0.4537 0.66209 0.40992 0.64479 0.43293 Metetra 0.54199 setgray 0.64479 0.43293 0.66209 0.40992 0.70242 0.37007 0.68645 0.39149 Metetra 0.43727 setgray 0.68645 0.39149 0.70242 0.37007 0.74322 0.33658 0.72812 0.35134 Metetra 0.33725 setgray 0.72812 0.35134 0.74322 0.33658 0.78499 0.31121 0.77004 0.31432 Metetra 0.49975 setgray 0.18726 0.54091 0.21241 0.56286 0.24636 0.57734 0.2217 0.55087 Metetra 0.58656 setgray 0.2217 0.55087 0.24636 0.57734 0.28162 0.59026 0.25732 0.55995 Metetra 0.66881 setgray 0.25732 0.55995 0.28162 0.59026 0.31829 0.59961 0.29421 0.56695 Metetra 0.7422 setgray 0.29421 0.56695 0.31829 0.59961 0.35637 0.60354 0.3324 0.57073 Metetra 0.80286 setgray 0.3324 0.57073 0.35637 0.60354 0.39575 0.60056 0.37186 0.57025 Metetra 0.84761 setgray 0.37186 0.57025 0.39575 0.60056 0.4362 0.58975 0.41246 0.56472 Metetra 0.8741 setgray 0.41246 0.56472 0.4362 0.58975 0.47744 0.57088 0.45406 0.55361 Metetra 0.88095 setgray 0.45406 0.55361 0.47744 0.57088 0.51917 0.5444 0.49644 0.53673 Metetra 0.86779 setgray 0.49644 0.53673 0.51917 0.5444 0.56109 0.51143 0.53939 0.51422 Metetra 0.83532 setgray 0.53939 0.51422 0.56109 0.51143 0.603 0.47361 0.58269 0.48659 Metetra 0.78524 setgray 0.58269 0.48659 0.603 0.47361 0.64479 0.43293 0.62617 0.45463 Metetra 0.72017 setgray 0.62617 0.45463 0.64479 0.43293 0.68645 0.39149 0.66969 0.41936 Metetra 0.64353 setgray 0.66969 0.41936 0.68645 0.39149 0.72812 0.35134 0.71319 0.38197 Metetra 0.55935 setgray 0.71319 0.38197 0.72812 0.35134 0.77004 0.31432 0.75669 0.3437 Metetra 0.49975 setgray 0.16137 0.51831 0.18726 0.54091 0.2217 0.55087 0.19637 0.52363 Metetra 0.56942 setgray 0.19637 0.52363 0.2217 0.55087 0.25732 0.55995 0.23244 0.5285 Metetra 0.63674 setgray 0.23244 0.5285 0.25732 0.55995 0.29421 0.56695 0.26964 0.53228 Metetra 0.69946 setgray 0.26964 0.53228 0.29421 0.56695 0.3324 0.57073 0.30802 0.53436 Metetra 0.75546 setgray 0.30802 0.53436 0.3324 0.57073 0.37186 0.57025 0.34758 0.53414 Metetra 0.80286 setgray 0.34758 0.53414 0.37186 0.57025 0.41246 0.56472 0.38828 0.5311 Metetra 0.84006 setgray 0.38828 0.5311 0.41246 0.56472 0.45406 0.55361 0.43007 0.52478 Metetra 0.86581 setgray 0.43007 0.52478 0.45406 0.55361 0.49644 0.53673 0.47283 0.51487 Metetra 0.87924 setgray 0.47283 0.51487 0.49644 0.53673 0.53939 0.51422 0.51645 0.50115 Metetra 0.87991 setgray 0.51645 0.50115 0.53939 0.51422 0.58269 0.48659 0.56079 0.48356 Metetra 0.86779 setgray 0.56079 0.48356 0.58269 0.48659 0.62617 0.45463 0.6057 0.4622 Metetra 0.84329 setgray 0.6057 0.4622 0.62617 0.45463 0.66969 0.41936 0.65104 0.4373 Metetra 0.80723 setgray 0.65104 0.4373 0.66969 0.41936 0.71319 0.38197 0.6967 0.40922 Metetra 0.76083 setgray 0.6967 0.40922 0.71319 0.38197 0.75669 0.3437 0.74256 0.37844 Metetra 0.49975 setgray 0.13469 0.49503 0.16137 0.51831 0.19637 0.52363 0.17035 0.49562 Metetra 0.55213 setgray 0.17035 0.49562 0.19637 0.52363 0.23244 0.5285 0.20697 0.49596 Metetra 0.60352 setgray 0.20697 0.49596 0.23244 0.5285 0.26964 0.53228 0.24459 0.4958 Metetra 0.65294 setgray 0.24459 0.4958 0.26964 0.53228 0.30802 0.53436 0.28325 0.49484 Metetra 0.69946 setgray 0.28325 0.49484 0.30802 0.53436 0.34758 0.53414 0.32299 0.49284 Metetra 0.7422 setgray 0.32299 0.49284 0.34758 0.53414 0.38828 0.5311 0.36381 0.48951 Metetra 0.78034 setgray 0.36381 0.48951 0.38828 0.5311 0.43007 0.52478 0.4057 0.48463 Metetra 0.81317 setgray 0.4057 0.48463 0.43007 0.52478 0.47283 0.51487 0.44863 0.47796 Metetra 0.84006 setgray 0.44863 0.47796 0.47283 0.51487 0.51645 0.50115 0.49258 0.4693 Metetra 0.8605 setgray 0.49258 0.4693 0.51645 0.50115 0.56079 0.48356 0.53749 0.45851 Metetra 0.8741 setgray 0.53749 0.45851 0.56079 0.48356 0.6057 0.4622 0.58329 0.44545 Metetra 0.88062 setgray 0.58329 0.44545 0.6057 0.4622 0.65104 0.4373 0.62992 0.43005 Metetra 0.87991 setgray 0.62992 0.43005 0.65104 0.4373 0.6967 0.40922 0.6773 0.4123 Metetra 0.87201 setgray 0.6773 0.4123 0.6967 0.40922 0.74256 0.37844 0.72533 0.39219 Metetra 0.49975 setgray 0.10721 0.47104 0.13469 0.49503 0.17035 0.49562 0.14362 0.4668 Metetra 0.53473 setgray 0.14362 0.4668 0.17035 0.49562 0.20697 0.49596 0.18088 0.46238 Metetra 0.56942 setgray 0.18088 0.46238 0.20697 0.49596 0.24459 0.4958 0.21903 0.4577 Metetra 0.60352 setgray 0.21903 0.4577 0.24459 0.4958 0.28325 0.49484 0.25811 0.45268 Metetra 0.63674 setgray 0.25811 0.45268 0.28325 0.49484 0.32299 0.49284 0.29813 0.44723 Metetra 0.66881 setgray 0.29813 0.44723 0.32299 0.49284 0.36381 0.48951 0.33913 0.44125 Metetra 0.69946 setgray 0.33913 0.44125 0.36381 0.48951 0.4057 0.48463 0.38113 0.43467 Metetra 0.72842 setgray 0.38113 0.43467 0.4057 0.48463 0.44863 0.47796 0.42415 0.4274 Metetra 0.75546 setgray 0.42415 0.4274 0.44863 0.47796 0.49258 0.4693 0.46818 0.41935 Metetra 0.78034 setgray 0.46818 0.41935 0.49258 0.4693 0.53749 0.45851 0.51325 0.41045 Metetra 0.80286 setgray 0.51325 0.41045 0.53749 0.45851 0.58329 0.44545 0.55936 0.40061 Metetra 0.82282 setgray 0.55936 0.40061 0.58329 0.44545 0.62992 0.43005 0.6065 0.38975 Metetra 0.84006 setgray 0.6065 0.38975 0.62992 0.43005 0.6773 0.4123 0.65466 0.37783 Metetra 0.85443 setgray 0.65466 0.37783 0.6773 0.4123 0.72533 0.39219 0.70384 0.36476 Metetra 0.49975 setgray 0.07887 0.44631 0.10721 0.47104 0.14362 0.4668 0.11613 0.43715 Metetra 0.51726 setgray 0.11613 0.43715 0.14362 0.4668 0.18088 0.46238 0.15415 0.42779 Metetra 0.53473 setgray 0.15415 0.42779 0.18088 0.46238 0.21903 0.4577 0.19295 0.41822 Metetra 0.55213 setgray 0.19295 0.41822 0.21903 0.4577 0.25811 0.45268 0.23256 0.40842 Metetra 0.56942 setgray 0.23256 0.40842 0.25811 0.45268 0.29813 0.44723 0.273 0.39838 Metetra 0.58656 