draw2d() 編
draw2d() は，関数の分母がゼロになったりしても文句を言わずにグラフを描く。
べき関数
$y = x^{-2}, \ x^{-1}, \ x^2, \ x^3$ のグラフ例。
draw2d(
line_width = 2,
color = 1, key = "x^{-2}",
explicit(x**(-2), x, -5, 5),
color = 2, key = "x^{-1}",
explicit(x**(-1), x, -5, 5),
color = 3, key = "x^{2}",
explicit(x**2, x, -5, 5),
color = 4, key = "x^{3}",
explicit(x**3, x, -5, 5),
xrange = [-5, 5], yrange = [-10, 10],
xtics = 1, ytics = 2.5, xlabel = "x",
xaxis = true, yaxis = true, grid = true
)$
$\displaystyle y = \sqrt{x}, \ \frac{1}{\sqrt{x}}$ のグラフ例。
draw2d(
line_width = 2,
color = 1, key = "x^{1/2}",
explicit(sqrt(x), x, 0, 5),
color = 2, key = "x^{-1/2}",
explicit(1/sqrt(x), x, 0, 5),
xrange = [0, 5], yrange = [0, 5],
xtics = 1, ytics = 1, xlabel = "x",
xaxis = true, yaxis = true, grid = true
)$
指数関数
$y = e^{-x}, \ e^x$ のグラフ例。
draw2d(
line_width = 2,
color = 1, key = "e^{-x}",
explicit(exp(-x), x, -5, 5),
color = 2, key = "e^{x}",
explicit(exp(x), x, -5, 5),
xrange = [-5, 5], yrange = [-1, 30],
xtics = 1, ytics = 5, xlabel = "x",
xaxis = true, yaxis = true, grid = true,
user_preamble = "set key sample 1;"
)$
三角関数
$ y = \sin x, \ \cos x, \ \tan x $ のグラフ例。
draw2d(
line_width = 2,
color = 1, key = "sin x",
explicit(sin(x), x, -2*%pi, 2*%pi+0.3),
color = 2, key = "cos x",
explicit(cos(x), x, -2*%pi, 2*%pi+0.3),
color = 3, key = "tan x",
explicit(tan(x), x, -2*%pi, 2*%pi+0.3),
xrange = [-2*%pi, 2*%pi+0.3], yrange = [-5, 5],
xtics = {["-2π",-2*%pi],["-3π/2",-1.5*%pi],["-π",-%pi],["-π/2",-0.5*%pi],
["0",0],
["2π", 2*%pi],["3π/2", 1.5*%pi],["π", %pi],["π/2", 0.5*%pi]},
ytics = 1,
xaxis = true, yaxis = true, grid = true, xlabel = "x",
user_preamble = "set key sample 1;"
)$
逆三角関数
$y = \sin^{-1} x = \arcsin x =$ asin(x) の定義域は $-1 \leq x \leq 1$
$y = \cos^{-1} x = \arccos x =$ acos(x) の定義域は $-1 \leq x \leq 1$
$y = \tan^{-1} x = \arctan x =$ atan(x) の定義域は $-\infty < x < \infty$
draw2d(
line_width = 2,
color = 1, key = "arcsin x",
explicit(asin(x), x, -1, 1),
color = 2, key = "arccos x",
explicit(acos(x), x, -1, 1),
xrange = [-1, 1], yrange = [-%pi/2, %pi],
xtics = 0.2,
ytics = {["-π/2",-%pi/2], ["-π/4",-%pi/4], ["0",0],
["π/4",%pi/4], ["π/2",%pi/2], ["3π/4", 3*%pi/4], ["π", %pi]},
xaxis = true, yaxis = true, grid = true, xlabel = "x"
)$
draw2d(
line_width = 2,
key = "arctan x",
explicit(atan(x), x, -30, 30),
xrange = [-30, 30], yrange = [-%pi/2, %pi/2],
xtics = 10,
ytics = {["-π/2",-%pi/2], ["-π/4",-%pi/4], ["0", 0],
["π/2", %pi/2], ["π/4", %pi/4]},
xaxis = true, yaxis = true, grid = true, xlabel = "x",
user_preamble = "set key top left;"
)$
双曲線関数
$y = \sinh x, \ \cosh x, \ \tanh x$ のグラフ例。
draw2d(
line_width = 2,
color = 1, key = "sinh x",
explicit(sinh(x), x, -5, 5),
color = 2, key = "cosh x",
explicit(cosh(x), x, -5, 5),
xrange = [-5, 5], yrange = [-50, 50],
xtics = 1, ytics = 20, xlabel = "x",
xaxis = true, yaxis = true, grid = true,
user_preamble = "set key bottom right;"
)$
draw2d(
line_width = 2,
key = "tanh x",
explicit(tanh(x), x, -5, 5),
xrange = [-5, 5], yrange = [-1, 1],
xtics = 1, ytics = 0.2, xlabel = "x",
xaxis = true, yaxis = true, grid = true,
user_preamble = "set key bottom right;"
)$
逆双曲線関数
$ y = \sinh^{-1} x = \mbox{arsinh}\ x = $ asinh(x) の定義域は $ -\infty < x < \infty$
$ y = \cosh^{-1} x = \mbox{arcosh}\ x = $ acosh(x) の定義域は $ 1 \leq x < \infty$
$ y = \tanh^{-1} x = \mbox{artanh}\ x = $ atanh(x) の定義域は $ -1 < x < 1$
draw2d(
line_width = 2,
color = 1, key = "sinh^{-1} x",
explicit(asinh(x), x, -20, 20),
color = 2, key = "cosh^{-1} x",
