library(OpenImageR)
maxima.options(engine.format = "latex",
engine.label = TRUE,
inline.format = "inline",
inline.label = FALSE)(%i1) L: sqrt(1 - 1/R^2);\[\mathtt{(\textit{%o}_{1})}\quad \sqrt{1-\frac{1}{R^2}}\]
(%i2) assume(R > 0);\[\mathtt{(\textit{%o}_{2})}\quad \left[ R>0 \right] \]
(%i3) 'integrate(x, x, 0, L) = integrate(x, x, 0, L);\[\mathtt{(\textit{%o}_{3})}\quad \int_{0}^{\sqrt{1-\frac{1}{R^2}}}{x\;dx}=\frac{R^2-1}{2\,R^2}\]
(%i4) 'L = L;\[\mathtt{(\textit{%o}_{4})}\quad L=\sqrt{1-\frac{1}{R^2}}\]
(%i5) 'integrate(x, x, 0, 'L) = integrate(x, x, 0, L);\[\mathtt{(\textit{%o}_{5})}\quad \int_{0}^{L}{x\;dx}=\frac{R^2-1}{2\,R^2}\]
This is an inline test: \(L=\sqrt{1-\frac{1}{R^2}}\) .
(%i7) sqrt(3/4);\[\mathtt{(\textit{%o}_{7})}\quad \frac{\sqrt{3}}{2}\]
(%i8) f(x) := e^(x^2)$
(%i9) diff(f(x), x);\[\mathtt{(\textit{%o}_{9})}\quad 2\,e^{x^2}\,\log e\,x\]
(%i10) %;\[\mathtt{(\textit{%o}_{10})}\quad 2\,e^{x^2}\,\log e\,x\]
(%i11) log(%o1);\[\mathtt{(\textit{%o}_{11})}\quad \frac{\log \left(1-\frac{1}{R^2}\right)}{2}\]
(%i12) r: (exp(cos(t))-2*cos(4*t)-sin(t/12)^5)$
(%i13) plot2d([parametric, r*sin(t), r*cos(t), [t,-8*%pi,8*%pi]]);(%i14) plot3d(log (x^2*y^2), [x, -2, 2], [y, -2, 2],[grid, 29, 29],
[palette, [gradient, red, orange, yellow, green]],
color_bar, [xtics, 1], [ytics, 1], [ztics, 4],
[color_bar_tics, 4]);(%i15) example1:
gr3d (title = "Controlling color range",
enhanced3d = true,
color = green,
cbrange = [-3,10],
explicit(x^2+y^2, x,-2,2,y,-2,2)) $
(%i16) example2:
gr3d (title = "Playing with tics in colorbox",
enhanced3d = true,
color = green,
cbtics = {["High",10],["Medium",05],["Low",0]},
cbrange = [0, 10],
explicit(x^2+y^2, x,-2,2,y,-2,2))$
(%i17) example3:
gr3d (title = "Logarithmic scale to colors",
enhanced3d = true,
color = green,
logcb = true,
logz = true,
palette = [-15,24,-9],
explicit(exp(x^2-y^2), x,-2,2,y,-2,2))$
(%i18) draw(
dimensions = [500,1500],
example1, example2, example3);(%i19) draw2d(
dimensions = [1000, 1000],
proportional_axes = xy,
fill_color = sea_green,
color = aquamarine,
line_width = 6,
ellipse(7,6,2,3,0,360));(%i20) draw3d(
dimensions = [1000, 1000],
surface_hide = true,
axis_3d = false,
proportional_axes = xyz,
color = blue,
cylindrical(z,z,-2,2,a,0,2*%pi),
color = brown,
cylindrical(3,z,-2,2,az,0,%pi),
color = green,
cylindrical(sqrt(25-z^2),z,-5,5,a,0,%pi));pft <- list.files(pattern = "(?:plot|draw)(2d|3d)?-[[:print:]]{6}\\.png", full.names = TRUE)
pref <- system.file("inst/extdata",
c("draw-ref.png",
"draw2d-ref.png",
"draw3d-ref.png",
"plot2d-ref.png",
"plot3d-ref.png"),
package = "rim",
mustWork = TRUE)
r1 <- readImage(pref[1])
r2 <- readImage(pref[2])
r3 <- readImage(pref[3])
r4 <- readImage(pref[4])
p1 <- readImage(pft[1])
p2 <- readImage(pft[2])
p3 <- readImage(pft[3])
p4 <- readImage(pft[4])
p1 <- rgb_2gray(RGB_image = p1)
p2 <- rgb_2gray(RGB_image = p2)
p3 <- rgb_2gray(RGB_image = p3)
p4 <- rgb_2gray(RGB_image = p4)
r1 <- rgb_2gray(RGB_image = r1)
r2 <- rgb_2gray(RGB_image = r2)
r3 <- rgb_2gray(RGB_image = r3)
r4 <- rgb_2gray(RGB_image = r4)
hs1 <- average_hash(p1, hash_size = 32, MODE = "binary")
hs2 <- average_hash(p2, hash_size = 32, MODE = "binary")
hs3 <- average_hash(p3, hash_size = 32, MODE = "binary")
hs4 <- average_hash(p4, hash_size = 32, MODE = "binary")
rs1 <- average_hash(r1, hash_size = 32, MODE = "binary")
rs2 <- average_hash(r2, hash_size = 32, MODE = "binary")
rs3 <- average_hash(r3, hash_size = 32, MODE = "binary")
rs4 <- average_hash(r4, hash_size = 32, MODE = "binary")