setgray 0.273 0.39838 0.29813 0.44723 0.33913 0.44125 0.3143 0.38808 Metetra 0.60352 setgray 0.3143 0.38808 0.33913 0.44125 0.38113 0.43467 0.35648 0.3775 Metetra 0.62026 setgray 0.35648 0.3775 0.38113 0.43467 0.42415 0.4274 0.39958 0.36662 Metetra 0.63674 setgray 0.39958 0.36662 0.42415 0.4274 0.46818 0.41935 0.44361 0.35543 Metetra 0.65294 setgray 0.44361 0.35543 0.46818 0.41935 0.51325 0.41045 0.4886 0.3439 Metetra 0.66881 setgray 0.4886 0.3439 0.51325 0.41045 0.55936 0.40061 0.53458 0.33202 Metetra 0.68433 setgray 0.53458 0.33202 0.55936 0.40061 0.6065 0.38975 0.58158 0.31976 Metetra 0.69946 setgray 0.58158 0.31976 0.6065 0.38975 0.65466 0.37783 0.62963 0.30711 Metetra 0.71417 setgray 0.62963 0.30711 0.65466 0.37783 0.70384 0.36476 0.67875 0.29405 Metetra 0.49975 setgray 0.04964 0.4208 0.07887 0.44631 0.11613 0.43715 0.08786 0.40664 Metetra 0.49975 setgray 0.08786 0.40664 0.11613 0.43715 0.15415 0.42779 0.12675 0.39224 Metetra 0.49975 setgray 0.12675 0.39224 0.15415 0.42779 0.19295 0.41822 0.16631 0.37759 Metetra 0.49975 setgray 0.16631 0.37759 0.19295 0.41822 0.23256 0.40842 0.20657 0.36267 Metetra 0.49975 setgray 0.20657 0.36267 0.23256 0.40842 0.273 0.39838 0.24755 0.3475 Metetra 0.49975 setgray 0.24755 0.3475 0.273 0.39838 0.3143 0.38808 0.28926 0.33205 Metetra 0.49975 setgray 0.28926 0.33205 0.3143 0.38808 0.35648 0.3775 0.33173 0.31632 Metetra 0.49975 setgray 0.33173 0.31632 0.35648 0.3775 0.39958 0.36662 0.37498 0.3003 Metetra 0.49975 setgray 0.37498 0.3003 0.39958 0.36662 0.44361 0.35543 0.41902 0.28399 Metetra 0.49975 setgray 0.41902 0.28399 0.44361 0.35543 0.4886 0.3439 0.46389 0.26737 Metetra 0.49975 setgray 0.46389 0.26737 0.4886 0.3439 0.53458 0.33202 0.50959 0.25044 Metetra 0.49975 setgray 0.50959 0.25044 0.53458 0.33202 0.58158 0.31976 0.55617 0.23319 Metetra 0.49975 setgray 0.55617 0.23319 0.58158 0.31976 0.62963 0.30711 0.60363 0.21561 Metetra 0.49975 setgray 0.60363 0.21561 0.62963 0.30711 0.67875 0.29405 0.65202 0.19769 Metetra 0 setgray 0.002 setlinewidth 0.64594 0.09301 moveto 0.89589 0.47534 lineto stroke 0.64594 0.09301 moveto 0.65863 0.31163 lineto stroke 0.92319 0.67509 moveto 0.65863 0.31163 lineto stroke 0.92319 0.67509 moveto 0.89589 0.47534 lineto stroke 0.06558 0.32026 moveto 0.03248 0.52913 lineto stroke 0.06558 0.32026 moveto 0.64594 0.09301 lineto stroke 0.65863 0.31163 moveto 0.64594 0.09301 lineto stroke 0.65863 0.31163 moveto 0.03248 0.52913 lineto stroke 0.03248 0.52913 moveto 0.65863 0.31163 lineto stroke 0.03248 0.52913 moveto 0.38687 0.8155 lineto stroke 0.92319 0.67509 moveto 0.38687 0.8155 lineto stroke 0.92319 0.67509 moveto 0.65863 0.31163 lineto stroke % End of Graphics MathPictureEnd :[inactive; endGroup; font = text; ] Mathematica generates all graphics in PostScript, so that you can resize pictures, and make use of the resolution available on different types of printers. ;[s] 2:0,1;11,0;157,-1; 3:1,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0;0,14,10,New York,0,10,0,0,0; :[inactive; startGroup; Cclosed; font = section; ] Animated Graphics ;[s] 2:0,1;18,0;19,-1; 2:1,19,14,New York,1,14,0,0,0;1,19,14,New York,1,14,65535,0,0; :[inactive; font = text; ] You can use sequences of graphics cells in a Notebook as frames in a "movie". To show a movie, you select its sequence of cells (by clicking the bracket that encloses all of them), then type Y. The movie appears in the first graphics cell you have selected, so be sure it is visible in the window before starting the animation. The movie is produced by showing in rapid succession the graphics cells in the selected sequence. A click anywhere will stop the animation. ;[s] 3:0,0;191,1;193,0;472,-1; 2:2,14,10,New York,0,10,0,0,0;1,15,12,Chicago,0,12,0,0,0; :[inactive; font = text; ] For information on other controls for viewing Mathematica movies, see the Notebook Read This First! ;[s] 5:0,0;46,1;57,0;84,2;100,0;101,-1; 3:3,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0;1,12,10,New York,1,10,0,0,0; :[inactive; font = text; ] This Notebook contains a sample of animation in Mathematica. Due to disk space limitations, this is a very simple two-dimensional example. Look in the "Animations" folder on your disk for other examples of animated graphics. ;[s] 4:0,0;48,1;59,0;226,0;227,-1; 6:3,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0;0,12,10,New York,2,10,0,0,0;0,14,10,New York,0,10,0,0,0;0,12,10,New York,2,10,0,0,0;0,14,10,New York,0,10,0,0,0; :[inactive; font = text; ] This animation shows how the curve of a Bessel function changes with the order of the Bessel function. (The movie looks best when run fairly slowly, with the frames shown cyclically.) :[font = input; ] <<Animation.m :[font = input; ] MoviePlot[BesselJ[n, x], {x, 0, 15}, {n, 1, 7, 0.2}, PlotRange->{-0.5, 1.0}] :[inactive; PICT; pictureID = 13084; output; startGroup; Cclosed; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 12426; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 26137; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 12558; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 14240; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 9142; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 22065; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 910; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 19887; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 28709; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 9183; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 20703; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 11535; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 