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#######
#
# E-scripts on Qdraw (for Maxima, by Ted Woollett)
#
# Note 1: use the eev command (defined in eev.el) and the
# ee alias (in my .zshrc) to execute parts of this file.
# Executing this file as a whole makes no sense.
# An introduction to eev can be found here:
#
# (find-eev-quick-intro)
# http://anggtwu.net/eev-intros/find-eev-quick-intro.html
#
# Note 2: be VERY careful and make sure you understand what
# you're doing.
#
# Note 3: If you use a shell other than zsh things like |&
# and the for loops may not work.
#
# Note 4: I always run as root.
#
# Note 5: some parts are too old and don't work anymore. Some
# never worked.
#
# Note 6: the definitions for the find-xxxfile commands are on my
# .emacs.
#
# Note 7: if you see a strange command check my .zshrc -- it may
# be defined there as a function or an alias.
#
# Note 8: the sections without dates are always older than the
# sections with dates.
#
# This file is at <http://anggtwu.net/e/qdraw.e>
# or at <http://anggtwu.net/e/qdraw.e.html>.
# See also <http://anggtwu.net/emacs.html>,
# <http://anggtwu.net/.emacs[.html]>,
# <http://anggtwu.net/.zshrc[.html]>,
# <http://anggtwu.net/escripts.html>,
# and <http://anggtwu.net/>.
#
#######
(find-es "maxima" "qdraw-pts")
(find-es "maxima" "2024.1-C3-intro")
# «.animations» (to "animations")
# «.colors» (to "colors")
# «.cut» (to "cut")
# «.defaults» (to "defaults")
# «.ex» (to "ex")
# «.ex1» (to "ex1")
# «.imp» (to "imp")
# «.imp1» (to "imp1")
# «.key» (to "key")
# «.label» (to "label")
# «.line» (to "line")
# «.loaded» (to "loaded")
# «.more» (to "more")
# «.para» (to "para")
# «.para-bug» (to "para-bug")
# «.point-types» (to "point-types")
# «.poly» (to "poly")
# «.polyline» (to "polyline")
# «.pts» (to "pts")
# «.repeated-options» (to "repeated-options")
# «.show_colors» (to "show_colors")
# «.terminal» (to "terminal")
# «.vector» (to "vector")
# «.xr-and-yr» (to "xr-and-yr")
#
# «.bezier-msg-1» (to "bezier-msg-1")
# «.2024.2-C3-traj-11» (to "2024.2-C3-traj-11")
# «.intro-core» (to "intro-core")
# «.some-conics» (to "some-conics")
# «.some-conics-bug» (to "some-conics-bug")
# «.mkanim1-low-level» (to "mkanim1-low-level")
#
# «.qdraw» (to "qdraw")
# «.qdraw-pts» (to "qdraw-pts")
# «.qdraw-to-pdf» (to "qdraw-to-pdf")
# «.terminal-pdf» (to "terminal-pdf")
# «.qdraw-poly» (to "qdraw-poly")
# «.parabola-boxes» (to "parabola-boxes")
# «.parabolas-2024.1» (to "parabolas-2024.1")
# «.myqdraw-flatten» (to "myqdraw-flatten")
# «.qdraw-taylor» (to "qdraw-taylor")
# «.qdraw-imp» (to "qdraw-imp")
# «.qdraw-orbita» (to "qdraw-orbita")
# «.qdraw-lissajous» (to "qdraw-lissajous")
# «.C3-lissajous» (to "C3-lissajous")
# «.qdraw-linearize» (to "qdraw-linearize")
# «.qdraw-proportional» (to "qdraw-proportional")
# «.qdraw-colors» (to "qdraw-colors")
# «.qdraw-ex-and-ex1» (to "qdraw-ex-and-ex1")
# «.qdraw-3Daxes» (to "qdraw-3Daxes")
# (find-angggrep "grep --color=auto -nH --null -e case MAXIMA/qdraw.mac")
#####
#
# animations
# 2024oct22
#
#####
# «animations» (to ".animations")
# (find-angg "MAXIMA/topdf1.mac" "quick-demo")
# (find-angg "MAXIMA/bezier2.mac")
# (find-es "maxima" "animations")
#####
#
# colors
# 2024oct07
#
#####
# «colors» (to ".colors")
# (find-mbe-links 13 10 "3.1 Default colors and available colors")
# (find-mbe13page 10 "3.1 Default colors and available colors")
# (find-mbe13text 10 "3.1 Default colors and available colors")
# (find-maximanode "")
# (find-maximanode "set_plot_option")
# (find-maximanode "color")
# (find-maximanode "Function and Variable Index" "color <1>")
# (find-maximanode "proportional_axes")
# (find-maximanode "Functions and Variables for draw" "#23ab0f")
/* Missing: light_magenta, light_turquoise, dark_pink, dark_yellow */
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
show_colors([white, black, gray0, grey0, gray10, grey10, gray20,
grey20, gray30, grey30, gray40, grey40, gray50, grey50, gray60,
grey60, gray70, grey70, gray80, grey80, gray90, grey90, gray100,
grey100, gray, grey, light_gray, light_grey, dark_gray, dark_grey],
20);
show_colors([red, light_red, dark_red, yellow, light_yellow], 12);
show_colors([green, light_green, dark_green, spring_green,
forest_green, sea_green], 12);
show_colors([blue, light_blue, dark_blue, midnight_blue, navy,
medium_blue, royalblue, skyblue], 12);
show_colors([cyan, light_cyan, dark_cyan, magenta, dark_magenta,
turquoise, dark_turquoise, pink, light_pink], 12);
show_colors([coral, light_coral, orange_red, salmon, light_salmon,
dark_salmon,
orange, dark_orange,
aquamarine, khaki,
light_goldenrod,
dark_khaki, goldenrod,
dark_goldenrod,
brown, gold, beige,
violet, dark_violet, plum, purple], 12);
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
show_colors([red, orange, yellow], 10);
show_colors([red, orange, yellow], 5);
#####
#
# cut
# 2024oct02
#
#####
# «cut» (to ".cut")
# (find-mbe13page 5 "no more than one yr(..), one cut(..)")
# (find-mbe13text 5 "no more than one yr(..), one cut(..)")
# (find-fline "~/MAXIMA/qdraw.mac" "case cut")
# (find-angggrep "grep --color=auto -nH --null -e 'cut(' MAXIMA/qdraw.mac")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
mypara : para(cos(t), sin(t), t,0,2*%pi);
qdraw1v (mypara);
qdraw1v (mypara, cut(all));
qdraw (mypara);
qdraw (mypara, cut(all));
qdraw (mypara, cut(edge));
qdraw (mypara, cut(grid));
qdraw (mypara, cut(grid,key));
qdraw (mypara, cut(key));
qdraw (mypara, cut(xyaxes));
