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[Maxima-commits] [git] Maxima CAS branch rtoy-highlightjs-example-maxima-blocks updated. branch-5_48-base-73-g826455014
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From: rtoy <rt...@us...> - 2025-08-21 20:52:17
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- Log -----------------------------------------------------------------
commit 826455014526baf70cb631a3ee0428c68f626300
Author: Raymond Toy <toy...@gm...>
Date: Thu Aug 21 13:50:52 2025 -0700
Run update_examples
This caused the results from `fft` to have the real parts have the
opposite sign. But this also makes the results match what `fft`
currently returns and matches what `fftpack5_fft` returns, which is
nice.
diff --git a/doc/info/Numerical.texi b/doc/info/Numerical.texi
index 747ff6812..5def4194b 100644
--- a/doc/info/Numerical.texi
+++ b/doc/info/Numerical.texi
@@ -140,19 +140,24 @@ Real data.
@c L2 : fft (L1);
@c lmax (abs (L2 - L));
@c ===end===
-@example
+@example maxima
(%i1) load ("fft") $
(%i2) fpprintprec : 4 $
(%i3) L : [1, 2, 3, 4, -1, -2, -3, -4] $
+@group
(%i4) L1 : inverse_fft (L);
-(%o4) [0.0, 14.49 %i - .8284, 0.0, 2.485 %i + 4.828, 0.0,
- 4.828 - 2.485 %i, 0.0, - 14.49 %i - .8284]
+(%o4) [0.0, - 14.49 %i - 0.8284, 0.0, 4.828 - 2.485 %i, 0.0,
+ 2.485 %i + 4.828, 0.0, 14.49 %i - 0.8284]
+@end group
+@group
(%i5) L2 : fft (L1);
-(%o5) [1.0, 2.0 - 2.168L-19 %i, 3.0 - 7.525L-20 %i,
-4.0 - 4.256L-19 %i, - 1.0, 2.168L-19 %i - 2.0,
-7.525L-20 %i - 3.0, 4.256L-19 %i - 4.0]
+(%o5) [1.0, 2.0 - 4.441e-16 %i, 3.0, 4.441e-16 %i + 4.0, - 1.0,
+ 4.441e-16 %i - 2.0, - 3.0, - 4.441e-16 %i - 4.0]
+@end group
+@group
(%i6) lmax (abs (L2 - L));
-(%o6) 3.545L-16
+(%o6) 4.441e-16
+@end group
@end example
Complex data.
@@ -165,20 +170,24 @@ Complex data.
@c L2 : fft (L1);
@c lmax (abs (L2 - L));
@c ===end===
-@example
+@example maxima
(%i1) load ("fft") $
-(%i2) fpprintprec : 4 $
+(%i2) fpprintprec : 4 $
(%i3) L : [1, 1 + %i, 1 - %i, -1, -1, 1 - %i, 1 + %i, 1] $
+@group
(%i4) L1 : inverse_fft (L);
-(%o4) [4.0, 2.711L-19 %i + 4.0, 2.0 %i - 2.0,
-- 2.828 %i - 2.828, 0.0, 5.421L-20 %i + 4.0, - 2.0 %i - 2.0,
-2.828 %i + 2.828]
+(%o4) [4.0, 2.828 %i + 2.828, - 2.0 %i - 2.0, 4.0, 0.0,
+ - 2.828 %i - 2.828, 2.0 %i - 2.0, 4.0]
+@end group
+@group
(%i5) L2 : fft (L1);
-(%o5) [4.066E-20 %i + 1.0, 1.0 %i + 1.0, 1.0 - 1.0 %i,
-1.55L-19 %i - 1.0, - 4.066E-20 %i - 1.0, 1.0 - 1.0 %i,
-1.0 %i + 1.0, 1.0 - 7.368L-20 %i]
-(%i6) lmax (abs (L2 - L));
-(%o6) 6.841L-17
+(%o5) [1.0, 1.0 %i + 1.0, 1.0 - 1.0 %i, - 1.0, - 1.0,
+ 1.0 - 1.0 %i, 1.0 %i + 1.0, 1.0]
+@end group
+@group
+(%i6) lmax (abs (L2 - L));
+(%o6) 0.0
+@end group
@end example
@opencatbox{Categories:}
@@ -268,19 +277,24 @@ Real data.