30976; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 9455; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 29084; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 30681; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 31488; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 4847; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 17950; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 18992; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 18147; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 8348; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 24678; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 8016; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 19083; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 15287; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 18030; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 26621; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 1088; output; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; PICT; pictureID = 30762; output; endGroup; endGroup; pictureLeft = 76; pictureWidth = 282; pictureHeight = 171; preserveAspect; font = postscript; ] :[inactive; startGroup; Cclosed; font = section; ] Programming in Mathematica ;[s] 4:0,2;15,1;26,2;27,0;28,-1; 3:1,19,14,New York,1,14,0,0,0;1,17,14,New York,3,14,65535,0,0;2,19,14,New York,1,14,65535,0,0; :[inactive; font = text; ] You can use Mathematica not only as a "calculator", but also as a full symbolic programming language. Many application packages covering specific areas have been or are being written in the Mathematica language. ;[s] 6:0,1;0,2;12,1;23,0;191,1;202,0;213,-1; 3:2,14,10,New York,0,10,0,0,0;3,12,10,New York,2,10,0,0,0;1,14,10,New York,0,10,0,0,0; :[inactive; startGroup; Cclosed; font = subsubsection; ] A Graphics Application Package :[font = input; ] <<Polyhedra.m :[inactive; font = text; ] This loads in a package that defines properties of polyhedra. The package defines, among other things, the geometry of a dodecahedron. :[startGroup; font = input; ] Dodecahedron[ ] // Short :[inactive; output; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] {Polygon[<<1>>], <<10>>, Polygon[{<<5>>}]} :[inactive; font = text; ] The Dodecahedron function gives the coordinates for the faces of a dodecahedron, shown here in shortened form. ;[s] 5:0,0;4,3;16,1;17,2;110,0;111,-1; 4:2,14,10,New York,0,10,0,0,0;1,11,9,Courier,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;1,12,10,New York,1,10,0,0,0; :[startGroup; font = input; ] Show[Graphics3D[ % ]] :[inactive; PostScript; output; pictureLeft = 50; pictureWidth = 282; pictureHeight = 277; preserveAspect; font = postscript; ] %! %%Creator: Mathematica Mpstart % Start of picture % Scaling calculations [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] Mscale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 moveto 1 0 lineto 1 1 lineto 0 1 lineto closepath clip newpath %%Object: Graphics3D gsave 0.002 setlinewidth 0.11508 0.25083 moveto 0.41985 0.55718 lineto stroke 0.11508 0.25083 moveto 0.04222 0.71406 lineto stroke 0.40493 0.97619 moveto 0.04222 0.71406 lineto stroke 0.40493 0.97619 moveto 0.41985 0.55718 lineto stroke 0.6624 0.02381 moveto 0.89738 0.40279 lineto stroke 0.6624 0.02381 moveto 0.69098 0.5095 lineto stroke 0.95778 0.84601 moveto 0.69098 0.5095 lineto stroke 0.95778 0.84601 moveto 0.89738 0.40279 lineto stroke 0.11508 0.25083 moveto 0.04222 0.71406 lineto stroke 0.11508 0.25083 moveto 0.6624 0.02381 lineto stroke 0.69098 0.5095 moveto 0.6624 0.02381 lineto stroke 0.69098 0.5095 moveto 0.04222 0.71406 lineto stroke 0.41985 0.55718 moveto 0.40493 0.97619 lineto stroke 0.41985 0.55718 moveto 0.89738 0.40279 lineto stroke 0.95778 0.84601 moveto 0.89738 0.40279 lineto stroke 0.95778 0.84601 moveto 0.40493 0.97619 lineto stroke 0.11508 0.25083 moveto 0.6624 0.02381 lineto stroke 0.11508 0.25083 moveto 0.41985 0.55718 lineto stroke 0.89738 0.40279 moveto 0.41985 0.55718 lineto stroke 0.89738 0.40279 moveto 0.6624 0.02381 lineto stroke 0.04222 0.71406 moveto 0.69098 0.5095 lineto stroke 0.04222 0.71406 moveto 0.40493 0.97619 lineto stroke 0.95778 0.84601 moveto 0.40493 0.97619 lineto stroke 0.95778 0.84601 moveto 0.69098 0.5095 lineto stroke grestore 0.685 0.624 0.781 setrgbcolor 0.54151 0.2477 moveto 0.47183 0.48399 lineto 0.66023 0.49041 lineto fill 0.685 0.624 0.781 setrgbcolor 0.54151 0.2477 moveto 0.39145 0.34124 lineto 0.47183 0.48399 lineto fill 0.693 0.541 0.675 setrgbcolor 0.47183 0.48399 moveto 0.70821 0.66865 lineto 0.66023 0.49041 lineto fill 0.693 0.541 0.675 setrgbcolor 0.47183 0.48399 moveto 0.53946 0.77362 lineto 0.70821 0.66865 lineto fill 0.693 0.541 0.675 setrgbcolor 0.47183 0.48399 moveto 0.39493 0.65364 lineto 0.53946 0.77362 lineto fill 0.792 0.661 0.718 setrgbcolor 0.24908 0.42461 moveto 0.47183 0.48399 lineto 0.39145 0.34124 lineto fill 0.792 0.661 0.718 setrgbcolor 0.24908 0.42461 moveto 0.39493 0.65364 lineto 0.47183 0.48399 lineto fill 0.508 0.426 0.699 setrgbcolor 0.66023 0.49041 moveto 0.81008 0.44139 lineto 0.71505 0.34865 lineto fill 0.508 0.426 0.699 setrgbcolor 0.66023 0.49041 moveto 0.80338 0.65602 lineto 0.81008 0.44139 lineto fill 0.508 0.426 0.699 setrgbcolor 0.66023 0.49041 moveto 0.70821 0.66865 lineto 0.80338 0.65602 lineto fill 0 0 0 setrgbcolor 0.002 setlinewidth 0.66023 0.49041 moveto 0.70821 0.66865 lineto stroke 0.685 0.624 0.781 setrgbcolor 0.54151 0.2477 moveto 0.66023 0.49041 lineto 0.71505 0.34865 lineto fill 0 0 0 setrgbcolor 0.66023 0.49041 moveto 0.70773 0.36757 lineto stroke 0 0 0 setrgbcolor 0.47183 