#####
#
# defaults
# 2024oct06
#
#####
# «defaults» (to ".defaults")
# (find-fline "~/MAXIMA/qdraw.mac" "drlist : cons(ip_grid_in =")
# (find-fline "~/MAXIMA/qdraw.mac" "if nargs = 3")
# (find-fline "~/MAXIMA/qdraw.mac" "case more")
# (find-fline "~/MAXIMA/qdraw.mac" "qdraw1([qda]) :=")
#
# ip_grid_in = [10, 10], (find-maximanode "ip_grid_in")
# grid = true, (find-maximanode "grid")
# nticks = 100, (find-maximanode "nticks")
# key = "", (find-maximanode "key")
# line_width = 3, (find-maximanode "line_width")
# transparent = true, (find-maximanode "transparent")
# point_size = 3, (find-maximanode "point_size")
# point_type = 7, (find-maximanode "point_type")
# label_alignment = left, (find-maximanode "label_alignment")
# head_type = nofilled, (find-maximanode "head_type")
# head_angle = 30, (find-maximanode "head_angle")
# head_length = 0.5, (find-maximanode "head_length")
# parametric(cos(t), sin(2 t), t, 0, 2 %pi), (find-maximanode "parametric(cos(t),")
# xaxis = true, (find-maximanode "xaxis")
# xaxis_width = 2, (find-maximanode "xaxis_width")
# yaxis = true, (find-maximanode "yaxis")
# yaxis_width = 2 (find-maximanode "yaxis_width")
#####
#
# ex
# 2024oct04
#
#####
# «ex» (to ".ex")
# «ex1» (to ".ex1")
# (find-mbe13page 6 "3 Quick Plots for Explicit Functions: ex(...) and ex1(...)")
# (find-mbe13text 6 "3 Quick Plots for Explicit Functions: ex(...) and ex1(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "case ex ")
# (find-fline "~/MAXIMA/qdraw.mac" "case ex1 ")
# (find-qdraw-links "x,x^2,x^3,x^4" "-2,2" "-2,2")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw(xr(-2,2),yr(-2,2), ex([x,x^2,x^3], x,-2,2)); /* ugly */
qdraw(xr(-2,2),yr(-2,2),
ex1(x, x,-2,2, lc(red), lk(x)),
ex1(x^2, x,-2,2, lc(orange), lk(x^2)),
ex1(x^3, x,-2,2, lc(forest_green), lk(x^3))
);
#####
#
# imp and imp1
# 2024oct03
#
#####
# «imp» (to ".imp")
# «imp1» (to ".imp1")
# (find-mbe13page 20 "6 Implicit plots with imp(...) and imp1(...)")
# (find-mbe13text 20 "6 Implicit plots with imp(...) and imp1(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "For quick plots, use ex(...) and imp(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "case imp ")
# (find-fline "~/MAXIMA/qdraw.mac" "case imp1 ")
# (find-fline "~/MAXIMA/qdraw.mac" "imp(eqnlist,x,xx1,xx2,y,yy1,yy2)")
# (find-fline "~/MAXIMA/qdraw.mac" "imp1(eqn,x,x1,x2,y,y1,y2,lc(c),lw(n),lk(string) )")
# (find-fline "~/MAXIMA/qdraw.mac" "clist : makelist(color=cc[ qval(kk) ],kk,1,lendr )")
# (find-fline "~/MAXIMA/qdraw.mac" "default color selection list for ex(..) and imp(...)")
# (find-myqdraw "myqdraw3.mac" "myimp")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_myqdraw();
C : x^2+y^2;
qdraw1v (imp([C=1,C=2,C=3,C=4], x,-2,2, y,-2,2));
qdraw1v (imp1(C=1, x,-2,2, y,-2,2, lc(red)),
imp1(C=2, x,-2,2, y,-2,2, lc(orange)),
imp1(C=3, x,-2,2, y,-2,2, lc(forest_green)));
qdraw (imp([C=1,C=2,C=3,C=4], x,-2,2, y,-2,2));
qdraw (imp1(C=1, x,-2,2, y,-2,2, lc(red)),
imp1(C=2, x,-2,2, y,-2,2, lc(orange)),
imp1(C=3, x,-2,2, y,-2,2, lc(forest_green)));
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_myqdraw();
C : x^2+y^2;
[xmin,ymin, xmax,ymax] : [-2,-2, 2,2];
myqdraw( myimp([C=1,C=2,C=3,C=4]));
myqdraw(xyrange(), myimp([C=1,C=2,C=3,C=4]));
myqdraw(xyrange(),
myimp1(C=1, lc(red)),
myimp1(C=2, lc(orange)),
myimp1(C=3, lc(forest_green)));
#####
#
# key
# 2024oct04
#
#####
# «key» (to ".key")
# (find-mbe13page 5 "key(bottom)")
# (find-mbe13text 5 "key(bottom)")
# (find-fline "~/MAXIMA/qdraw.mac" "case key")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw1v (ex1(x^2, x,-2,2, lc(orange), lk("x^2")));
qdraw1v (ex1(x^2, x,-2,2, lc(orange), lk("x^2")), key(bottom));
qdraw (ex1(x^2, x,-2,2, lc(orange), lk("x^2")));
qdraw (ex1(x^2, x,-2,2, lc(orange), lk("x^2")), key(bottom));
#####
#
# label
# 2024oct07
#
#####
# «label» (to ".label")
# (find-mbe13page 50 "The qdraw.mac function label")
# (find-mbe13text 50 "The qdraw.mac function label")
# (find-mbe13page 52 "/Helvetica=18")
# (find-mbe13text 52 "/Helvetica=18")
# (find-mbe13page 52 "label_align(c)")
# (find-mbe13text 52 "label_align(c)")
# (find-maximanode "label")
# (find-maximanode "label_alignment")
# (find-maximanode "Functions and Variables for draw" "Graphic object: label")
# (find-fline "~/MAXIMA/qdraw.mac" "case label")
# (find-es "maxima" "qdraw-label")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw(xr(0,3), yr(0,3),
label(["a",1,1]),
label(["b",2,1])
)$
#####
#
# line
# 2024oct06
#
#####
# «line» (to ".line")
# (find-mbe13page 5 "line(x1,y1,x2,y2,lc(c),lw(n),lk(string) )")
# (find-mbe13text 5 "line(x1,y1,x2,y2,lc(c),lw(n),lk(string) )")
# (find-mbe13page 39 "11.1 line(...)")
# (find-mbe13text 39 "11.1 line(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "case line")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw(xr(0,3), yr(0,3), line(1,2, 1.1,2.2, lc(red)));
qdraw(xr(0,3), yr(0,3), line(1,2, 1.1,2.2, lc(red), lc(orange)));
qdraw(xr(0,3), yr(0,3), line(1,2, 1.1,2.2, lc(orange), lc(red)));
#####
#
# Check if qdraw has been loaded
# 2024nov01
#
#####
# «loaded» (to ".loaded")
# (find-fline "~/MAXIMA/qdraw.mac" "fll")
# (find-fline "~/MAXIMA/qdraw.mac" "fll(x) :=")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
myqdraw_qdraw_loaded() := is(fll([42])=[42,42,1]);
myqdraw_qdraw_loaded();
if not myqdraw_qdraw_loaded() then load_qdraw();
myqdraw_qdraw_loaded();
if not myqdraw_qdraw_loaded() then load_qdraw();
#####
#
# more
# 2024oct06
#
#####
# «more» (to ".more")
# (find-mbe13page 56 "the qdraw function more(...)")
# (find-mbe13text 56 "the qdraw function more(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "case more")
# (find-maximanode "proportional_axes")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw1v (ex1(x^3, x,-2,2, lc(orange)));
qdraw1v (ex1(x^3, x,-2,2, lc(orange)), more(proportional_axes=xy));
qdraw (ex1(x^3, x,-2,2, lc(orange)));
qdraw (ex1(x^3, x,-2,2, lc(orange)), more(proportional_axes=xy));