@c L2 : inverse_fft (L1);
@c lmax (abs (L2 - L));
@c ===end===
-@example
+@example maxima
(%i1) load ("fft") $
(%i2) fpprintprec : 4 $
(%i3) L : [1, 2, 3, 4, -1, -2, -3, -4] $
+@group
(%i4) L1 : fft (L);
-(%o4) [0.0, 1.811 %i - .1036, 0.0, 0.3107 %i + .6036, 0.0,
- 0.6036 - 0.3107 %i, 0.0, (- 1.811 %i) - 0.1036]
+(%o4) [0.0, 1.811 %i - 0.1036, 0.0, 0.3107 %i + 0.6036, 0.0,
+ 0.6036 - 0.3107 %i, 0.0, - 1.811 %i - 0.1036]
+@end group
+@group
(%i5) L2 : inverse_fft (L1);
-(%o5) [1.0, 2.168L-19 %i + 2.0, 7.525L-20 %i + 3.0,
-4.256L-19 %i + 4.0, - 1.0, - 2.168L-19 %i - 2.0,
-- 7.525L-20 %i - 3.0, - 4.256L-19 %i - 4.0]
+(%o5) [1.0, 4.441e-16 %i + 2.0, 3.0, 4.0 - 4.441e-16 %i, - 1.0,
+ - 4.441e-16 %i - 2.0, - 3.0, 4.441e-16 %i - 4.0]
+@end group
+@group
(%i6) lmax (abs (L2 - L));
-(%o6) 3.545L-16
+(%o6) 4.441e-16
+@end group
@end example
Complex data.
@@ -293,18 +307,24 @@ Complex data.
@c L2 : inverse_fft (L1);
@c lmax (abs (L2 - L));
@c ===end===
-@example
+@example maxima
(%i1) load ("fft") $
(%i2) fpprintprec : 4 $
(%i3) L : [1, 1 + %i, 1 - %i, -1, -1, 1 - %i, 1 + %i, 1] $
+@group
(%i4) L1 : fft (L);
-(%o4) [0.5, 0.5, 0.25 %i - 0.25, (- 0.3536 %i) - 0.3536, 0.0, 0.5,
- (- 0.25 %i) - 0.25, 0.3536 %i + 0.3536]
+(%o4) [0.5, 0.5, 0.25 %i - 0.25, - 0.3536 %i - 0.3536, 0.0, 0.5,
+ - 0.25 %i - 0.25, 0.3536 %i + 0.3536]
+@end group
+@group
(%i5) L2 : inverse_fft (L1);
-(%o5) [1.0, 1.0 %i + 1.0, 1.0 - 1.0 %i, - 1.0, - 1.0, 1.0 - 1.0 %i,
- 1.0 %i + 1.0, 1.0]
+(%o5) [1.0, 1.0 %i + 1.0, 1.0 - 1.0 %i, - 1.0, - 1.0,
+ 1.0 - 1.0 %i, 1.0 %i + 1.0, 1.0]
+@end group
+@group
(%i6) lmax (abs (L2 - L));
-(%o6) 0.0
+(%o6) 0.0
+@end group
@end example
Computation of sine and cosine coefficients.
@@ -331,7 +351,7 @@ Computation of sine and cosine coefficients.
@c f(j) := sum (a[k] * cos (2*%pi*j*k / n) + b[k] * sin (2*%pi*j*k / n), k, 0, n/2) $
@c makelist (float (f (j)), j, 0, n - 1);
@c ===end===
-@example
+@example maxima
(%i1) load ("fft") $
(%i2) fpprintprec : 4 $
(%i3) L : [1, 2, 3, 4, 5, 6, 7, 8] $
@@ -343,20 +363,27 @@ Computation of sine and cosine coefficients.
(%i9) b : make_array (any, n/2 + 1) $
(%i10) a[0] : realpart (y[0]) $
(%i11) b[0] : 0 $
+@group
(%i12) for k : 1 thru n/2 - 1 do
(a[k] : realpart (y[k] + y[n - k]),
b[k] : imagpart (y[n - k] - y[k]));
(%o12) done
+@end group
(%i13) a[n/2] : y[n/2] $
(%i14) b[n/2] : 0 $
+@group
(%i15) listarray (a);
(%o15) [4.5, - 1.0, - 1.0, - 1.0, - 0.5]
+@end group
+@group
(%i16) listarray (b);
-(%o16) [0, - 2.414, - 1.0, - .4142, 0]
-(%i17) f(j) := sum (a[k]*cos(2*%pi*j*k/n) + b[k]*sin(2*%pi*j*k/n),
- k, 0, n/2) $
+(%o16) [0, 2.414, 1.0, 0.4142, 0]
+@end group
+(%i17) f(j) := sum (a[k] * cos (2*%pi*j*k / n) + b[k] * sin (2*%pi*j*k / n), k, 0, n/2) $
+@group
(%i18) makelist (float (f (j)), j, 0, n - 1);
-(%o18) [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]
+(%o18) [1.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0]
+@end group
@end example
@opencatbox{Categories:}
@@ -603,21 +630,30 @@ generate programs to be run in Fortran. See also @mrefdot{stringout}
@c ev (expr, x=1e155);
@c ev (expr2, x=1e155);
@c ===end===
-@example
+@example maxima
+@group
(%i1) expr: 1e-155*x^2 - 5.5*x + 5.2e155;
- 2
-(%o1) 1.e-155 x - 5.5 x + 5.2e+155
+ 2
+(%o1) 1.0e-155 x - 5.5 x + 5.2e155
+@end group
+@group
(%i2) expr2: horner (%, x), keepfloat: true;
-(%o2) 1.0 ((1.e-155 x - 5.5) x + 5.2e+155)
+(%o2) 1.0 ((1.0e-155 x - 5.5) x + 5.2e155)
+@end group
+@group
(%i3) ev (expr, x=1e155);
Maxima encountered a Lisp error:
- arithmetic error FLOATING-POINT-OVERFLOW signalled
+ Arithmetic error FLOATING-POINT-OVERFLOW signalled.