0.48399 moveto 0.66023 0.49041 lineto stroke 0.792 0.49 0.479 setrgbcolor 0.25435 0.63046 moveto 0.53946 0.77362 lineto 0.39493 0.65364 lineto fill 0.792 0.661 0.718 setrgbcolor 0.24908 0.42461 moveto 0.25435 0.63046 lineto 0.39493 0.65364 lineto fill 0 0 0 setrgbcolor 0.39145 0.34124 moveto 0.47183 0.48399 lineto stroke 0 0 0 setrgbcolor 0.39493 0.65364 moveto 0.47183 0.48399 lineto stroke 0.396 0.056 0.267 setrgbcolor 0.53946 0.77362 moveto 0.80338 0.65602 lineto 0.70821 0.66865 lineto fill 0.396 0.056 0.267 setrgbcolor 0.53946 0.77362 moveto 0.67629 0.76911 lineto 0.80338 0.65602 lineto fill 0.396 0.056 0.267 setrgbcolor 0.53946 0.77362 moveto 0.50394 0.84276 lineto 0.67629 0.76911 lineto fill 0 0 0 setrgbcolor 0.53946 0.77362 moveto 0.70821 0.66865 lineto stroke 0.792 0.49 0.479 setrgbcolor 0.25435 0.63046 moveto 0.50394 0.84276 lineto 0.53946 0.77362 lineto fill 0 0 0 setrgbcolor 0.39493 0.65364 moveto 0.53946 0.77362 lineto stroke 0.469 0.871 0.704 setrgbcolor 0.50404 0.26518 moveto 0.39145 0.34124 lineto 0.54151 0.2477 lineto fill 0.469 0.871 0.704 setrgbcolor 0.50404 0.26518 moveto 0.24908 0.42461 lineto 0.39145 0.34124 lineto fill 0 0 0 setrgbcolor 0.30561 0.39151 moveto 0.39145 0.34124 lineto stroke 0 0 0 setrgbcolor 0.39145 0.34124 moveto 0.50839 0.26835 lineto stroke 0.786 0.33 0.159 setrgbcolor 0.54151 0.2477 moveto 0.71505 0.34865 lineto 0.81008 0.44139 lineto fill 0.792 0.49 0.479 setrgbcolor 0.25435 0.63046 moveto 0.31169 0.74873 lineto 0.50394 0.84276 lineto fill 0 0 0 setrgbcolor 0.28997 0.63633 moveto 0.39493 0.65364 lineto stroke 0.324 0.286 0.66 setrgbcolor 0.24908 0.42461 moveto 0.31169 0.74873 lineto 0.25435 0.63046 lineto fill 0.786 0.33 0.159 setrgbcolor 0.54151 0.2477 moveto 0.6831 0.39597 lineto 0.50404 0.26518 lineto fill 0.786 0.33 0.159 setrgbcolor 0.54151 0.2477 moveto 0.81008 0.44139 lineto 0.6831 0.39597 lineto fill 0 0 0 setrgbcolor 0.54151 0.2477 moveto 0.71505 0.34865 lineto stroke 0 0 0 setrgbcolor 0.71505 0.34865 moveto 0.81008 0.44139 lineto stroke 0.324 0.286 0.66 setrgbcolor 0.24908 0.42461 moveto 0.34862 0.60088 lineto 0.31169 0.74873 lineto fill 0 0 0 setrgbcolor 0.25435 0.63046 moveto 0.31169 0.74873 lineto stroke 0.469 0.871 0.704 setrgbcolor 0.50404 0.26518 moveto 0.30446 0.38588 lineto 0.24908 0.42461 lineto fill 0.324 0.286 0.66 setrgbcolor 0.24908 0.42461 moveto 0.30446 0.38588 lineto 0.34862 0.60088 lineto fill 0 0 0 setrgbcolor 0.24908 0.42461 moveto 0.30446 0.38588 lineto stroke 0 0 0 setrgbcolor 0.24908 0.42461 moveto 0.25435 0.63046 lineto stroke 0 0 0 setrgbcolor 0.50404 0.26518 moveto 0.54151 0.2477 lineto stroke 0.824 0.693 0.719 setrgbcolor 0.59066 0.61149 moveto 0.80338 0.65602 lineto 0.67629 0.76911 lineto fill 0.824 0.693 0.719 setrgbcolor 0.59066 0.61149 moveto 0.81008 0.44139 lineto 0.80338 0.65602 lineto fill 0 0 0 setrgbcolor 0.67629 0.76911 moveto 0.80338 0.65602 lineto stroke 0.675 0.639 0.806 setrgbcolor 0.31169 0.74873 moveto 0.67629 0.76911 lineto 0.50394 0.84276 lineto fill 0.824 0.693 0.719 setrgbcolor 0.59066 0.61149 moveto 0.6831 0.39597 lineto 0.81008 0.44139 lineto fill 0 0 0 setrgbcolor 0.6831 0.39597 moveto 0.81008 0.44139 lineto stroke 0 0 0 setrgbcolor 0.80338 0.65602 moveto 0.81008 0.44139 lineto stroke 0.675 0.639 0.806 setrgbcolor 0.31169 0.74873 moveto 0.59066 0.61149 lineto 0.67629 0.76911 lineto fill 0 0 0 setrgbcolor 0.50394 0.84276 moveto 0.67629 0.76911 lineto stroke 0.675 0.639 0.806 setrgbcolor 0.31169 0.74873 moveto 0.34862 0.60088 lineto 0.59066 0.61149 lineto fill 0 0 0 setrgbcolor 0.31169 0.74873 moveto 0.34862 0.60088 lineto stroke 0 0 0 setrgbcolor 0.31169 0.74873 moveto 0.50394 0.84276 lineto stroke 0 0 0 setrgbcolor 0.59066 0.61149 moveto 0.67629 0.76911 lineto stroke 0.689 0.531 0.667 setrgbcolor 0.30446 0.38588 moveto 0.50404 0.26518 lineto 0.6831 0.39597 lineto fill 0.689 0.531 0.667 setrgbcolor 0.30446 0.38588 moveto 0.59066 0.61149 lineto 0.34862 0.60088 lineto fill 0.689 0.531 0.667 setrgbcolor 0.30446 0.38588 moveto 0.6831 0.39597 lineto 0.59066 0.61149 lineto fill 0 0 0 setrgbcolor 0.6831 0.39597 moveto 0.59066 0.61149 lineto stroke 0 0 0 setrgbcolor 0.30446 0.38588 moveto 0.50404 0.26518 lineto stroke 0 0 0 setrgbcolor 0.50404 0.26518 moveto 0.6831 0.39597 lineto stroke 0 0 0 setrgbcolor 0.30446 0.38588 moveto 0.34862 0.60088 lineto stroke 0 0 0 setrgbcolor 0.34862 0.60088 moveto 0.59066 0.61149 lineto stroke 0 setgray 0.6624 0.02381 moveto 0.89738 0.40279 lineto stroke 0.6624 0.02381 moveto 0.69098 0.5095 lineto stroke 0.95778 0.84601 moveto 0.69098 0.5095 lineto stroke 0.95778 0.84601 moveto 0.89738 0.40279 lineto stroke 0.11508 0.25083 moveto 0.04222 0.71406 lineto stroke 0.11508 0.25083 moveto 0.6624 0.02381 lineto stroke 0.69098 0.5095 moveto 0.6624 0.02381 lineto stroke 0.69098 0.5095 moveto 0.04222 0.71406 lineto stroke 0.04222 0.71406 moveto 0.69098 0.5095 lineto stroke 0.04222 0.71406 moveto 0.40493 0.97619 lineto stroke 0.95778 0.84601 moveto 0.40493 0.97619 lineto stroke 0.95778 0.84601 moveto 0.69098 0.5095 lineto stroke % End of Graphics Mpend % End of picture :[inactive; output; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics3D- :[inactive; font = text; ] This shows the dodecahedron as a three-dimensional graphical object. As another example, we can use the definitions from the polyhedra package to create an image of a stellated icosahedron, which is often used as an icon for the Mathematica system. ;[s] 3:0,0;230,1;241,0;250,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] Show[ Graphics3D[ Stellate[ Icosahedron[ ] ] ] ] :[inactive; PostScript; output; pictureLeft = 50; pictureWidth = 282; pictureHeight = 277; preserveAspect; font = postscript; ] %! %%Creator: Mathematica Mpstart % Start of picture % Scaling calculations [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] Mscale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 moveto 1 0 lineto 1 1 lineto 0 1 lineto closepath clip newpath %%Object: Graphics3D gsave 0.002 setlinewidth 0.1653 0.21413 moveto 0.44669 0.50914 lineto stroke 0.1653 0.21413 moveto 0.09299 0.72825 lineto stroke 0.43422 0.97619 moveto 0.09299 0.72825 lineto stroke 0.43422 0.97619 moveto 0.44669 0.50914 lineto stroke 0.62173 0.02381 moveto 0.84794 0.37696 lineto stroke 0.62173 0.02381 moveto 0.6444 0.55961 lineto stroke 0.90701 0.86706 moveto 0.6444 0.55961 lineto stroke 0.90701 0.86706 moveto 0.84794 0.37696 lineto stroke 0.1653 0.21413 moveto 0.09299 0.72825 lineto stroke 0.1653 0.21413 moveto 0.62173 0.02381 lineto stroke 0.6444 0.55961 moveto 0.62173 0.02381 lineto stroke 0.6444 0.55961 moveto 0.09299 0.72825 lineto stroke 0.44669 0.50914 moveto 0.43422 0.97619 lineto stroke 0.44669 0.50914 moveto 0.84794 0.37696 lineto stroke 0.90701 0.86706 moveto 0.84794 0.37696 lineto stroke 0.90701 0.86706 moveto 0.43422 0.97619 lineto stroke 0.1653 0.21413 moveto 0.62173 0.02381 lineto stroke 0.1653 0.21413 moveto 0.44669 0.50914 lineto stroke 0.84794 0.37696 moveto 0.44669 0.50914 lineto stroke 0.84794 0.37696 moveto 0.62173 0.02381 lineto stroke 0.09299 0.72825 moveto 0.6444 0.55961 lineto stroke 0.09299 0.72825 moveto 0.43422 0.97619 lineto stroke 0.90701 0.86706 moveto 0.43422 0.97619 lineto stroke 0.90701 0.86706 moveto 0.6444 0.55961 lineto stroke grestore 0.511 0.781 0.993 setrgbcolor 0.54969 0.46553 moveto 0.6316 0.44942 lineto 0.44809 0.43703 lineto fill 0.508 0.342 0.591 setrgbcolor 0.54969 0.46553 moveto 0.53186 0.59662 lineto 0.6316 0.44942 lineto fill 0 0 0 setrgbcolor 0.002 setlinewidth 0.54969 0.46553 moveto 0.6316 0.44942 lineto stroke 0.82 0.629 0.644 setrgbcolor 0.54969 0.46553 moveto 0.44809 0.43703 lineto 0.53186 0.59662 lineto fill 0 0 0 setrgbcolor 0.44809 0.43703 moveto 0.54969 0.46553 lineto stroke 0 0 0 setrgbcolor 0.53186 0.59662 moveto 0.54969 0.46553 lineto stroke 0.645 0.565 0.75 setrgbcolor 0.38737 0.55534 moveto 0.53186 0.59662 lineto 0.44809 0.43703 lineto fill 0 0 0 setrgbcolor 0.44809 0.43703 moveto 0.53186 0.59662 lineto stroke 0.681 0.3 0.318 setrgbcolor 0.38737 0.55534 moveto 0.36945 0.59512 lineto 0.53186 0.59662 lineto fill 0 0 0 setrgbcolor 0.38901 0.55581 moveto 0.53186 0.59662 lineto stroke 0 0 0 setrgbcolor 0.38737 0.55534 moveto 0.44809 0.43703 lineto 0.36945 0.59512 lineto fill 0.603 0.217 0.284 setrgbcolor 0.69272 0.5776 moveto 0.53186 0.59662 lineto 0.67618 0.61803 lineto fill 0.735 0.641 0.754 setrgbcolor 0.69272 0.5776 moveto 0.6316 0.44942 lineto 0.53186 0.59662 lineto fill 0 0 0 setrgbcolor 0.53186 0.59662 moveto 0.6316 0.44942 lineto stroke 0 0 0 setrgbcolor 0.53186 0.59662 moveto 0.66631 0.58072 lineto stroke 0.966 0.676 0.429 setrgbcolor 0.69272 0.5776 moveto 0.67618 0.61803 lineto 0.6316 0.44942 lineto fill 0.619 0.535 0.737 setrgbcolor 0.61878 0.74666 moveto 0.67618 0.61803 lineto 0.53186 0.59662 lineto fill 0 0 0 setrgbcolor 0.53186 0.59662 moveto 0.67618 0.61803 lineto stroke 0.825 0.599 0.596 setrgbcolor 0.61878 0.74666 moveto 0.53186 0.59662 lineto 0.51025 0.71306 lineto fill 0 0 0 setrgbcolor 0.53186 0.59662 moveto 0.57713 0.67476 lineto stroke 0.487 0.278 0.521 setrgbcolor 0.42366 0.73096 moveto 0.51025 0.71306 lineto 0.53186 0.59662 lineto fill 0 0 0 setrgbcolor 0.51025 0.71306 moveto 0.53186 0.59662 lineto stroke 0.755 0.65 0.744 setrgbcolor 0.42366 0.73096 moveto 0.53186 0.59662 lineto 0.36945 0.59512 lineto fill 0 0 0 setrgbcolor 0.46716 0.67696 moveto 0.53186 0.59662 lineto stroke 0 0 0 setrgbcolor 0.36945 0.59512 moveto 0.53186 0.59662 lineto stroke 0.554 0.544 0.797 setrgbcolor 0.42366 0.73096 moveto 0.36945 0.59512 lineto 0.51025 0.71306 lineto fill 0 0 0 setrgbcolor 0.37563 0.61059 moveto 0.42366 0.73096 lineto stroke 0.7 0.554 0.685 setrgbcolor 0.55236 0.30182 moveto 0.44809 0.43703 lineto 0.6316 0.44942 lineto fill 0 0 0 setrgbcolor 0.44809 0.43703 moveto 0.6316 0.44942 lineto stroke 0 0 0 setrgbcolor 0.55236 0.30182 moveto 0.53463 0.34181 lineto 0.44809 0.43703 lineto fill 0 0 0 setrgbcolor 0.52436 0.33813 moveto 0.55236 0.30182 lineto stroke 0.919 0.594 0.41 setrgbcolor 0.55236 0.30182 moveto 0.6316 0.44942 lineto 0.53463 0.34181 lineto fill 0 0 0 setrgbcolor 0.55236 0.30182 moveto 0.56994 0.33457 lineto stroke 0 0 0 setrgbcolor 0.53463 0.34181 moveto 0.55236 0.30182 lineto stroke 0.772 0.717 0.8 setrgbcolor 0.61878 0.74666 moveto 0.51025 0.71306 lineto 0.67618 0.61803 lineto fill 0 0 0 setrgbcolor 0.61878 0.74666 moveto 0.67261 0.62602 lineto stroke 0.632 0.579 0.777 setrgbcolor 0.37702 0.28534 moveto 0.44809 0.43703 lineto 0.53463 0.34181 lineto fill 0 0 0 setrgbcolor 0.44809 0.43703 moveto 0.48257 0.39909 lineto stroke 0.866 0.673 0.639 setrgbcolor 0.37702 0.28534 moveto 0.36225 0.4352 lineto 0.44809 0.43703 lineto fill 0 0 0 setrgbcolor 0.43003 0.39848 moveto 0.44809 0.43703 lineto stroke 0.343 0.807 0.927 setrgbcolor 0.27283 0.45254 moveto 0.44809 0.43703 lineto 0.36225 0.4352 lineto fill 0.716 0.559 0.674 setrgbcolor 0.27283 0.45254 moveto 0.36945 0.59512 lineto 0.44809 0.43703 lineto fill 0 0 0 setrgbcolor 0.36945 0.59512 moveto 0.44809 0.43703 lineto stroke 0 0 0 setrgbcolor 0.36267 0.44459 moveto 0.44809 0.43703 lineto stroke 0.359 0.21 0.538 setrgbcolor 0.71062 0.30574 moveto 0.6316 0.44942 lineto 0.68599 0.45713 lineto fill 0.737 0.665 0.779 setrgbcolor 