#####
#
# para
# 2024oct02
#
#####
# «para» (to ".para")
# (find-mbe-links 13 18 "4 Parametric plots with para(...)")
# (find-mbe13page 18 "4 Parametric plots with para(...)")
# (find-mbe13text 18 "4 Parametric plots with para(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "para( xofu,yofu,u,u1,u2,lc(c),lw(n),lk(string) )")
# (find-fline "~/MAXIMA/qdraw.mac" "para(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "case para")
# (find-maximanode "plot2d")
# (find-maximanode "plot2d" "parametric")
# (find-maximanode "plot2d" "3. Parametric function")
# (find-angg "MAXIMA/myqdraw2.mac" "mypara")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw1v ([qda]) := mapconcat('string, apply('qdraw1, qda), newline);
P(t) := [cos(t), sin(2*t)];
qdraw1 (para(P(t)[1], P(t)[2], t,0,2*%pi));
qdraw1v (para(P(t)[1], P(t)[2], t,0,2*%pi));
qdraw (para(P(t)[1], P(t)[2], t,0,2*%pi));
#####
#
# para-bug
# 2024oct09
#
#####
# «para-bug» (to ".para-bug")
# (find-es "maxima" "draw2d-parametric-bug")
# (find-maximamsg "58826903 202410 10" "Edrx: /* redefine as */")
# (to "2024.2-C3-traj-11")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
** (find-myqdraw "myqdraw3.mac")
load_myqdraw();
P(t) := if t <= 6 then [t,4] else [6,10-t]; /* redefine as: */
P(t) := [if t <= 6 then t else 6, /* x */
if t <= 6 then 4 else 10-t]; /* y */
myqdraw(xr(-1,8),yr(-1,8),
para(P(t)[1],P(t)[2], t,0,10));
mypara(xy,[rest]) := myapply('para,xy[1],xy[2],rest);
myqdraw(xr(-1,8),yr(-1,8),
mypara(P(t), t,0,10));
#####
#
# point-types
# 2024oct21
#
#####
# «point-types» (to ".point-types")
# (find-mbe13page 16 "The optional argument pt(ntype)")
# (find-mbe13text 16 "The optional argument pt(ntype)")
# (find-fline "~/MAXIMA/qdraw.mac" "point_types() produces")
# (find-angg "MAXIMA/myqdraw3.mac" "pts_open")
# (find-maximanode "points_joined")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw(point_types());
[pt_open,pt_closed] : [pt(6),pt(7)];
qdraw(xr(-1,4),yr(-1,3),
para(x,1, x,1,3),
pts([[1,1]], pt_closed, pc(white)),
pts([[1,1]], pt_open),
pts([[2,1]], pt_open),
pts([[3,1]], pt_closed));
#####
#
# poly
# 2024oct03
#
#####
# «poly» (to ".poly")
# (find-mbe-links 13 5 "poly(")
# (find-mbe13page 5 "poly(")
# (find-mbe13text 5 "poly(")
# (find-fline "~/MAXIMA/qdraw.mac" "poly([ [x1,y1],[x2,y2],.,[xN,yN] ], lc(c),lw(n),fill(cc) )")
# (find-fline "~/MAXIMA/qdraw.mac" "case poly")
# (find-maximanode "polygon")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
to_rad(deg) := deg/180*%pi;
P_rad(t_rad) := [cos(t_rad), sin(t_rad)];
P(t_deg) := P_rad(to_rad(t_deg));
mypoly : [P(0), P(30), P(90), P(180)];
qdraw1v (poly(mypoly));
qdraw1v (poly(mypoly, lc(red), fill(yellow)));
qdraw (poly(mypoly));
qdraw (poly(mypoly, lc(red), fill(yellow)));
#####
#
# polyline
# 2024oct30
#
#####
# «polyline» (to ".polyline")
# (find-es "pict2e" "manual")
# (find-pict2epage 9 "\\polyline( X1,Y1 )( X2,Y2 ). . . ( Xn,Yn )")
# (find-pict2etext 9 "\\polyline( X1,Y1 )( X2,Y2 ). . . ( Xn,Yn )")
# (find-maximanode "Function and Variable Index" "* line_type:")
# (to "pts")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
** (find-myqdraw "myqdraw3.mac")
load_myqdraw();
polyline(Pts,[opts]) := myapply_fl('pts, Pts, pt(0), opts);
myqdraw(xyrange(), line(1,1,2,2));
myqdraw(xyrange(), polyline([[1,1],[2,2],[3,2]], pc(red), pj(2)));
myqdraw(xyrange(), polyline([[1,1],[2,2],[3,2]], pc(orange), pj(4)));
#####
#
# pts
# 2024oct03
#
#####
# «pts» (to ".pts")
# (find-mbe13page 9 "We can use pts(...)")
# (find-mbe13text 9 "We can use pts(...)")
# (find-mbe13page 10 "Repeated use of pts(..) does not cycle")
# (find-mbe13text 10 "Repeated use of pts(..) does not cycle")
# (find-mbe13page 16 "3.3 Placing discrete points: the syntax of pts(...)")
# (find-mbe13text 16 "3.3 Placing discrete points: the syntax of pts(...)")
# (find-mbe13page 16 "pj(nwidth), (points joined)")
# (find-mbe13text 16 "pj(nwidth), (points joined)")
# (find-mbe13page 36 "The most basic plot of this data uses the pts(...) function defaults:")
# (find-mbe13text 36 "The most basic plot of this data uses the pts(...) function defaults:")
# (find-fline "~/MAXIMA/qdraw.mac" "pts( [ [x1,y1],[x2,y2],.,[xN,yN] ],")
# (find-fline "~/MAXIMA/qdraw.mac" "case pts")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
degs : %pi/180;
P(t) := [cos(t*degs), sin(t*degs)];
mypts : [P(0), P(30), P(90), P(180)];
qdraw(pts(mypts));
qdraw(pts(mypts, pc(red), pj(1)));
qdraw(pts(mypts, pc(red), pj(1), pt(0)));
qdraw(pts(mypts, pc(red), pj(2), pt(0)));
#####
#
# repeated-options
# 2024oct06
#
#####
# «repeated-options» (to ".repeated-options")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw(xr(0,3), yr(0,3), line(1,2, 1.1,2.2, lc(red)));
qdraw(xr(0,3), yr(0,3), line(1,2, 1.1,2.2, lc(red), lc(orange))); /* -> red */
qdraw(xr(0,3), yr(0,3), line(1,2, 1.1,2.2, lc(orange), lc(red))); /* -> orange */
#####
#
# show_colors
# 2024oct03
#
#####
# «show_colors» (to ".show_colors")
# (find-fline "~/MAXIMA/qdraw.mac" "show_colors(color_list, nlw) :=")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
show_colors([red, green, blue], 4);
#####
#
# terminal
# 2024oct04
#
#####
# «terminal» (to ".terminal")
# (find-angg "MAXIMA/myqdraw1.mac" "myQdraw-pdf")
# (find-es "maxima" "terminal-tikz")
# (find-es "maxima" "qdraw-to-pdf")
# (find-es "maxima" "terminal-pdf")
# (find-es "maxima" "log-constants-anim")
# (find-qdraw-links "x,x^2,x^3,x^4" "-2,2" "-2,2")
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-fline "/tmp/qdraw/")
rm -Rfv /tmp/qdraw/
mkdir /tmp/qdraw/
cd /tmp/qdraw/
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
mycolors : [red, orange, forest_green];
myqdraw1([dra]) := flatten([dra])$
myqdraw ([dra]) := apply('qdraw, flatten([dra]))$
mypreamble() := [xr(-2,2),yr(-2,2)]$
mycurve(k) := ex1(x^k, x,-2,2, lc(mycolors[k]))$
mydrawing(k) := [mypreamble(), makelist(mycurve(k),k,1,k)];
topdf(n) := more(terminal=pdf, file_name=concat("/tmp/qdraw/test", n))$
myqdraw1(mydrawing(1));
myqdraw1(mydrawing(2));
myqdraw1(mydrawing(1), topdf(1));
myqdraw1(mydrawing(2), topdf(2));