+Operation was *, operands (1.0e155 NIL).
Automatically continuing.
To enable the Lisp debugger set *debugger-hook* to nil.
+@end group
+@group
(%i4) ev (expr2, x=1e155);
-(%o4) 7.00000000000001e+154
+(%o4) 7.000000000000006e154
+@end group
@end example
@opencatbox{Categories:}
@@ -719,32 +755,58 @@ Examples:
@c bf_find_root (exp(x) = y, x, 0, 100), y = 10;
@c log(10b0);
@c ===end===
-@example
+@example maxima
+@group
(%i1) f(x) := sin(x) - x/2;
x
(%o1) f(x) := sin(x) - -
2
+@end group
+@group
(%i2) find_root (sin(x) - x/2, x, 0.1, %pi);
(%o2) 1.895494267033981
+@end group
+@group
(%i3) find_root (sin(x) = x/2, x, 0.1, %pi);
(%o3) 1.895494267033981
+@end group
+@group
(%i4) find_root (f(x), x, 0.1, %pi);
(%o4) 1.895494267033981
+@end group
+@group
(%i5) find_root (f, 0.1, %pi);
(%o5) 1.895494267033981
+@end group
+@group
(%i6) find_root (exp(x) = y, x, 0, 100);
x
(%o6) find_root(%e = y, x, 0.0, 100.0)
+@end group
+@group
(%i7) find_root (exp(x) = y, x, 0, 100), y = 10;
(%o7) 2.302585092994046
+@end group
+@group
(%i8) log (10.0);
(%o8) 2.302585092994046
+@end group
+@group
(%i9) fpprec:32;
-(%o9) 32
-(%i10) bf_find_root (exp(x) = y, x, 0, 100), y = 10;
-(%o10) 2.3025850929940456840179914546844b0
-(%i11) log(10b0);
-(%o11) 2.3025850929940456840179914546844b0
+(%o9) 32
+@end group
+@group
+(%i10) 32;
+(%o10) 32
+@end group
+@group
+(%i11) bf_find_root (exp(x) = y, x, 0, 100), y = 10;
+(%o11) 2.3025850929940456840179914546844b0
+@end group
+@group
+(%i12) log(10b0);
+(%o12) 2.3025850929940456840179914546844b0
+@end group
@end example
@opencatbox{Categories:}
@@ -783,20 +845,32 @@ Examples:
@c newton (x^2 - a^2, x, a/2, a^2/100);
@c ev (x^2 - a^2, x = %);
@c ===end===
-@example
+@example maxima
+@group
(%i1) load ("newton1");
-(%o1) /maxima/share/numeric/newton1.mac
+(%o1) /maxima/share/numeric/newton1.mac
+@end group
+@group
(%i2) newton (cos (u), u, 1, 1/100);
-(%o2) 1.570675277161251
+(%o2) 1.5706752771612507
+@end group
+@group
(%i3) ev (cos (u), u = %);
-(%o3) 1.2104963335033529e-4
+(%o3) 1.2104963335033528e-4
+@end group
+@group
(%i4) assume (a > 0);
(%o4) [a > 0]
+@end group
+@group
(%i5) newton (x^2 - a^2, x, a/2, a^2/100);
-(%o5) 1.00030487804878 a
+(%o5) 1.0003048780487804 a
+@end group
+@group
(%i6) ev (x^2 - a^2, x = %);
2
(%o6) 6.098490481853958e-4 a
+@end group
@end example
@opencatbox{Categories:}
@@ -1016,7 +1090,7 @@ To show the direction field of the differential equation @math{y' = exp(-x) + y}
@c ===beg===
@c plotdf(exp(-x)+y,[trajectory_at,2,-0.1])$
@c ===end===
-@example
+@example maxima
(%i1) plotdf(exp(-x)+y,[trajectory_at,2,-0.1])$
@end example