0.71062 0.30574 moveto 0.53463 0.34181 lineto 0.6316 0.44942 lineto fill 0 0 0 setrgbcolor 0.56752 0.37831 moveto 0.6316 0.44942 lineto stroke 0 0 0 setrgbcolor 0.6316 0.44942 moveto 0.64467 0.42565 lineto stroke 0 0.535 0.818 setrgbcolor 0.80123 0.48887 moveto 0.68599 0.45713 lineto 0.6316 0.44942 lineto fill 0.683 0.529 0.671 setrgbcolor 0.80123 0.48887 moveto 0.6316 0.44942 lineto 0.67618 0.61803 lineto fill 0 0 0 setrgbcolor 0.6316 0.44942 moveto 0.6857 0.462 lineto stroke 0 0 0 setrgbcolor 0.6316 0.44942 moveto 0.67618 0.61803 lineto stroke 0.549 0.506 0.76 setrgbcolor 0.27283 0.45254 moveto 0.36225 0.4352 lineto 0.36945 0.59512 lineto fill 0 0 0 setrgbcolor 0.27283 0.45254 moveto 0.36225 0.4352 lineto stroke 0 0 0 setrgbcolor 0.27283 0.45254 moveto 0.3019 0.49543 lineto stroke 0.711 0.537 0.651 setrgbcolor 0.32953 0.75661 moveto 0.51025 0.71306 lineto 0.36945 0.59512 lineto fill 0 0 0 setrgbcolor 0.39861 0.61954 moveto 0.40275 0.62301 lineto stroke 0.178 0.029 0.429 setrgbcolor 0.32953 0.75661 moveto 0.36945 0.59512 lineto 0.39984 0.61712 lineto fill 0 0 0 setrgbcolor 0.32953 0.75661 moveto 0.36625 0.60806 lineto stroke 0.482 0 0 setrgbcolor 0.22676 0.57042 moveto 0.39984 0.61712 lineto 0.36945 0.59512 lineto fill 0.776 0.684 0.762 setrgbcolor 0.22676 0.57042 moveto 0.36945 0.59512 lineto 0.36225 0.4352 lineto fill 0 0 0 setrgbcolor 0.36348 0.46257 moveto 0.36945 0.59512 lineto stroke 0.785 0.7 0.77 setrgbcolor 0.80123 0.48887 moveto 0.67618 0.61803 lineto 0.68599 0.45713 lineto fill 0 0 0 setrgbcolor 0.7488 0.54303 moveto 0.80123 0.48887 lineto stroke 0 0 0 setrgbcolor 0.68599 0.45713 moveto 0.80123 0.48887 lineto stroke 0.686 0.509 0.64 setrgbcolor 0.37702 0.28534 moveto 0.53463 0.34181 lineto 0.36225 0.4352 lineto fill 0 0 0 setrgbcolor 0.37702 0.28534 moveto 0.42655 0.30309 lineto stroke 0 0 0 setrgbcolor 0.36225 0.4352 moveto 0.37702 0.28534 lineto stroke 0.577 0.519 0.754 setrgbcolor 0.79987 0.61288 moveto 0.68599 0.45713 lineto 0.67618 0.61803 lineto fill 0 0 0 setrgbcolor 0.67618 0.61803 moveto 0.68258 0.51314 lineto stroke 0.689 0.517 0.648 setrgbcolor 0.67574 0.78497 moveto 0.67618 0.61803 lineto 0.51025 0.71306 lineto fill 0.898 0.691 0.612 setrgbcolor 0.67574 0.78497 moveto 0.60713 0.63279 lineto 0.67618 0.61803 lineto fill 0 0 0 setrgbcolor 0.67574 0.78497 moveto 0.67616 0.62566 lineto stroke 0.148 0 0 setrgbcolor 0.79987 0.61288 moveto 0.67618 0.61803 lineto 0.60713 0.63279 lineto fill 0.711 0.532 0.644 setrgbcolor 0.71062 0.30574 moveto 0.68599 0.45713 lineto 0.53463 0.34181 lineto fill 0 0 0 setrgbcolor 0.68599 0.45713 moveto 0.71062 0.30574 lineto stroke 0 0 0 setrgbcolor 0.64654 0.31887 moveto 0.71062 0.30574 lineto stroke 0.618 0.578 0.787 setrgbcolor 0.67574 0.78497 moveto 0.51025 0.71306 lineto 0.60713 0.63279 lineto fill 0 0 0 setrgbcolor 0.53828 0.72523 moveto 0.67574 0.78497 lineto stroke 0 0 0 setrgbcolor 0.60713 0.63279 moveto 0.67574 0.78497 lineto stroke 0.202 0 0.277 setrgbcolor 0.48727 0.79372 moveto 0.60713 0.63279 lineto 0.51025 0.71306 lineto fill 0.741 0.678 0.789 setrgbcolor 0.32953 0.75661 moveto 0.39984 0.61712 lineto 0.51025 0.71306 lineto fill 0 0 0 setrgbcolor 0.32953 0.75661 moveto 0.39984 0.61712 lineto stroke 0 0 0 setrgbcolor 0.32953 0.75661 moveto 0.45404 0.7266 lineto stroke 0.885 0.608 0.512 setrgbcolor 0.48727 0.79372 moveto 0.51025 0.71306 lineto 0.39984 0.61712 lineto fill 0.584 0.552 0.785 setrgbcolor 0.63842 0.2904 moveto 0.53463 0.34181 lineto 0.68599 0.45713 lineto fill 0.399 0.168 0.444 setrgbcolor 0.63842 0.2904 moveto 0.5112 0.44816 lineto 0.53463 0.34181 lineto fill 0 0 0 setrgbcolor 0.53463 0.34181 moveto 0.63842 0.2904 lineto stroke 0.764 0.697 0.788 setrgbcolor 0.41109 0.27661 moveto 0.36225 0.4352 lineto 0.53463 0.34181 lineto fill 0.846 0.599 0.565 setrgbcolor 0.41109 0.27661 moveto 0.53463 0.34181 lineto 0.5112 0.44816 lineto fill 0 0 0 setrgbcolor 0.41109 0.27661 moveto 0.53463 0.34181 lineto stroke 0 0 0 setrgbcolor 0.5112 0.44816 moveto 0.53463 0.34181 lineto stroke 0.605 0.528 0.74 setrgbcolor 0.41109 0.27661 moveto 0.5112 0.44816 lineto 0.36225 0.4352 lineto fill 0 0 0 setrgbcolor 0.41109 0.27661 moveto 0.5112 0.44816 lineto stroke 0 0 0 setrgbcolor 0.36225 0.4352 moveto 0.41109 0.27661 lineto stroke 0.68 0.523 0.666 setrgbcolor 0.22676 0.57042 moveto 0.36225 0.4352 lineto 0.39984 0.61712 lineto fill 0 0 0 setrgbcolor 0.22676 0.57042 moveto 0.3183 0.47907 lineto stroke 0 0 0 setrgbcolor 0.22676 0.57042 moveto 0.39984 0.61712 lineto stroke 0.924 0.674 0.54 setrgbcolor 0.31155 0.46764 moveto 0.39984 0.61712 lineto 0.36225 0.4352 lineto fill 0.492 0.009 0.036 setrgbcolor 0.31155 0.46764 moveto 0.36225 0.4352 lineto 0.5112 0.44816 lineto fill 0 0 0 setrgbcolor 0.31155 0.46764 moveto 0.36225 0.4352 lineto stroke 0 0 0 setrgbcolor 0.36225 0.4352 moveto 0.5112 0.44816 lineto stroke 0.717 0.557 0.671 setrgbcolor 0.79987 0.61288 moveto 0.60713 0.63279 lineto 0.68599 0.45713 lineto fill 0 0 0 setrgbcolor 0.60713 0.63279 moveto 0.79987 0.61288 lineto stroke 0 0 0 setrgbcolor 0.68599 0.45713 moveto 0.79987 0.61288 lineto stroke 0 0 0.211 setrgbcolor 0.69453 0.49418 moveto 0.68599 0.45713 lineto 0.60713 0.63279 lineto fill 0.617 0.142 0.104 setrgbcolor 0.69453 0.49418 moveto 0.5112 0.44816 lineto 0.68599 0.45713 lineto fill 0 0 0 setrgbcolor 0.68599 0.45713 moveto 0.69453 0.49418 lineto stroke 0.761 0.659 0.749 setrgbcolor 0.63842 0.2904 moveto 0.68599 0.45713 lineto 0.5112 0.44816 lineto fill 0 0 0 setrgbcolor 0.63842 0.2904 moveto 0.68599 0.45713 lineto stroke 0 0 0 setrgbcolor 0.5112 0.44816 moveto 0.68599 0.45713 lineto stroke 0 