myqdraw (mydrawing(1)); /* draw */
myqdraw (mydrawing(2)); /* draw */
myqdraw (mydrawing(1), topdf(1)); /* save */
myqdraw (mydrawing(2), topdf(2)); /* save */
myqdraw (mydrawing(3), topdf(3)); /* save */
** (find-pdf-page "/tmp/qdraw/test1.pdf")
** (find-pdf-page "/tmp/qdraw/test2.pdf")
** (find-pdf-page "/tmp/qdraw/test3.pdf")
#####
#
# vector
# 2024oct04
#
#####
# «vector» (to ".vector")
# (find-mbe13page 47 "11.5 vector(...)")
# (find-mbe13text 47 "11.5 vector(...)")
# (find-fline "~/MAXIMA/qdraw.mac" "vector( [x,y],[dx,dy],lw(n),lc(c),lk(string),")
# (find-fline "~/MAXIMA/qdraw.mac" "ha(deg),hb(v),hl(v),ht(t) )")
# (find-fline "~/MAXIMA/qdraw.mac" "case vector")
# (find-fline "~/MAXIMA/qdraw.mac" "case vector" "head length")
# (find-fline "~/MAXIMA/qdraw.mac" "case vector" "head type" "ht(f) for" "filled")
# (find-fline "~/MAXIMA/qdraw.mac" "case arrowhead")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
P(t) := [cos(t),sin(t)];
define(vel(t), diff(P(t), x));
drawing : [xr(0,4),yr(0,4),
pts ([[3,2]]),
vector([3,2], [0,1], hl(0.2), ht(f))];
apply(qdraw1v, drawing);
apply(qdraw, drawing);
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
** (find-angg "MAXIMA/myqdraw2.mac")
load ("~/MAXIMA/myqdraw2.mac");
P(t) := [cos(t),sin(t)];
define(vel(t), diff(P(t), x));
myPvec(P,v,Popts,[vopts]) :=
[myapply_fl('pts, [P], Popts),
myapply_fl('vector, P,v, vopts)];
drawing : [xr(0,4),yr(0,4), myPvec([3,2], [0,1], [pc(red)], hl(0.2), ht(f), lc(orange))];
myqdraw (drawing);
drawing : [xr(0,4),yr(0,4),
pts ([[3,2]]),
vector([3,2], [0,1], hl(0.2), ht(f))];
drawing : [xr(0,4),yr(0,4),
pts ([[3,2]]),
vector([3,2], [0,1], hl(0.2), ht(f))];
myqdraw1v(drawing);
myqdraw (drawing);
#####
#
# xr-and-yr
# 2024oct10
#
#####
# «xr-and-yr» (to ".xr-and-yr")
# (find-fline "~/MAXIMA/qdraw.mac" "case xr")
# (find-fline "~/MAXIMA/qdraw.mac" "case yr")
# (to "vector")
#####
#
# bezier-msg-1
# 2024oct11
#
#####
# «bezier-msg-1» (to ".bezier-msg-1")
#####
#
# 2024.2-C3-traj-11
# 2024oct22
#
#####
# «2024.2-C3-traj-11» (to ".2024.2-C3-traj-11")
# (find-angg "MAXIMA/myqdraw3.mac" "pts_open")
# http://anggtwu.net/2024.2-C3/C3-quadros.pdf#page=16
# http://anggtwu.net/LATEX/2024-1-C3-trajetorias.pdf#page=22
# (c3m241trajp 22 "bico-e-teleporte")
# (c3m241traja "bico-e-teleporte")
# (to "para-bug")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
** (find-myqdraw "myqdraw3.mac")
load_myqdraw();
[xmin,ymin, xmax,ymax] : [0,0, 8,7];
R(t) := if t <= 6 then [t,4] else [5,11-t]; /* redefine as: */
R(t) := [if t <= 6 then t else 5, /* x */
if t <= 6 then 4 else 11-t]; /* y */
color_traco : orange;
color_pts : blue;
/* Ruim: */
traco : [mypara(R(t), t,0,11, lc(color_traco))]$
myqdraw(xyrange(), traco);
/* Bom: */
traco : [mypara(R(t), t,0,5.999, lc(color_traco)),
mypara(R(t), t,6.001,11, lc(color_traco)),
pts ([R(5.999)], ps(2),pc(color_traco)),
pts_open([R(6.001)], ps(2),pc(color_traco))]$
myqdraw(xyrange(), traco);
Rsec (t0,epsilon) := myPPe_c(R(t0),R(t0+epsilon),epsilon,color_pts);
Rsecs(t0,epsilons) := makelist(Rsec(t0,epsilon), epsilon, epsilons);
myqdraw(xyrange(), traco, Rsecs(1, [1/2, 1/4]));
myqdraw(xyrange(), traco, Rsecs(6, [5, 4, 3, 2.5, 2.0, 1.5, 1, 0.75, 0.5, 0.25]));
#####
#
# intro-core
# 2024nov02
#
#####
# «intro-core» (to ".intro-core")
# (to "C3-lissajous")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
P : [cos(t), sin(2*t)];
ts : [0, %pi/4, %pi/2];
define(P(t), P);
define(Pt(t), diff(P,t));
define(Ptt(t), diff(P,t,2));
qdraw(xr(-4,4),yr(-4,4),
para(P[1],P[2], t,0,2*%pi, lc(orange)),
vector(P(0), Pt(0), hl(0.1),lc(red)),
vector(P(%pi/4),Pt(%pi/4), hl(0.1),lc(red)),
vector(P(0), Ptt(0), hl(0.1),lc(forest_green)),
vector(P(%pi/4),Ptt(%pi/4), hl(0.1),lc(forest_green))
);
myqdraw([drargs]) := apply('qdraw, flatten([drargs]));
myqdraw(xr(-4,4),yr(-4,4),
para(P[1],P[2], t,0,2*%pi, lc(orange)),
makelist(vector(P(t),Pt (t), hl(0.1),lc(red)), t, ts),
makelist(vector(P(t),Ptt(t), hl(0.1),lc(forest_green)), t, ts)
);
#####
#
# some-conics
# 2024nov03
#
#####
# «some-conics» (to ".some-conics")
# http://anggtwu.net/myqdraw/some_conics.gif
# http://anggtwu.net/myqdraw/some_conics.pdf
# (find-es "maxima" "stringdisp")
* (setq last-kbd-macro (kbd "C-a %M SPC C-a <down>"))