if((d <- sum(abs(hs1 - rs1))) < 100) {
paste0("OK")
} else {
paste0("Not OK: ", d)
}## [1] "OK"if((d <- sum(abs(hs2 - rs2))) < 100) {
paste0("OK")
} else {
paste0("Not OK: ", d)
}## [1] "OK"if((d <- sum(abs(hs3 - rs3))) < 100) {
paste0("OK")
} else {
paste0("Not OK: ", d)
}## [1] "OK"if((d <- sum(abs(hs4 - rs4))) < 100) {
paste0("OK")
} else {
paste0("Not OK: ", d)
}## [1] "OK"(%i21) area(dist) := integrate(dist, x, minf, inf)$
(%i22) mean(dist) := area(dist*x)$
(%i23) EX2(dist) := area(dist*x^2)$
(%i24) variance(dist) := EX2(dist) - mean(dist)^2$
(%i25) mgf(dist) := area(dist*%e^(x*t))$(%i26) normal(x) :=
(2*%pi*sigma^2)^(-1/2) *
exp(-(x-mu)^2/(2*sigma^2));\[\mathtt{(\textit{%o}_{26})}\quad \textit{normal}\left(x\right):=\left(2\,\pi\,\sigma^2\right)^{\frac{-1}{2}}\,\exp \left(\frac{-\left(x-\mu\right)^2}{2\,\sigma^2}\right)\]
(%i27) assume(sigma > 0)$
(%i28) area(normal(x));\[\mathtt{(\textit{%o}_{28})}\quad 1\]
(%i29) mean(normal(x));\[\mathtt{(\textit{%o}_{29})}\quad \mu\]
(%i30) variance(normal(x));\[\mathtt{(\textit{%o}_{30})}\quad \frac{2^{\frac{3}{2}}\,\sqrt{\pi}\,\sigma^3+2^{\frac{3}{2}}\,\sqrt{\pi}\,\mu^2\,\sigma}{2^{\frac{3}{2}}\,\sqrt{\pi}\,\sigma}-\mu^2\]
(%i31) mgf(normal(x));\[\mathtt{(\textit{%o}_{31})}\quad e^{\frac{\sigma^2\,t^2+2\,\mu\,t}{2}}\]
(%i32) laplace(x) := (2*b)^-1 * exp(-abs(x - mu)/b);\[\mathtt{(\textit{%o}_{32})}\quad \textit{laplace}\left(x\right):=\left(2\,b\right)^ {- 1 }\,\exp \left(\frac{-\left| x-\mu\right| }{b}\right)\]
(%i33) load("abs_integrate")$
(%i34) assume(b > 0)$
(%i35) area(laplace(x));\[\mathtt{(\textit{%o}_{35})}\quad 1\]
(%i36) mean(laplace(x));\[\mathtt{(\textit{%o}_{36})}\quad \mu\]
(%i37) variance(laplace(x));\[\mathtt{(\textit{%o}_{37})}\quad \frac{2\,b\,\mu^2+4\,b^3}{2\,b}-\mu^2\]
(%i38) expo(x) := unit_step(x) * lambda * exp(-lambda * x);\[\mathtt{(\textit{%o}_{38})}\quad \textit{expo}\left(x\right):=\textit{unit\_step}\left(x\right)\,\lambda\,\exp \left(\left(-\lambda\right)\,x\right)\]
(%i39) assume(lambda > 0)$
(%i40) area(expo(x));\[\mathtt{(\textit{%o}_{40})}\quad 1\]
(%i41) mean(expo(x));\[\mathtt{(\textit{%o}_{41})}\quad \frac{1}{\lambda}\]
(%i42) variance(expo(x));\[\mathtt{(\textit{%o}_{42})}\quad \frac{1}{\lambda^2}\]
(%i43) m: matrix([0, 1, a], [1, 0, 1], [1, 1, 0]);\[\mathtt{(\textit{%o}_{43})}\quad \begin{pmatrix}0 & 1 & a \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix}\]
(%i44) transpose(m);\[\mathtt{(\textit{%o}_{44})}\quad \begin{pmatrix}0 & 1 & 1 \\ 1 & 0 & 1 \\ a & 1 & 0 \\ \end{pmatrix}\]
(%i45) determinant(m);\[\mathtt{(\textit{%o}_{45})}\quad a+1\]
(%i46) f: invert(m), detout;\[\mathtt{(\textit{%o}_{46})}\quad \frac{\begin{pmatrix}-1 & a & 1 \\ 1 & -a & a \\ 1 & 1 & -1 \\ \end{pmatrix}}{a+1}\]
(%i47) m . f;\[\mathtt{(\textit{%o}_{47})}\quad \begin{pmatrix}0 & 1 & a \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix}\cdot \left(\frac{\begin{pmatrix}-1 & a & 1 \\ 1 & -a & a \\ 1 & 1 & -1 \\ \end{pmatrix}}{a+1}\right)\]
(%i48) expand(%);\[\mathtt{(\textit{%o}_{48})}\quad \begin{pmatrix}\frac{a}{a+1}+\frac{1}{a+1} & 0 & 0 \\ 0 & \frac{a}{a+1}+\frac{1}{a+1} & 0 \\ 0 & 0 & \frac{a}{a+1}+\frac{1}{a+1} \\ \end{pmatrix}\]
(%i49) factor(%);\[\mathtt{(\textit{%o}_{49})}\quad \begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}\]
(%i50) x: 1234;\[\mathtt{(\textit{%o}_{50})}\quad 1234\]
(%i51) y: 2345;\[\mathtt{(\textit{%o}_{51})}\quad 2345\]
(%i52) if x > y
then x
else y;\[\mathtt{(\textit{%o}_{52})}\quad 2345\]