0 0 setrgbcolor 0.5112 0.44816 moveto 0.63842 0.2904 lineto stroke 0.445 0.272 0.55 setrgbcolor 0.4864 0.61131 moveto 0.39984 0.61712 lineto 0.5112 0.44816 lineto fill 0.247 0.723 0.938 setrgbcolor 0.4864 0.61131 moveto 0.60713 0.63279 lineto 0.39984 0.61712 lineto fill 0 0 0 setrgbcolor 0.39984 0.61712 moveto 0.4864 0.61131 lineto stroke 0.739 0.649 0.76 setrgbcolor 0.31155 0.46764 moveto 0.5112 0.44816 lineto 0.39984 0.61712 lineto fill 0 0 0 setrgbcolor 0.31155 0.46764 moveto 0.5112 0.44816 lineto stroke 0 0 0 setrgbcolor 0.39984 0.61712 moveto 0.5112 0.44816 lineto stroke 0 0 0 setrgbcolor 0.31155 0.46764 moveto 0.39984 0.61712 lineto stroke 0.699 0.551 0.682 setrgbcolor 0.48727 0.79372 moveto 0.39984 0.61712 lineto 0.60713 0.63279 lineto fill 0 0 0 setrgbcolor 0.39984 0.61712 moveto 0.48727 0.79372 lineto stroke 0 0 0 setrgbcolor 0.39984 0.61712 moveto 0.60713 0.63279 lineto stroke 0 0 0 setrgbcolor 0.48727 0.79372 moveto 0.60713 0.63279 lineto stroke 0.636 0.563 0.755 setrgbcolor 0.69453 0.49418 moveto 0.60713 0.63279 lineto 0.5112 0.44816 lineto fill 0 0 0 setrgbcolor 0.60713 0.63279 moveto 0.69453 0.49418 lineto stroke 0 0 0 setrgbcolor 0.5112 0.44816 moveto 0.69453 0.49418 lineto stroke 0.839 0.637 0.628 setrgbcolor 0.4864 0.61131 moveto 0.5112 0.44816 lineto 0.60713 0.63279 lineto fill 0 0 0 setrgbcolor 0.4864 0.61131 moveto 0.5112 0.44816 lineto stroke 0 0 0 setrgbcolor 0.5112 0.44816 moveto 0.60713 0.63279 lineto stroke 0 0 0 setrgbcolor 0.60713 0.63279 moveto 0.4864 0.61131 lineto stroke 0 setgray 0.62173 0.02381 moveto 0.84794 0.37696 lineto stroke 0.62173 0.02381 moveto 0.6444 0.55961 lineto stroke 0.90701 0.86706 moveto 0.6444 0.55961 lineto stroke 0.90701 0.86706 moveto 0.84794 0.37696 lineto stroke 0.1653 0.21413 moveto 0.09299 0.72825 lineto stroke 0.1653 0.21413 moveto 0.62173 0.02381 lineto stroke 0.6444 0.55961 moveto 0.62173 0.02381 lineto stroke 0.6444 0.55961 moveto 0.09299 0.72825 lineto stroke 0.09299 0.72825 moveto 0.6444 0.55961 lineto stroke 0.09299 0.72825 moveto 0.43422 0.97619 lineto stroke 0.90701 0.86706 moveto 0.43422 0.97619 lineto stroke 0.90701 0.86706 moveto 0.6444 0.55961 lineto stroke % End of Graphics Mpend % End of picture :[inactive; output; endGroup; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics3D- :[inactive; startGroup; Cclosed; font = subsubsection; ] More on Programming :[inactive; font = text; ] There are several styles of programming in Mathematica. One of them is procedural programming, as you would find in a standard structured programming language such as C or Pascal. Another is "rule-based programming". The idea is to give transformation rules which specify how Mathematica should transform expressions it receives as input. You can give rules that mimic the formulas you might find in a mathematics textbook. Here is an example of how you might teach Mathematica about a new form of logarithm function, called nlog. ;[s] 9:0,0;43,1;54,0;279,1;290,0;472,1;483,0;531,2;535,0;537,-1; 4:5,14,10,New York,0,10,0,0,0;3,12,10,New York,2,10,0,0,0;1,11,9,Courier,0,10,0,0,0;0,11,9,Courier,1,10,0,0,0; :[startGroup; font = input; ] nlog[a b c d^2] :[inactive; output; endGroup; font = output; ] nlog[a*b*c*d^2] ;[o] 2 nlog[a b c d ] :[inactive; font = text; ] Mathematica initially knows nothing about our new function, so it does nothing to expressions involving nlogs. ;[s] 2:0,1;11,0;111,-1; 2:1,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[font = input; ] nlog[x_ y_] := nlog[x] + nlog[y] :[inactive; font = text; ] This tells Mathematica how to expand out logarithms of products. ;[s] 3:0,0;11,1;22,0;65,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] nlog[a b c d^2] :[inactive; output; endGroup; font = output; ] nlog[a] + nlog[b] + nlog[c] + nlog[d^2] ;[o] 2 nlog[a] + nlog[b] + nlog[c] + nlog[d ] :[inactive; font = text; ] Now Mathematica can expand the nlog out. ;[s] 5:0,0;4,1;15,0;31,2;35,0;42,-1; 3:3,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0;1,11,9,Courier,0,10,0,0,0; :[font = input; ] nlog[x_^n_] := n nlog[x] :[inactive; font = text; ] This gives a rule for nlog of a power. ;[s] 3:0,0;22,1;26,0;39,-1; 2:2,14,10,New York,0,10,0,0,0;1,11,9,Courier,0,10,0,0,0; :[startGroup; font = input; ] nlog[a b c d^2] :[inactive; output; endGroup; font = output; ] nlog[a] + nlog[b] + nlog[c] + 2*nlog[d] ;[o] nlog[a] + nlog[b] + nlog[c] + 2 nlog[d] :[inactive; endGroup; endGroup; font = text; ] Now Mathematica can expand the expression out completely. ;[s] 3:0,0;4,1;15,0;58,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[inactive; startGroup; Cclosed; font = section; ] Mathematica's User Interface ;[s] 3:0,1;11,2;28,0;29,-1; 3:1,19,14,New York,1,14,0,0,0;1,17,14,New York,3,14,65535,0,0;1,19,14,New York,1,14,65535,0,0; :[inactive; font = text; ] Mathematica consists of two parts — the "kernel", which actually does computations, and the "front end", which deals with interaction with the user. The kernel of Mathematica is essentially the same on all computers that support Mathematica. The front end, on the other hand, works differently on different kinds of computer. On the Macintosh, Mathematica has a sophisticated front end that takes advantage of the Macintosh's unique user interface capabilities. (You can actually use the Macintosh front end even if you are using a "remote kernel", say on a supercomputer connected through a network.) ;[s] 8:0,1;11,0;164,1;175,0;230,1;241,0;348,1;359,0;607,-1; 3:4,14,10,New York,0,10,0,0,0;4,12,10,New York,2,10,0,0,0;0,14,10,New York,0,10,0,0,0; :[inactive; startGroup; Cclosed; font = subsubsection; ] Notebooks :[inactive; font = text; ] One of the most important aspects of the Macintosh front end is its ability to support Mathematica "Notebooks". This file is an example of a Notebook. Notebooks consist of a mixture of text, graphics, and Mathematica input. Notebooks can be used like "interactive textbooks" — you read the text in the Notebook, then use the Mathematica input in the Notebook to perform calculations. ;[s] 7:0,0;87,1;98,0;209,1;220,0;330,1;341,0;389,-1; 4:4,14,10,New York,0,10,0,0,0;3,12,10,New York,2,10,0,0,0;0,11,9,Helvetica,1,10,0,0,0;0,12,10,Geneva,1,10,0,0,0; :[inactive; font = text; ] Here is a sample Mathematica Notebook called Point Plots and Space Curves. ;[s] 5:0,0;17,1;28,0;45,2;73,0;77,-1; 3:3,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0;1,12,10,New York,4,10,0,0,0; :[inactive; startGroup; Cclosed; font = title; ] Point Plots and Space Curves by Theodore W. Gray ;[s] 4:0,1;28,0;29,2;48,0;49,-1; 4:2,23,17,New York,1,18,0,0,0;1,17,14,New York,1,14,0,0,0;1,15,12,New York,2,12,0,0,0;0,12,10,New York,1,10,0,0,0; :[inactive; font = text; ] This Notebook defines the functions PointPlot, PointPlot3D, PointParamPlot3D, SpaceCurve, and PointSpaceCurve. These functions let you make discrete point plots in two and three dimensions. The SpaceCurve and PointSpaceCurve functions let you make three-dimensional functions of one parameter (lines or points in 3D). (Note: This demonstration copy does not include the actual definitions of the functions, only examples of their use.) ;[s] 7:0,0;65,1;70,0;216,2;231,0;327,3;332,0;444,-1; 4:4,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;1,12,10,New York,1,10,65535,0,0; :[inactive; startGroup; Cclosed; font = section; ] Examples :[inactive; font = text; ] Each of the functions defined in this Notebook is a variation of either Plot, Plot3D, or ParametricPlot3D. The arguments are quite similar to these standard functions. Following are descriptions of each of the functions. :[inactive; startGroup; Cclosed; font = subsection; ] PointPlot :[inactive; font = text; ] PointPlot[ f, {x, min, max, (step)}] produces a plot of f(x) vs. x. Here is an example: ;[s] 3:0,0;66,1;69,0;94,-1; 2:2,14,10,New York,0,10,0,0,0;1,12,10,New York,2,10,0,0,0; :[startGroup; font = input; ] PointPlot[Sin[x], {x, 0, 2 Pi, 0.2}] :[inactive; PICT; pictureID = 20909; output; pictureLeft = 67; pictureWidth = 243; pictureHeight = 147; preserveAspect; font = postscript; ] :[inactive; output; endGroup; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[inactive; startGroup; Cclosed; font = subsection; ] PointPlot3D :[inactive; font = text; ] PointPlot3D[ f, {x, min, max, (step)}, {y, min, max, (step)}] produces a plot of f(x, y), plotted with points instead of surfaces. ;[s] 5:0,0;42,1;65,0;93,3;135,0;136,-1; 6:3,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0; :[startGroup; font = input; ] PointPlot3D[x y, {x, -4, 4, 0.5}, {y, -4, 4, 0.5}, BoxRatios->{1,1,1}] ;[s] 3:0,0;32,1;73,0;75,-1; 2:2,14,10,Courier,1,12,0,0,65535;1,14,10,Courier,1,12,0,0,65535; :[inactive; PICT; pictureID = 12547; output; pictureLeft = 107; pictureWidth = 202; pictureHeight = 198; preserveAspect; font = postscript; ] :[inactive; output; endGroup; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics3D- :[inactive; startGroup; Cclosed; font = subsection; ] PointParamPlot3D :[inactive; font = text; ] PointParamPlot3D[{x,y,z}, {u, min, max, (step)}, {v, min, max, (step)}] produces a parametric plot of (x(u,v), y(u,v), z(u,v)), plotted with points instead of surfaces. ;[s] 8:0,0;52,1;75,0;116,2;126,3;133,4;172,3;173,0;174,-1; 5:3,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;2,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0; :[startGroup; font = input; ] PointParamPlot3D[{Sin[u] Cos[v], Sin[u] Sin[v], Cos[u]}, {u, 0, Pi, Pi/15}, {v, 0, 2 Pi, Pi/15}, BoxRatios->{1,1,1}] :[inactive; PICT; pictureID = 23646; output; pictureLeft = 113; pictureWidth = 205; pictureHeight = 201; preserveAspect; font = postscript; ] :[inactive; output; endGroup; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics3D- :[inactive; startGroup; Cclosed; font = subsection; ] SpaceCurve :[inactive; font = text; ] SpaceCurve[{x,y,z}, {u, min, max, (step)}] produces a parametric plot of (x(u), y(u), z(u)), with the calculated points connected by straight lines. ;[s] 6:0,0;15,0;46,0;85,2;93,3;153,0;154,-1; 5:4,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0; :[startGroup; font = input; ] SpaceCurve[{u Sin[u], u Cos[u], u}, {u, 0, 15, 0.15}, BoxRatios->{1,1,1}] :[inactive; PICT; pictureID = 32679; output; pictureLeft = 107; pictureWidth = 202; pictureHeight = 198; preserveAspect; font = postscript; ] :[inactive; output; endGroup; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics3D- :[inactive; startGroup; Cclosed; font = subsection; ] PointSpaceCurve :[inactive; font = text; ] PointSpaceCurve[{x,y,z}, {u, min, max, (step)}] produces a parametric plot of (x(u), y(u), z(u)), with the calculated points shown as dots. ;[s] 6:0,0;19,0;50,0;89,2;97,3;143,0;144,-1; 5:4,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;1,14,10,New York,0,10,0,0,0;0,14,10,New York,0,10,0,0,0; :[startGroup; font = input; ] PointSpaceCurve[{u Sin[u], u Cos[u], u^2}, {u, 0, 15, 0.30}, BoxRatios->{1,1,1}] :[inactive; PICT; pictureID = 13244; output; pictureLeft = 114; pictureWidth = 198; pictureHeight = 194; preserveAspect; font = postscript; ] :[inactive; output; endGroup; endGroup; endGroup; endGroup; endGroup; endGroup; endGroup; font = output; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics3D- ^*) 