* (find-sh0 "rm -fv /tmp/some_conics*")
* (find-sh0 "rm -fv ~/LATEX/2024-2-C3/test*")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("/usr/share/emacs/site-lisp/maxima/emaxima.lisp")$
:lisp (setf (get '$display2d 'assign) nil)
/* load("~/MAXIMA/barematrix1.mac")$ */
load_myqdraw();
display2d:'emaxima$
stringdisp : false;
topdf_opts : "height=2cm"$
[topdf_a,topdf_b,topdf_c,topdf_n] : ["/tmp/", "", "conic", 0]$
[topdf_a,topdf_b,topdf_c,topdf_n] : ["/tmp/", "", "some_conics", 0]$
[topdf_a,topdf_b,topdf_c,topdf_n] : ["~/LATEX/", "2024-2-C3/", "test", 0]$
myqdrawp_to_screen();
myqdrawp_to_new_pdf();
linenum:0;
[xmin,ymin, xmax,ymax] : [-2,-2, 2,2]$
[color[-2], color[-1], color[0], color[1], color[2]] :
[blue, forest_green, gold, orange, red]$
arrayinfo(color);
conic (a,b) := (x^2 + a*y + b*y^2 = 1)$
draw_abck(a,b,c) := myimp1(conic(a,b), lc(color[c]), lk(conic(a,b)))$
draw_abc (a,b,c) := myimp1(conic(a,b), lc(color[c]))$
draw_abk (a,b) := draw_abck(a,b,b)$
draw_ab (a,b) := draw_abc (a,b,b)$
draw_a (a) := makelist(draw_ab(a,b), b, [2,1,0,-1,-2])$
makeM1() := matrix([ "", "", f(0,1), "", ""],
[ "", f(-1,0), f(0,0), f(1,0), ""],
[f(-2,-1), "", "", "", f(2,-1)])$
makeM2() := matrix([g(-2), g(-1), g(0), g(1), g(2) ])$
f(a,b) := myqdrawp(xyrange(), draw_abk(a,b))$
g(a) := myqdrawp(xyrange(), draw_a(a))$
M1 : makeM1()$
M2 : makeM2()$
stringdisp : false;
M1;
M2;
myqdrawp(xyrange(), draw_abk( 0, 1)); /* circle */
myqdrawp(xyrange(), draw_abk( 0, 0)); /* degenerated parabola */
myqdrawp(xyrange(), draw_abk(-1, 0)); /* parabola */
myqdrawp(xyrange(), draw_abk( 1, 0)); /* parabola */
myqdrawp(xyrange(), draw_abk( 2,-1)); /* degenerated hyperbole */
myqdrawp(xyrange(), draw_abk(-2,-1)); /* degenerated hyperbole */
#####
#
# some-conics-bug
# 2024nov03
#
#####
# «some-conics-bug» (to ".some-conics-bug")
* (setq last-kbd-macro (kbd "C-a %M SPC C-a <down>"))
* (find-sh0 "rm -fv /tmp/some_conics*")
* (find-sh0 "rm -fv ~/LATEX/2024-2-C3/test*")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("/usr/share/emacs/site-lisp/maxima/emaxima.lisp")$
:lisp (setf (get '$display2d 'assign) nil)
load("~/MAXIMA/barematrix1.mac")$
load_myqdraw();
display2d:'emaxima$
stringdisp : false;
linenum:0;
[xmin,ymin, xmax,ymax] : [-2,-2, 2,2]$
[color[-2], color[-1], color[0], color[1], color[2]] :
[blue, forest_green, gold, orange, red]$
topdf_opts : "height=1cm"$
[topdf_a,topdf_b,topdf_c,topdf_n] : ["~/LATEX/", "2024-2-C3/", "test", 0]$
myqdrawp_to_new_pdf();
conic (a,b) := (x^2 + a*y + b*y^2 = 1)$
draw_abck(a,b,c) := myimp1(conic(a,b), lc(color[c]), lk(conic(a,b)))$
draw_abk (a,b) := draw_abck(a,b,b)$
stringdisp : false;
makeM1() := matrix([ "", "", f(0,1), "", ""],
[ "", f(-1,0), f(0,0), f(1,0), ""],
[f(-2,-1), "", "", "", f(2,-1)]);
f(a,b) := myqdrawp(xyrange(), draw_abk(a,b))$
stringdisp;
stringdisp : false;
M1 : makeM1();
stringdisp : false;
M1;
M1[1];
M1[1][1];
stringdisp : false;
M1[1][1];
stringp(M1[1][1]);
M1;
f(a,b) := includegraphics("foo","bar");
draw_abc (a,b,c) := myimp1(conic(a,b), lc(color[c]))$
draw_ab (a,b) := draw_abc (a,b,b)$
draw_a (a) := makelist(draw_ab(a,b), b, [2,1,0,-1,-2])$
myqdrawp(xyrange(), draw_abk( 0, 1)); /* circle */
myqdrawp(xyrange(), draw_abk( 0, 0)); /* degenerated parabola */
myqdrawp(xyrange(), draw_abk(-1, 0)); /* parabola */
myqdrawp(xyrange(), draw_abk( 1, 0)); /* parabola */
myqdrawp(xyrange(), draw_abk( 2,-1)); /* degenerated hyperbole */
myqdrawp(xyrange(), draw_abk(-2,-1)); /* degenerated hyperbole */
makeM2() := matrix([g(-2), g(-1), g(0), g(1), g(2) ]);
g(a) := myqdrawp(xyrange(), draw_a(a))$
M2 : makeM2();
[topdf_a,topdf_b,topdf_c,topdf_n] : ["/tmp/", "", "conic", 0];
[topdf_a,topdf_b,topdf_c,topdf_n] : ["~/LATEX/", "2024-2-C3/", "test", 0];
myqdrawp_to_new_pdf();
myqdraw(xyrange(), draw_a(0));
myqdraw(xyrange(), draw_a(-1));
myqdraw(xyrange(), draw_a(2));
myqdraw(xyrange(), draw_a(-2));
conic(0,0);
conic(1,0);
conic(-1,0);
myqdraw(xyrange(), draw_a(0));
myqdraw(xyrange(), draw_a(1));
myqdraw(xyrange(), draw_a(2));
draw_abc(0,0,0);
myqdrawp(xyrange(), makelist(drawab(a,b), a, [2,1,0,-1,-2]));
draw_b(b) := makelist(drawab(a,b), a, [2,1,0,-1,-2])