@@ -1031,7 +1105,7 @@ To obtain the direction field for the equation @math{diff(y,x) = x - y^2} and th
@c [trajectory_at,-1,3], [direction,forward],
@c [y,-5,5], [x,-4,16])$
@c ===end===
-@example
+@example maxima
@group
(%i1) plotdf(x-y^2,[xfun,"sqrt(x);-sqrt(x)"],
[trajectory_at,-1,3], [direction,forward],
@@ -1055,7 +1129,7 @@ fixed at 2):
@c plotdf([v,-k*z/m], [z,v], [parameters,"m=2,k=2"],
@c [sliders,"m=1:5"], [trajectory_at,6,0])$
@c ===end===
-@example
+@example maxima
@group
(%i1) plotdf([v,-k*z/m], [z,v], [parameters,"m=2,k=2"],
[sliders,"m=1:5"], [trajectory_at,6,0])$
@@ -1073,7 +1147,7 @@ To plot the direction field of the Duffing equation, @math{m*x''+c*x'+k*x+b*x^3
@c [parameters,"k=-1,m=1.0,c=0,b=1"],
@c [sliders,"k=-2:2,m=-1:1"],[tstep,0.1])$
@c ===end===
-@example
+@example maxima
@group
(%i1) plotdf([y,-(k*x + c*y + b*x^3)/m],
[parameters,"k=-1,m=1.0,c=0,b=1"],
@@ -1098,7 +1172,7 @@ the two state variables as a function of time:
@c [a,-10,2], [w,-14,14], [direction,forward],
@c [nsteps,300], [sliders,"m=0.1:1"], [versus_t,1])$
@c ===end===
-@example
+@example maxima
@group
(%i1) plotdf([w,-g*sin(a)/l - b*w/m/l], [a,w],
[parameters,"g=9.8,l=0.5,m=0.3,b=0.05"],
@@ -1145,7 +1219,7 @@ Example:
@c V: 900/((x+1)^2+y^2)^(1/2)-900/((x-1)^2+y^2)^(1/2)$
@c ploteq(V,[x,-2,2],[y,-2,2],[fieldlines,"blue"])$
@c ===end===
-@example
+@example maxima
(%i1) V: 900/((x+1)^2+y^2)^(1/2)-900/((x-1)^2+y^2)^(1/2)$
(%i2) ploteq(V,[x,-2,2],[y,-2,2],[fieldlines,"blue"])$
@end example
@@ -1227,7 +1301,7 @@ increments of 0.1 for t, use:
@c results: rk(t-x^2,x,1,[t,0,8,0.1])$
@c plot2d ([discrete, results])$
@c ===end===
-@example
+@example maxima
(%i1) results: rk(t-x^2,x,1,[t,0,8,0.1])$
(%i2) plot2d ([discrete, results])$
@end example
@@ -1253,11 +1327,15 @@ for t between 0 and 4, and with values of -1.25 and 0.75 for x and y at t=0:
@c plot2d([discrete, makelist([p[1], p[3]], p, sol)], [xlabel, "t"],
@c [ylabel, "y"])$
@c ===end===
-@example
+@example maxima
+@group
(%i1) sol: rk([4-x^2-4*y^2, y^2-x^2+1], [x, y], [-1.25, 0.75],
- [t, 0, 4, 0.02])$
+ [t,0,4,0.02])$
+@end group
+@group
(%i2) plot2d([discrete, makelist([p[1], p[3]], p, sol)], [xlabel, "t"],
[ylabel, "y"])$
+@end group
@end example
The plot will show the solution for variable @var{y} as a function of @var{t}.
commit 6067a18af6d4402f88e8eda9706e6feb96ea42ca
Author: Raymond Toy <toy...@gm...>
Date: Thu Aug 21 07:47:13 2025 -0700
Run update_examples
diff --git a/doc/info/Differential.texi b/doc/info/Differential.texi
index a9a6a7bcc..46952d585 100644
--- a/doc/info/Differential.texi
+++ b/doc/info/Differential.texi
@@ -68,33 +68,41 @@ calling @code{desolve} by using @mref{atvalue}.
@c desolve([%o1,%o2],[f(x),g(x)]);
@c [%o1,%o2],%o5,diff;
@c ===end===
-@example
+@example maxima
+@group
(%i1) 'diff(f(x),x)='diff(g(x),x)+sin(x);
d d
(%o1) -- (f(x)) = -- (g(x)) + sin(x)
dx dx
-(%i2) 'diff(g(x),x,2)='diff(f(x),x)-cos(x);
+@end group
@group
+(%i2) 'diff(g(x),x,2)='diff(f(x),x)-cos(x);
2
d d
(%o2) --- (g(x)) = -- (f(x)) - cos(x)
2 dx
dx
@end group
+@group
(%i3) atvalue('diff(g(x),x),x=0,a);
(%o3) a
+@end group
+@group
(%i4) atvalue(f(x),x=0,1);
(%o4) 1
+@end group
+@group
(%i5) desolve([%o1,%o2],[f(x),g(x)]);
- x
-(%o5) [f(x) = a %e - a + 1, g(x) =
-
- x
- cos(x) + a %e - a + g(0) - 1]
+ x
+(%o5) [f(x) = %e a - a + 1, g(x) =
+ x
+ cos(x) + %e a - a + g(0) - 1]
+@end group
+@group
(%i6) [%o1,%o2],%o5,diff;
- x x x x
-(%o6) [a %e = a %e , a %e - cos(x) = a %e - cos(x)]
-
+ x x x x
+(%o6) [%e a = %e a, %e a - cos(x) = %e a - cos(x)]
+@end group
@end example
If @code{desolve} cannot obtain a solution, it returns @code{false}.
@@ -191,43 +199,56 @@ Example:
@c ratsimp (ic2(soln2,x=0,y=0,'diff(y,x)=2));
@c bc2 (soln2,x=0,y=1,x=1,y=3);
@c ===end===
-@example
-(%i1) x^2*'diff(y,x)+3*x*y = sin(x)/x;
- 2 dy sin(x)
-(%o1) 3 x y + x -- = ------
- dx x
-(%i2) soln1:ode2(%,y,x);
- %c - cos(x)
-(%o2) y = -----------
- 3
- x
-(%i3) ic1(soln1,x = %pi,y = 0);
- 1 + cos(x)
-(%o3) y = - ----------
- 3
- x
-(%i4) 'diff(y,x,2)+y*('diff(y,x))^3 = 0;
- 2
- dy 3 d y
-(%o4) y (--) + --- = 0
- dx 2
- dx
-(%i5) soln2:ode2(%,y,x);
- 3
- 6 %k1 y + y
-(%o5) ------------ = %k2 + x
- 6
-(%i6) ratsimp(ic2(soln2,x = 0,y = 0,'diff(y,x) = 2));
- 3
- 3 y + y
-(%o6) -------- = x
- 6
-(%i7) bc2(soln2,x = 0,y = 1,x = 1,y = 3);
-
- 3
- - 10 y + y 3
-(%o7) ----------- = - - + x
- 6 2
+@example maxima
+@group
+(%i1) x^2*'diff(y,x) + 3*y*x = sin(x)/x;
+ 2 dy sin(x)
+(%o1) x -- + 3 x y = ------
+ dx x
+@end group
+@group
+(%i2) soln1: ode2(%,y,x);
+ %c - cos(x)
+(%o2) y = -----------
+ 3
+ x
+@end group
+@group
+(%i3) ic1 (soln1,x=%pi,y=0);
+ cos(x) + 1
+(%o3) y = - ----------
+ 3
+ x
+@end group
+@group
+(%i4) 'diff(y,x,2) + y*'diff(y,x)^3 = 0;
+ 2
+ d y dy 3
+(%o4) --- + y (--) = 0
+ 2 dx
+ dx
+@end group
+@group
+(%i5) soln2: ode2(%,y,x);
+ 3
+ y + 6 %k1 y
+(%o5) ------------ = x + %k2
+ 6
+@end group
+@group
+(%i6) ratsimp (ic2(soln2,x=0,y=0,'diff(y,x)=2));
+ 3
+ y + 3 y
+(%o6) -------- = x
+ 6
+@end group
+@group
+(%i7) bc2 (soln2,x=0,y=1,x=1,y=3);
+ 3
+ y - 10 y 3
+(%o7) --------- = x - -
+ 6 2
+@end group
@end example
@opencatbox{Categories:}
-----------------------------------------------------------------------
Summary of changes:
doc/info/Differential.texi | 115 +++++++++++++++-----------
doc/info/Numerical.texi | 200 +++++++++++++++++++++++++++++++--------------
2 files changed, 207 insertions(+), 108 deletions(-)
hooks/post-receive
--
Maxima CAS
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