options(width = 80)
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);\[\mathtt{(\textit{%o}_{11})}\quad \frac{\log \left(1-\frac{1}{R^2}\right)}{2}\]
moo## $o11
## ((1L/2L) * log((1L + (-1L * (R^-2L)))))eval(moo[[1]], list(R = 12))## [1] -0.003484335(%i12) /* aa is a variable of interest */ aa : 1234;\[\mathtt{(\textit{%o}_{12})}\quad 1234\]
(%i13) bb : aa^2; /* Value of bb depends on aa */ \[\mathtt{(\textit{%o}_{13})}\quad 1522756\]
(%i14) /* User-defined infix operator */ infix ("Q");\[\mathtt{(\textit{%o}_{14})}\quad \mbox{ Q }\]
(%i15) /* Parses same as a b c, not abc */ a/* foo */Q/* bar */c;\[\mathtt{(\textit{%o}_{15})}\quad \textit{aQc}\]
(%i16) /* Comments /* can be nested /* to any depth */ */ */ 1 + xyz;\[\mathtt{(\textit{%o}_{16})}\quad \textit{xyz}+1\]
(%i17) load(fourier_elim)$
(%i18) fourier_elim([x^2-1>0], [x]);\[\mathtt{(\textit{%o}_{18})}\quad \left[ 1<x \right] \lor \left[ x<-1 \right] \]
# from previous chunk: output.var = "boollist"
boollist## $o18
## (((1L < x)) | ((x < -1L)))eval(boollist[["o18"]], list(x = seq(-10, 10, 0.5)))## [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13] TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [25] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [37] TRUE TRUE TRUE TRUE TRUE(%i19) r: (exp(cos(t))-2*cos(4*t)-sin(t/12)^5)$
(%i20) plot2d([parametric, r*sin(t), r*cos(t), [t,-8*%pi,8*%pi]]);(%i21) 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]);(%i22) example1:
gr3d (title = "Controlling color range",
enhanced3d = true,
color = green,
cbrange = [-3,10],
explicit(x^2+y^2, x,-2,2,y,-2,2)) $
(%i23) 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))$
(%i24) 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))$
(%i25) draw(
dimensions = [500,1500],
example1, example2, example3);(%i26) draw2d(
dimensions = [1000, 1000],
proportional_axes = xy,
fill_color = sea_green,
color = aquamarine,
line_width = 6,
ellipse(7,6,2,3,0,360));(%i27) 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)
if(length(pft) == 5L) {
paste0("OK")
} else {
paste0("Error: Unexpected number of Maxima plots: ",
paste0(pft, collapse = ", "))
}## [1] "OK"if(length(pft)) {
if(all(as.logical(file.size(pft)))) {
paste0("OK")
}
else {
errfiles <- pft[file.size(pft) == 0]
paste0("Error: Maxima plot file(s) ", paste0(errfiles, collapse = ", "),
"are empty.")
}
}## [1] "OK"(%i33) normal(x) :=
(2*%pi*sigma^2)^(-1/2) *
exp(-(x-mu)^2/(2*sigma^2));\[\mathtt{(\textit{%o}_{33})}\quad \textit{normal}\left(x\right):=\left(2\,\pi\,\sigma^2\right)^{\frac{-1}{2}}\,\exp \left(\frac{-\left(x-\mu\right)^2}{2\,\sigma^2}\right)\]
(%i34) assume(sigma > 0)$
(%i35) area(normal(x));\[\mathtt{(\textit{%o}_{35})}\quad 1\]
(%i36) mean(normal(x));\[\mathtt{(\textit{%o}_{36})}\quad \mu\]
(%i37) variance(normal(x));\[\mathtt{(\textit{%o}_{37})}\quad \frac{2^{\frac{3}{2}}\,\sqrt{\pi}\,\sigma^3+2^{\frac{3}{2}}\,\sqrt{\pi}\,\mu^2\,\sigma}{2^{\frac{3}{2}}\,\sqrt{\pi}\,\sigma}-\mu^2\]
(%i38) mgf(normal(x));\[\mathtt{(\textit{%o}_{38})}\quad e^{\frac{\sigma^2\,t^2+2\,\mu\,t}{2}}\]
(%i39) m: matrix([0, 1, a], [1, 0, 1], [1, 1, 0]);\[\mathtt{(\textit{%o}_{39})}\quad \begin{pmatrix}0 & 1 & a \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix}\]
(%i40) transpose(m);\[\mathtt{(\textit{%o}_{40})}\quad \begin{pmatrix}0 & 1 & 1 \\ 1 & 0 & 1 \\ a & 1 & 0 \\ \end{pmatrix}\]
(%i41) determinant(m);\[\mathtt{(\textit{%o}_{41})}\quad a+1\]
(%i42) f: invert(m), detout;\[\mathtt{(\textit{%o}_{42})}\quad \frac{\begin{pmatrix}-1 & a & 1 \\ 1 & -a & a \\ 1 & 1 & -1 \\ \end{pmatrix}}{a+1}\]
(%i43) m . f;\[\mathtt{(\textit{%o}_{43})}\quad \begin{pmatrix}0 & 1 & a \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix}\cdot \left(\frac{\begin{pmatrix}-1 & a & 1 \\ 1 & -a & a \\ 1 & 1 & -1 \\ \end{pmatrix}}{a+1}\right)\]
(%i44) expand(%);\[\mathtt{(\textit{%o}_{44})}\quad \begin{pmatrix}\frac{a}{a+1}+\frac{1}{a+1} & 0 & 0 \\ 0 & \frac{a}{a+1}+\frac{1}{a+1} & 0 \\ 0 & 0 & \frac{a}{a+1}+\frac{1}{a+1} \\ \end{pmatrix}\]
(%i45) factor(%);\[\mathtt{(\textit{%o}_{45})}\quad \begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}\]
(%i46) x: 1234;\[\mathtt{(\textit{%o}_{46})}\quad 1234\]
(%i47) y: 2345;\[\mathtt{(\textit{%o}_{47})}\quad 2345\]
(%i48) if x > y
then x
else y;\[\mathtt{(\textit{%o}_{48})}\quad 2345\]