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
ls -lAF /tmp/some_conics*
~/myqdraw/mkanim1.sh \
DENSITY=50 DELAY=25 \
makeboth /tmp/some_conics.gif /tmp/some_conics.pdf /tmp/some_conics_*
ls -lAF /tmp/some_conics*
# (brg "file:///tmp/some_conics.gif")
# (find-pdf-page "/tmp/some_conics.pdf")
#####
#
# mkanim1-low-level
# 2024nov05
#
#####
# «mkanim1-low-level» (to ".mkanim1-low-level")
# https://github.com/qpdf/qpdf/issues/11#issuecomment-18768487 do echo $i 1-z
# https://apple.stackexchange.com/questions/86177/imagemagick-convert-multipage-pdf-to-animated-gif
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
cd /tmp/
ls -lAF frame*
add_1zs () { for i in $*; do echo $i 1-z; done; }
add_1zs frame_*.pdf
qpdf --empty --pages $(add_1zs frame_*.pdf) -- frames.pdf
ls -lAF frame*
**
** Inspect frames.pdf with:
** (find-fline "/tmp/" "frames.pdf")
** (find-pdf-page "/tmp/frames.pdf")
convert -alpha deactivate -verbose -delay 50 -loop 0 -density 150 \
/tmp/frames.pdf /tmp/frames.gif
ls -lAF frame*
**
** See: file:///tmp/frames.gif
** (brg "/tmp/frames.gif")
#####
#
# qdraw
# 2023jul09
#
#####
# «qdraw» (to ".qdraw")
# «qdraw-pts» (to ".qdraw-pts")
# (find-es "qdraw")
# (find-angg ".maxima/maxima-init.mac" "load_qdraw")
# (find-mbefile "" "mbe13qdraw.pdf")
# (find-mbe13page)
# (find-mbe13text)
# (find-mbefile "" "qdraw.mac")
# (find-mbefile "qdraw.mac")
# (find-mbefile "qdrawcode.txt")
# (find-mbe-links 13 1 "")
# (find-mbe-links 13 8 "")
# (find-mbe-links 13 39 "11.1 line(...)")
# (find-mbe-links 13 18 "4 Parametric plots with para(...)")
# (find-mbe13page 18 "4 Parametric plots with para(...)")
# (find-mbe13text 18 "4 Parametric plots with para(...)")
# (find-mbe13page 47 "11.5 vector(...)")
# (find-mbe13text 47 "11.5 vector(...)")
# (find-mbe13page 56 "13 Even More with more(...)")
# (find-mbe13text 56 "13 Even More with more(...)")
# (find-mbe13page 9 "pts ( [ [-1,-1], [0,0],[1,1] ], ps(2), pc(magenta))")
# (find-mbe13text 9 "pts ( [ [-1,-1], [0,0],[1,1] ], ps(2), pc(magenta))")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw(
ex ( [x,x^2,x^3],x,-3,3),
line ( -3,0,3,0, lc(brown), lw(1)),
more (xlabel = "X", title = "Using ex(..) for three functions")
)$
qdraw(xr(-1.5,2),yr(-2,2),
para(sin(t),sin(2*t),t,0,2*%pi ),
pts( [ [0,0] ],ps(1),pc(brown),pk("t = 0")),
pts( [ [sin(%pi/8),sin(%pi/4)] ],ps(1),pc(red),pk("t = pi/8")),
pts( [ [1,0] ],ps(1),pc(green),pk("t = pi/2")),
more (title = "parametric plot", xlabel = "sin(t)", ylabel = "sin(2*t)"))$
#####
#
# qdraw-to-pdf
# 2024jul20
#
#####
# «qdraw-to-pdf» (to ".qdraw-to-pdf")
# «terminal-pdf» (to ".terminal-pdf")
# (to "terminal-tikz")
# (find-maximanode "Plotting Options" "Plot option: pdf_file")
# (find-maximanode "Gnuplot Options" "gnuplot_term [gnuplot_term, <terminal_name>]")
# (find-angg ".maxima/maxima-init.mac" "load_qdraw")
# (find-myqdraw "myqdraw3.mac" "myterminalpdf")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
** (find-angg "MAXIMA/zpts1.mac")
load ("~/MAXIMA/zpts1.mac")$
myqdraw(
xr(0,2*%pi), yr(-2,2), more(proportional_axes=xy),
ex([sin(x), cos(x)], x,0,2*%pi)
);
myqdraw0(
more(terminal=pdf, file_name="/tmp/test"),
more(terminal=pdf, file_name="/tmp/test"),
myqdraw_body
);
myqdraw0(
more(terminal=pdf),
more(file_name="/tmp/test"),
myqdraw_body
);
** (find-fline "/tmp/" "test.pdf")
** (find-pdf-page "/tmp/test.pdf")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
** (find-myqdraw "myqdraw3.mac")
load_myqdraw();
myqdraw(
more(terminal=tikz, file_name="/tmp/test"),
xr(0,2*%pi), yr(-2,2), more(proportional_axes=xy),
ex([sin(x), cos(x)], x,0,2*%pi)
);
#####
#
# Draw boxes on the 5 "simplest" points of a parabola using qdraw
# 2023sep25
#
#####
# «qdraw-poly» (to ".qdraw-poly")
# «parabola-boxes» (to ".parabola-boxes")
# (find-mbe-links 13 5 "poly(")
# (find-mbe13page 5 "poly(")
# (find-mbe13text 5 "poly(")
# (find-TH "eev-maxima" "maxima-by-example")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
myqdraw([lists]) := apply('qdraw, apply('append, lists));
P : [cos(t), sin(t)];
Pt : diff(P, t);
Ptt : diff(P, t, 2);
define(P(t), P);
define(Pt(t), Pt);
define(Ptt(t), Ptt);
t0 : %pi/4;
t0 : 0;
[A,uu,vv] : [P(t0), Pt(t0), Ptt(t0)];
B(u,v) := A + u*uu + v*vv/2;
B(0,0);
Q : P(t0) + t*Pt(t0) + t^2*Ptt(t0)/2;
define(Q(t), Q);
qdraw(
xr(-4.5,4.5), yr(-4,4),
poly([B(0,0), B( 1,0), B( 1,1), B(0,1)], lc(brown)),
poly([B(0,0), B(-1,0), B(-1,1), B(0,1)], lc(brown)),
poly([B(0,0), B( 2,0), B( 2,4), B(0,4)], lc(brown)),
poly([B(0,0), B(-2,0), B(-2,4), B(0,4)], lc(brown)),
para(P[1],P[2], t, 0,2*%pi, lc(red)),
para(Q[1],Q[2], t, -2,2, lc(orange))
)$
[Q(0), Q(1) , Q(2)];
[Q(0), Q(-1), Q(-2)];
#####
#
# parabolas-2024.1
# 2024mar27
#
#####
# «parabolas-2024.1» (to ".parabolas-2024.1")
# «myqdraw-flatten» (to ".myqdraw-flatten")
# (find-angg ".maxima/maxima-init.mac" "load_qdraw")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
myqdraw0([lists]) := apply('qdraw, flatten([lists]));
myqdraw ([lists]) := block([], myqdraw_body : lists, apply('myqdraw0, lists));
mypoly([pts]) := poly(pts, lc(orange));
myvec(xy, dxdy) := vector(xy, dxdy, hl(0.1), lw(5), lc(purple));
defs1() := block([],
define(Pt(t), diff(P(t),t)),
define(Ptt(t), diff(P(t),t,2)),
[A,uu,vv] : [P(0), Pt(0), Ptt(0)],
B(u,v) := A + u*uu + v*vv/2,
PP(t) := A + t*uu + t^2/2 * vv
)$
parabola_rects() := [
mypoly(B(0,0), B( 1,0), B( 1,1), B(0,1)),
mypoly(B(0,0), B(-1,0), B(-1,1), B(0,1)),
mypoly(B(0,0), B( 2,0), B( 2,4), B(0,4)),
mypoly(B(0,0), B(-2,0), B(-2,4), B(0,4))
]$
parabola_vecs() := [
myvec(P(0), Pt(0)),
myvec(P(1), Pt(1)),
myvec(P(-1), Pt(-1)),
myvec(P(-2), Pt(-2))
]$
P(t) := [3,1] + t*[1,0] + t^2*[0,1];
defs1();
P(t);
PP(t);
P(t) := [cos(t), sin(t)];
defs1();
P(t);
PP(t);
P(t) := [2,6] + t*[1,1] + t^2*[2,-1];
defs1();
myqdraw(
xr(0,12), yr(0,8), more(proportional_axes=xy),
parabola_rects(),
parabola_vecs(),
para(P(t)[1],P(t)[2], t, -2,2, lc(red))
)$
myqdraw0(
more(terminal=pdf, file_name="/tmp/parabola"),
myqdraw_body
)$
** (find-maximanode "flatten")
** (find-pdf-page "/tmp/parabola.pdf")
** (find-pdf-text "/tmp/parabola.pdf")
#####
#
# qdraw-taylor
# 2023oct03
#
#####
# «qdraw-taylor» (to ".qdraw-taylor")
# (to "2023-2-raio-conv")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
DDef1(fxy) := buildq([f:op(fxy),xy:args(fxy)], define(f(splice(xy)),f));
DDef([fxys]) ::= map('DDef1,fxys);
colors : [black, red, orange, forest_green, blue, dark_violet]$
f : sin(x);
derivsf : makelist(diff(f,x,k), k, 0,7);
derivsf0 : subst([x=0], derivsf);
derivsfk(k) := diff(f,x,k);
derivsf0k(k) := subst([x=0], derivsfk(k));
termk(k) := derivsf0k(k) * x^k/k!;
newf(K) := sum(termk(k), k, 0, K);
newf(7);
f0 : newf(0);
f1 : newf(1);
f3 : newf(3);
f5 : newf(5);
f7 : newf(7);
r : 2*%pi;
r : 3*%pi;
qdraw(xr(-r,r), yr(-r,r),
ex1(f, x, -r,r, lc(colors[1]), lk("orig")),
ex1(f0, x, -r,r, lc(colors[2]), lk("grau 0")),
ex1(f1, x, -r,r, lc(colors[3]), lk("grau 1")),
ex1(f3, x, -r,r, lc(colors[4]), lk("grau 3")),
ex1(f5, x, -r,r, lc(colors[5]), lk("grau 5")),
ex1(f7, x, -r,r, lc(colors[6]), lk("grau 7"))
);
define(f7(x), f7);
sin(0.1);
f7(0.1);
sin(0.1) - f7(0.1);
define(f5(x), f5);
sin(0.1);
f5(0.1);
sin(0.1) - f5(0.1);