explicit(acosh(x), x, 1, 20),
xrange = [-20, 20], yrange = [-4, 4],
xtics = 5, ytics = 1,
xaxis = true, yaxis = true, grid = true,
user_preamble = "set key top left;"
)$
draw2d(
line_width = 2,
key = "tanh^{-1} x",
explicit(atanh(x), x, -0.99999, 0.99999),
xrange = [-1.05, 1.05], yrange = [-6, 6],
xtics = 0.25, ytics = 2, xlabel = "x",
xaxis = true, yaxis = true, grid = true,
user_preamble = "set key top left;"
)$
plot2d() 編
plot2d() は，関数の分母がゼロになったりすると文句を言うが，ちゃんとグラフを描いてくれる。
べき関数
$y = x^{-2}, \ x^{-1}, \ x^2, \ x^3$ のグラフ例。
plot2d(
[x**(-2), x**(-1), x**2, x**3], [x, -5, 5],
[style, [lines, 2], [lines, 2], [lines, 2], [lines, 2]],
[legend, "x^{-2}", "x^{-1}", "x^2", "x^3"],
[y, -10, 10], grid2d, [xtics, 1], [ytics, 2.5],
[gnuplot_preamble, "set key sample 1"]
)$
$\displaystyle y = \sqrt{x}, \ \frac{1}{\sqrt{x}}$ のグラフ例。
plot2d(
[sqrt(x), 1/sqrt(x)], [x, 0, 5],
[style, [lines, 2], [lines, 2]],
[legend, "x^{1/2}", "x^{-1/2}"],
[y, 0, 5], grid2d, [xtics, 1], [ytics, 1],
[gnuplot_preamble, "set key sample 1"]
)$
指数関数
$y = e^{-x}, \ e^x$ のグラフ例。
plot2d(
[exp(-x), exp(x)], [x, -5, 5],
[style, [lines, 2], [lines, 2]],
[legend, "e^{-x}", "e^x"],
[y, -1, 30], grid2d, [xtics, 1], [ytics, 5]
)$
三角関数
$ y = \sin x, \ \cos x, \ \tan x $ のグラフ例。
plot2d(
[sin(x), cos(x), tan(x)], [x, -2*%pi, 2*%pi+1],
[style, [lines, 2], [lines, 2], [lines, 2]],
[legend, "sin x", "cos x", "tan x"],
[y, -5, 5], grid2d, [xtics, %pi/2], [ytics, 1],
[gnuplot_preamble, "set format x '%3.1P π';set key sample 1;"]
)$
逆三角関数
$y = \sin^{-1} x = \arcsin x =$ asin(x) の定義域は $-1 \leq x \leq 1$
$y = \cos^{-1} x = \arccos x =$ acos(x) の定義域は $-1 \leq x \leq 1$
$y = \tan^{-1} x = \arctan x =$ atan(x) の定義域は $-\infty < x < \infty$
plot2d(
[asin(x), acos(x)], [x, -1, 1],
[style, [lines, 2], [lines, 2]],
[legend, "arcsin x", "arccos x"],
[y, -%pi/2, %pi], grid2d, [xtics, 0.2], [ytics, %pi/4],
[gnuplot_preamble, "set format y '%4.2P π';"]
)$
plot2d(
atan(x), [x, -30, 30],
[style, [lines, 2]],
[legend, "arctan x"], [ylabel, ""],
[y, -%pi/2, %pi/2], grid2d, [xtics, 10], [ytics, %pi/4],
[gnuplot_preamble, "set format y '%4.2P π';set key top left;"]
)$
双曲線関数
$y = \sinh x, \ \cosh x, \ \tanh x$ のグラフ例。
plot2d(
[sinh(x), cosh(x)], [x, -5, 5],
[style, [lines, 2], [lines, 2]],
[legend, "sinh x", "cosh x"],
[y, -50, 50], grid2d, [xtics, 1], [ytics, 20],
[gnuplot_preamble, "set key bottom right;"]
)$
plot2d(
tanh(x), [x, -5, 5],
[style, [lines, 2]], [ylabel, ""],
[legend, "tanh x"],
[y, -1.1, 1.1], grid2d, [xtics, 1], [ytics, 0.2],
[gnuplot_preamble, "set key bottom right;"]
)$
逆双曲線関数
$ y = \sinh^{-1} x = \mbox{arsinh}\ x = $ asinh(x) の定義域は $-\infty < x < \infty$
$ y = \cosh^{-1} x = \mbox{arcosh}\ x = $ acosh(x) の定義域は $1 \leq x < \infty$
$ y = \tanh^{-1} x = \mbox{artanh}\ x = $ atanh(x) の定義域は $-1 < x < 1$
plot2d(
asinh(x), [x, -20, 20],
[style, [lines, 2]],
[legend, "sinh^{-1} x"], [ylabel, ""],
[y, -4, 4], grid2d, [xtics, 5], [ytics, 1],
[gnuplot_preamble, "set key top left;"]
)$
Maxima の plot2d() では $x$ の範囲の異なるグラフを一緒には描けないようだ。$y = \cosh^{-1} x$ は $ 1 \leq x < \infty$ なので，$y = \sinh^{-1} x$ とは別にグラフにする。
plot2d(
acosh(x), [x, 1, 20],
[style, [lines, 2]],
[legend, "cosh^{-1} x"], [ylabel, ""],
[x, -20, 20], [y, -4, 4], grid2d, [xtics, 5], [ytics, 1],
[gnuplot_preamble, "set key top left;"]
)$
plot2d(
atanh(x), [x, -0.99999, 0.99999],
[style, [lines, 2]],
[legend, "tanh^{-1} x"], [ylabel, ""],
[x, -1.1, 1.1], [y, -6, 6], grid2d, [xtics, 0.2], [ytics, 2],
[gnuplot_preamble, "set key top left;"]
)$