#####
#
# qdraw-imp
# 2023sep28
#
#####
# «qdraw-imp» (to ".qdraw-imp")
# (find-mbe-links 13 20 "6 Implicit plots with imp(...) and imp1(...)")
# (find-mbe13page 20 "6 Implicit plots with imp(...) and imp1(...)")
# (find-mbe13text 20 "6 Implicit plots with imp(...) and imp1(...)")
# (to "matrixify")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
e : sin(2*x)*cos(y)$
qdraw(imp( e=0.4,x,-3,3,y,-3,3 ),
cut(key),
more(title=" sin(2 x) cos(y) = 0.4 ",
xlabel = "x",
ylabel = "y"))$
qdraw(imp( [e=0.4,e=0.7,e=0.9],x,-3,3,y,-3,3 ),
cut(key),
more(title=" sin(2 x) cos(y) = 0.4,0.7,0.9 ",
xlabel = "x",
ylabel = "y"))$
#####
#
# qdraw-orbita
# 2023sep26
#
#####
# «qdraw-orbita» (to ".qdraw-orbita")
# See: (c3m232trp 9 "orbita")
# (c3m232tra "orbita")
# (c3m221orbitap 3 "orbita")
# (c3m221orbitaa "orbita")
# Based on: (to "C3-lissajous")
# Uses: (to "DDef")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
myqdraw([lists]) := apply('qdraw, apply('append, lists));
seqn(a,b,n) := makelist(a + (b-a)*k/n, k, 0, n);
DDef1(fxy) := buildq([f:op(fxy),xy:args(fxy)], define(f(splice(xy)),f));
DDef([fxys]) ::= map('DDef1,fxys);
h : 2*%pi / 12;
/* configs */
[adjvel,adjacc,r,ts] : [1, 1, 9, seqn(0*h, 12*h, 6)];
[adjvel,adjacc,r,ts] : [1/4, 1/4, 3, seqn(0*h, 12*h, 6)];
[adjvel,adjacc,r,ts] : [1/4, 1/10, 3, seqn(0*h, 12*h, 6)];
[adjvel,adjacc,r,ts] : [1/4, 1/4, 3, seqn(0*h, 12*h, 3)];
[adjvel,adjacc,r,ts] : [1/4, 1/4, 3, seqn(2*h, 14*h, 3)];
[adjvel,adjacc,r,ts] : [1, 1, 9, seqn(0*h, 12*h, 3)];
[adjvel,adjacc,r,ts] : [1, 1, 9, seqn(2*h, 14*h, 3)];
[adjvel,adjacc,r,ts];
P : [cos(t), sin(t)];
R : 1/2 * [cos(4*t), sin(4*t)];
S : P + R;
St : diff(S, t);
Stt : diff(S, t, 2);
vel : vector([S[1],S[2]], [St [1],St [2]]*adjvel, hl(0.1), lc(orange));
acc : vector([S[1],S[2]], [Stt[1],Stt[2]]*adjacc, hl(0.1), lc(purple));
define(vel(t), vel);
define(acc(t), acc);
vels : makelist(vel(t), t, ts);
accs : makelist(acc(t), t, ts);
bbox : [ xr(-r,r), yr(-r,r) ];
orbit : [ para(S[1],S[2], t, 0,2*%pi, lc(red)) ];
myqdraw(bbox, orbit, vels, accs);
vel(0);
vel(%pi);
acc(0);
acc(%pi);
vels;
adjvel : 1;
adjacc : 1;
myqdraw(orbit, vels, accs);
acc(0);
acc(%pi);
myqdraw([ xr(-2,2),yr(-2,2),
para(S[1], S[2], t, 0,2*%pi, lc(red))
]);
S(t)[1];
S(t);
#####
#
# Exercises on Lissajous figures (for Calculus 3)
# 2023oct07
#
#####
# «qdraw-lissajous» (to ".qdraw-lissajous")
# «C3-lissajous» (to ".C3-lissajous")
# (c3m232trp 8 "lissajous")
# (c3m232tra "lissajous")
# (to "intro-core")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
P : [cos(t), sin(2*t)];
ts : [0, %pi/4, %pi/2];
define(P(t), P);
define(Pt(t), diff(P,t));
define(Ptt(t), diff(P,t,2));
qdraw(xr(-4,4),yr(-4,4),
para(P[1],P[2], t,0,2*%pi, lc(orange)),
vector(P(0), Pt(0), hl(0.1),lc(red)),
vector(P(%pi/4),Pt(%pi/4), hl(0.1),lc(red)),
vector(P(0), Ptt(0), hl(0.1),lc(forest_green)),
vector(P(%pi/4),Ptt(%pi/4), hl(0.1),lc(forest_green))
);
myqdraw([drargs]) := apply('qdraw, flatten([drargs]));
myqdraw(xr(-4,4),yr(-4,4),
para(P[1],P[2], t,0,2*%pi, lc(orange)),
makelist(vector(P(t),Pt (t), hl(0.1),lc(red)), t, ts),
makelist(vector(P(t),Ptt(t), hl(0.1),lc(forest_green)), t, ts)
);
myvector(xy,dxdy,color) := vector(xy,dxdy,hl(0.1),lc(color));
myqdraw(drawing);
,
makelist(myvector(P(t),Pt(t),red), t, ts)
para(P[1],P[2], t, 0,2*%pi, lc(red))
], vels, accs);
shrink : 4; /* how much to shrink the vectors */
Pt : diff(P, t) / shrink;
Ptt : diff(P, t, 2) / shrink;
vel : vector([P[1],P[2]], [Pt [1],Pt [2]], hl(0.1), lc(orange));
acc : vector([P[1],P[2]], [Ptt[1],Ptt[2]], hl(0.1), lc(purple));
vel(t1) := subst([t=t1], vel);
acc(t1) := subst([t=t1], acc);
vels : makelist(vel(t1), t1, ts);
accs : makelist(acc(t1), t1, ts);
myqdraw([ xr(-2,2),yr(-2,2),
para(P[1],P[2], t, 0,2*%pi, lc(red))
], vels, accs);
/* original: */
qdraw( xr(-2,2),yr(-2,2),
para(P[1],P[2], t, 0,2*%pi, lc(red)),
vel(0),
acc(0) );
#####
#
# qdraw-linearize
# 2023oct03
#
#####
# «qdraw-linearize» (to ".qdraw-linearize")
# (find-mbe-links 13 18 "4 Parametric plots with para(...)")
# (find-mbe13page 18 "4 Parametric plots with para(...)")
# (find-mbe13text 18 "4 Parametric plots with para(...)")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
myqdraw([lists]) := apply('qdraw, apply('append, lists));
colors;
colors : [red, orange, forest_green, blue, dark_violet];
F : sqrt(1-x^2);
x0 : 0.3;
x1 : 0.8;
[xx1,xx2,xx3,xx4] : [-1.5,-1,1,1.5];
Fx : diff(F, x);
DDef(F(x), Fx(x));
L : F(x0) + (x-x0)*Fx(x0);
DDef(L(x));
qdraw(xr(xx1,xx4),yr(xx1,xx4),
ex1(F, x, xx2, xx3, lc(colors[1])),
ex1(L, x, xx1, xx4, lc(colors[2])),
pts( [ [x0,0], [x0,F(x0)], [0,F(x0)] ],ps(1.5),pc(colors[3]),pk("(x0,f(x0))")),
pts( [ [x1,0], [x1,F(x1)], [0,F(x1)] ],ps(1.5),pc(colors[4]),pk("(x1,f(x1))")),
pts( [ [x1,L(x1)], [0,L(x1)] ],ps(1.5),pc(colors[5]),pk("(x1,L(x1))"))
)$
FL(x1) := [F(x1), L(x1), F(x1)-L(x1)];
FL(4.1);
FL(4.01);
FL(4.001);
#####
#
# qdraw-proportional
# 2023nov18
#
#####
# «qdraw-proportional» (to ".qdraw-proportional")
# (find-anggfile "MAXIMA/eigshow1.mac" "proportional_axes")
# (find-maximanode "Functions and Variables for draw" "proportional_axes")
# (find-mbe-links 13 56 "13 Even More with more(...)")
# (find-mbe13page 56 "13 Even More with more(...)")
# (find-mbe13text 56 "13 Even More with more(...)")
#####
#
# qdraw-colors
# 2023oct03
#
#####
# «qdraw-colors» (to ".qdraw-colors")
# (to "colors")
# (find-mbe-links 13 10 "3.1 Default colors and available colors")
# (find-mbe13page 10 "3.1 Default colors and available colors")
# (find-mbe13text 10 "3.1 Default colors and available colors")
# (find-maximanode "")
# (find-maximanode "set_plot_option")
# (find-maximanode "color")
# (find-maximanode "proportional_axes")
# (find-maximanode "Functions and Variables for draw" ": color")
# (find-maximanode "Functions and Variables for draw" "#23ab0f")
# (find-maximanode "Functions and Variables for draw" "proportional_axes")
/* Missing: light_magenta, light_turquoise, dark_pink, dark_yellow */
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
show_colors([white, black, gray0, grey0, gray10, grey10, gray20,
grey20, gray30, grey30, gray40, grey40, gray50, grey50, gray60,
grey60, gray70, grey70, gray80, grey80, gray90, grey90, gray100,
grey100, gray, grey, light_gray, light_grey, dark_gray, dark_grey],
20);
show_colors([red, light_red, dark_red, yellow, light_yellow], 12);
show_colors([green, light_green, dark_green, spring_green,
forest_green, sea_green], 12);
show_colors([blue, light_blue, dark_blue, midnight_blue, navy,
medium_blue, royalblue, skyblue], 12);
show_colors([cyan, light_cyan, dark_cyan, magenta, dark_magenta,
turquoise, dark_turquoise, pink, light_pink], 12);
show_colors([coral, light_coral, orange_red, salmon, light_salmon,
dark_salmon,
orange, dark_orange,
aquamarine, khaki,
light_goldenrod,
dark_khaki, goldenrod,
dark_goldenrod,
brown, gold, beige,
violet, dark_violet, plum, purple], 12);
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
show_colors([red, orange, yellow], 3);
show_colors([red, orange, yellow], 2);
#####
#
# qdraw-ex-and-ex1
# 2023nov09
#
#####
# «qdraw-ex-and-ex1» (to ".qdraw-ex-and-ex1")
# (find-mbe-links 13 6 "3 Quick Plots for Explicit Functions: ex(...) and ex1(...)")
# (find-mbe13page 6 "3 Quick Plots for Explicit Functions: ex(...) and ex1(...)")
# (find-mbe13text 6 "3 Quick Plots for Explicit Functions: ex(...) and ex1(...)")
# (find-mbe-links 13 10 "3.1 Default colors and available colors")
# (find-mbefile "qdraw.mac")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load_qdraw();
qdraw();
qdraw1();
/*(%i3)*/ qdraw ( ex (cos(x), x, 0, 6))$
/*(%i4)*/ qdraw ( ex (cos(x), x, 0, 6, lc(red)))$
/*(%i5)*/ qdraw ( ex1 (cos(x), x, 0, 6, lc(red)))$
/*(%i6)*/ qdraw ( ex1 (cos(x), x, 0, 6, lc(red)),
more (xlabel = "X", ylabel = "COS(X)", title = "single function"))$
/*(%i7)*/ qdraw ( ex1 (cos(x), x, 0, 6, lc(red)),
line ( 0,0,6,0, lc(brown), lw(1)),
more (xlabel = "X", ylabel = "COS(X)", title = "single function"))$
/*(%i8)*/ qdraw ( ex1 (cos(x), x, 0, 6, lc(red)), yr (-1.2, 1.2),
line ( 0,0,6,0, lc(brown), lw(1)),
more (xlabel = "X", ylabel = "COS(X)", title = "single function"))$
/*(%i9)*/ qdraw ( ex ( [x,x^2,x^3],x,-3,3),
line ( -3,0,3,0, lc(brown), lw(1)),
more (xlabel = "X", title = "Using ex(..) for three functions"))$
/*(%i10)*/ qdraw ( ex ( [x,x^2,x^3],x,-3,3), yr (-2, 2),
line ( -3,0,3,0, lc(brown), lw(1)), key (bottom),
more (xlabel = "X", title = "Using ex(..) for three functions"))$
/*(%i11)*/ qdraw ( ex ( [x,x^2,x^3],x,-3,3), yr (-2, 2),
line ( -3,0,3,0, lc(brown), lw(1)), key (bottom),
pts ( [ [-1,-1], [0,0],[1,1] ] ),
more (xlabel = "X", title = "Using ex(..) for three functions"))$
/*(%i12)*/ qdraw ( ex ( [x,x^2,x^3],x,-3,3), yr (-2, 2),
line ( -3,0,3,0, lc(brown), lw(1)), key (bottom),
pts ( [ [-1,-1], [0,0],[1,1] ], ps(2), pc(magenta)),
more (xlabel = "X", title = "Using ex(..) for three functions"))$
/*(%i13)*/ qdraw ( ex ( [x,x^2,x^3],x,-3,3), yr (-2, 2),
line ( -3,0,3,0, lc(brown), lw(1)), key (bottom),
pts ( [ [-1,-1], [0,0],[1,1] ], ps(2), pc(magenta), pk("intersections")),
more (xlabel = "X", title = "Using ex(..) for three functions"))$
/*(%i14)*/ default_colors(15)$
/*(%i15)*/ (L1:[[-1,-1],[-1,0],[-1,1]], L2:[[1,-1],[1,0],[1,1]],
qdraw ( pts(L1), pts(L2), xr(-2,2),yr(-2,2)))$
/*(%i16)*/ mycL : [aquamarine,beige,blue,brown,cyan,gold,goldenrod,green,khaki,
magenta,orange,pink,plum,purple,red,salmon,skyblue,turquoise,
violet,yellow ]$
/*(%i17)*/ show_colors(mycL,10)$
/*(%i18)*/ qdraw( ex1(bessel_j(0,x),x,0,20,lc(red),lw(6),lk("bessel_j ( 0, x)") ),
ex1(bessel_j(1,x),x,0,20,lc(blue),lw(5),lk("bessel_j ( 1, x)")),
ex1(bessel_j(2,x),x,0,20,lc(brown),lw(4),lk("bessel_j ( 2, x)") ),
ex1(bessel_j(3,x),x,0,20,lc(green),lw(3),lk("bessel_j ( 3, x)") ) )$
/*(%i19)*/ qdraw(line(0,0,50,0,lc(red),lw(2) ),
ex1(bessel_j(0, sqrt(x)),x,0,50 ,lc(blue),
lw(7),lk("J0( sqrt(x) )") ) )$
# Local Variables:
# coding: utf-8-unix
# End: