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[Maxima-commits] [git] Maxima CAS branch rtoy-mathfunctions-update-examples created. branch-5_48-base-73-g1a3ababfb
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From: rtoy <rt...@us...> - 2025-08-23 22:25:03
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This is an automated email from the git hooks/post-receive script. It was
generated because a ref change was pushed to the repository containing
the project "Maxima CAS".
The branch, rtoy-mathfunctions-update-examples has been created
at 1a3ababfb7e40af302a4ab845c78f3ea3dd3bf32 (commit)
- Log -----------------------------------------------------------------
commit 1a3ababfb7e40af302a4ab845c78f3ea3dd3bf32
Author: Raymond Toy <toy...@gm...>
Date: Sat Aug 23 15:24:38 2025 -0700
Run update_examples to regenerate examples
This also allows syntax highlighting if enabled.
diff --git a/doc/info/MathFunctions.texi.m4 b/doc/info/MathFunctions.texi.m4
index a97f6df96..fa376e956 100644
--- a/doc/info/MathFunctions.texi.m4
+++ b/doc/info/MathFunctions.texi.m4
@@ -46,7 +46,7 @@ distributes over the elements of a list.
@c abs(%e+%i);
@c abs([inf, infinity, minf]);
@c ===end===
-@example
+@example maxima
@group
(%i1) abs([-4, 0, 1, 1+%i]);
(%o1) [4, 0, 1, sqrt(2)]
@@ -74,7 +74,7 @@ Simplification of expressions containing @code{abs}:
@c abs(abs(x));
@c abs(conjugate(x));
@c ===end===
-@example
+@example maxima
@group
(%i1) abs(x^2);
2
@@ -109,7 +109,7 @@ transform of @code{abs}: see @mrefdot{laplace}
@c integrate(abs(x),x,-2,%pi);
@c laplace(abs(x),x,s);
@c ===end===
-@example
+@example maxima
@group
(%i1) diff(x*abs(x),x),expand;
(%o1) 2 abs(x)
@@ -183,7 +183,7 @@ Here are examples of the simplifications that @code{ceiling} knows about:
@c ceiling (x);
@c tex (ceiling (a));
@c ===end===
-@example
+@example maxima
@group
(%i1) ceiling (ceiling (x));
(%o1) ceiling(x)
@@ -224,7 +224,7 @@ can use this information; for example:
@c floor (f(x));
@c ceiling (f(x) - 1);
@c ===end===
-@example
+@example maxima
(%i1) declare (f, integervalued)$
@group
(%i2) floor (f(x));
@@ -253,7 +253,7 @@ Example use:
@c unitfrac (36/37);
@c apply ("+", %);
@c ===end===
-@example
+@example maxima
@group
(%i1) unitfrac(r) := block([uf : [], q],
if not(ratnump(r)) then
@@ -353,7 +353,7 @@ are examples of the simplifications that @code{floor} knows about:
@c floor (x);
@c tex (floor (a));
@c ===end===
-@example
+@example maxima
@group
(%i1) floor (ceiling (x));
(%o1) ceiling(x)
@@ -394,7 +394,7 @@ can use this information; for example:
@c floor (f(x));
@c ceiling (f(x) - 1);
@c ===end===
-@example
+@example maxima
(%i1) declare (f, integervalued)$
@group
(%i2) floor (f(x));
@@ -654,7 +654,7 @@ calculates the absolute value of @code{x + %i*y} as
@c cabs (exp (3/2 * %pi * %i));
@c cabs (17 * exp (2 * %i));
@c ===end===
-@example
+@example maxima
@group
(%i1) cabs (1);
(%o1) 1
@@ -691,7 +691,7 @@ some properties of the variables involved not being known:
@c assume(a>0,b>0);
@c cabs (a+%i*b);
@c ===end===
-@example
+@example maxima
@group
(%i1) cabs (a+%i*b);
2 2
@@ -746,7 +746,7 @@ Examples with @mref{sqrt} and @mrefdot{sin}
@c cabs(sqrt(1+%i*x));
@c cabs(sin(x+%i*y));
@c ===end===
-@example
+@example maxima
@group
(%i1) cabs(sqrt(1+%i*x));
2 1/4
@@ -765,7 +765,7 @@ the calculation of the absolute value with a complex argument:
@c ===beg===
@c cabs(erf(x+%i*y));
@c ===end===
-@example
+@example maxima
@group
(%i1) cabs(erf(x+%i*y));
2
@@ -786,7 +786,7 @@ example for @mrefdot{bessel_j}
@c ===beg===
@c cabs(bessel_j(1,%i));
@c ===end===
-@example
+@example maxima
@group
(%i1) cabs(bessel_j(1,%i));
(%o1) bessel_i(1, 1)
@@ -822,7 +822,7 @@ Examples:
@c carg (exp (3/2 * %pi * %i));
@c carg (17 * exp (2 * %i));
@c ===end===
-@example
+@example maxima
@group
(%i1) carg (1);
(%o1) 0
@@ -867,7 +867,7 @@ some properties of the variables involved not being known:
@c assume(a>0,b>0);
@c carg (a+%i*b);
@c ===end===
-@example
+@example maxima
@group
(%i1) carg (a+%i*b);
(%o1) atan2(b, a)
@@ -910,7 +910,7 @@ Returns the complex conjugate of @var{x}.
@c conjugate (ii);
@c conjugate (xx + yy);
@c ===end===
-@example
+@example maxima
@group
(%i1) declare ([aa, bb], real, cc, complex, ii, imaginary);
(%o1) done
@@ -959,7 +959,7 @@ Example:
@c imagpart (1);
@c imagpart (sqrt(2)*%i);
@c ===end===
-@example
+@example maxima
@group
(%i1) imagpart (a+b*%i);
(%o1) b
@@ -999,11 +999,11 @@ Example:
@c polarform(1+%i);
@c polarform(1+2*%i);
@c ===end===
-@example
+@example maxima
@group
(%i1) polarform(a+b*%i);
- 2 2 %i atan2(b, a)
-(%o1) sqrt(b + a ) %e
+ %i atan2(b, a) 2 2
+(%o1) %e sqrt(b + a )
@end group
@group
(%i2) polarform(1+%i);
@@ -1041,7 +1041,7 @@ Example:
@c realpart (sqrt(2)*%i);
@c realpart (1);
@c ===end===
-@example
+@example maxima
@group
(%i1) realpart (a+b*%i);
(%o1) a
@@ -1079,7 +1079,7 @@ Example:
@c rectform(sqrt(b^2+a^2)*%e^(%i*atan2(b, a)));
@c rectform(sqrt(5)*%e^(%i*atan(2)));
@c ===end===
-@example
+@example maxima
@group
(%i1) rectform(sqrt(2)*%e^(%i*%pi/4));
(%o1) %i + 1
@@ -1151,7 +1151,7 @@ Examples:
@c binomial (x + 7, x);
@c binomial (11, y);
@c ===end===
-@example
+@example maxima
@group
(%i1) binomial (11, 7);
(%o1) 330
@@ -1204,7 +1204,7 @@ Example:
@c (n + 1)*(n + 1)*n!;
@c factcomb (%);
@c ===end===
-@example
+@example maxima
@group
(%i1) sumsplitfact;
(%o1) true
@@ -1287,7 +1287,7 @@ evaluated in float or bigfloat precision.
@c [4,77!, (1.0+%i)!];
@c [2.86b0!, (1.0b0+%i)!];
@c ===end===
-@example
+@example maxima
@group
(%i1) factlim : 10;
(%o1) 10
@@ -1317,7 +1317,7 @@ operand.
@c [(%i + 1)!, %pi!, %e!, (cos(1) + sin(1))!];
@c ev (%, numer, %enumer);
@c ===end===
-@example
+@example maxima
@group
(%i1) [(%i + 1)!, %pi!, %e!, (cos(1) + sin(1))!];
(%o1) [(%i + 1)!, %pi!, %e!, (sin(1) + cos(1))!]
@@ -1349,7 +1349,7 @@ Thus @code{x!} may be replaced even in a quoted expression.
@c ===beg===
@c '([0!, (7/2)!, 4.77!, 8!, 20!]);
@c ===end===
-@example
+@example maxima
@group
(%i1) '([0!, (7/2)!, 4.77!, 8!, 20!]);
105 sqrt(%pi)
@@ -1364,7 +1364,7 @@ Maxima knows the derivative of the factorial function.
@c ===beg===
@c diff(x!,x);
@c ===end===
-@example
+@example maxima
@group
(%i1) diff(x!,x);
(%o1) x! psi (x + 1)
@@ -1378,7 +1378,7 @@ simplification of expressions with the factorial function.
@c ===beg===
@c (n+1)!/n!,factorial_expand:true;
@c ===end===
-@example
+@example maxima
@group
(%i1) (n+1)!/n!,factorial_expand:true;
(%o1) n + 1
@@ -1453,7 +1453,7 @@ which differ by an integer.
@c n!/(n+2)!;
@c minfactorial (%);
@c ===end===
-@example
+@example maxima
@group
(%i1) n!/(n+2)!;
n!
@@ -1490,7 +1490,7 @@ When @code{sumsplitfact} is @code{false},
@c n!/(n+2)!;
@c factcomb(%);
@c ===end===
-@example
+@example maxima
@group
(%i1) sumsplitfact;
(%o1) true
@@ -1581,7 +1581,7 @@ When @code{%emode} is @code{false}, no special simplification of
@c %e^(%pi*%i*120/144);
@c %e^(%pi*%i*121/144);
@c ===end===
-@example
+@example maxima
@group
(%i1) %emode;
(%o1) true
@@ -1651,7 +1651,7 @@ See also @mref{ev} and @mrefdot{numer}
@c 2*%e^1;
@c 2*%e^x;
@c ===end===
-@example
+@example maxima
@group
(%i1) %enumer;
(%o1) false
@@ -1723,7 +1723,7 @@ See @mrefdot{%emode}
@c demoivre: not demoivre;
@c %e^(a + b*%i);
@c ===end===
-@example
+@example maxima
@group
(%i1) demoivre;
(%o1) false
@@ -1804,87 +1804,65 @@ Examples:
@c map (lambda ([x], li [2] (x)), L);
@c map (lambda ([x], li [3] (x)), L);
@c ===end===
-@example
+RETRIEVE: End of file encountered.
+ -- an error. To debug this try: debugmode(true);
+@example maxima
@group
(%i1) assume (x > 0);
(%o1) [x > 0]
@end group
@group
(%i2) integrate ((log (1 - t)) / t, t, 0, x);
-(%o2) - li (x)
- 2
+Is x - 1 positive, negative or zero?
+
@end group
@group
-(%i3) li[4](1);
- 4
- %pi
-(%o3) ----
- 90
+Is x - 1 positive, negative or zero?
+li[4](1);
@end group
@group
-(%i4) li[5](1);
-(%o4) zeta(5)
+Is x - 1 positive, negative or zero?
+li[5](1);
@end group
@group
-(%i5) li[2](1/2);
- 2 2
- %pi log (2)
-(%o5) ---- - -------
- 12 2
+Is x - 1 positive, negative or zero?
+li[2](1/2);
@end group
@group
-(%i6) li[2](%i);
- 2
- %pi
-(%o6) %catalan %i - ----
- 48
+Is x - 1 positive, negative or zero?
+li[2](%i);
@end group
@group
-(%i7) li[2](1+%i);
- 2
- %i %pi log(2) %pi
-(%o7) ------------- + ---- + %catalan %i
- 4 16
+Is x - 1 positive, negative or zero?
+li[2](1+%i);
@end group
@group
-(%i8) li [2] (7);
-(%o8) li (7)
- 2
+Is x - 1 positive, negative or zero?
+li [2] (7);
@end group
@group
-(%i9) li [2] (7), numer;
-(%o9) 1.2482731820994244 - 6.1132570288179915 %i
+Is x - 1 positive, negative or zero?
+li [2] (7), numer;
@end group
@group
-(%i10) li [3] (7);
-(%o10) li (7)
- 3
+Is x - 1 positive, negative or zero?
+li [3] (7);
@end group
@group
-(%i11) li [2] (7), numer;
-(%o11) 1.2482731820994244 - 6.1132570288179915 %i
+Is x - 1 positive, negative or zero?
+li [2] (7), numer;
@end group
@group
-(%i12) L : makelist (i / 4.0, i, 0, 8);
-(%o12) [0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0]
+Is x - 1 positive, negative or zero?
+L : makelist (i / 4.0, i, 0, 8);
@end group
@group
-(%i13) map (lambda ([x], li [2] (x)), L);
-(%o13) [0.0, 0.2676526390827326, 0.5822405264650125,
-0.978469392930306, 1.6449340668482264,
-2.1901770114416452 - 0.7010261415046585 %i,
-2.3743952702724798 - 1.2738062049196004 %i,
-2.448686765338203 - 1.7580848482107874 %i,
-2.4674011002723395 - 2.177586090303602 %i]
+Is x - 1 positive, negative or zero?
+map (lambda ([x], li [2] (x)), L);
@end group
@group
-(%i14) map (lambda ([x], li [3] (x)), L);
-(%o14) [0.0, 0.25846139579657335, 0.5372131936080402,
-0.8444258088622044, 1.2020569031595942,
-1.6428668813178295 - 0.07821473138972386 %i,
-2.0608775073202805 - 0.258241985293288 %i,
-2.433418898226189 - 0.49192601879440423 %i,
-2.762071906228924 - 0.7546938294602477 %i]
+Is x - 1 positive, negative or zero?
+map (lambda ([x], li [3] (x)), L);
@end group
@end example
@@ -2015,7 +1993,7 @@ subexpressions of the form @code{a1*log(b1) + a2*log(b2) + c} into
@c 2*(a*log(x) + 2*a*log(y))$
@c logcontract(%);
@c ===end===
-@example
+@example maxima
(%i1) 2*(a*log(x) + 2*a*log(y))$
@group
(%i2) logcontract(%);
@@ -2062,7 +2040,7 @@ When @code{logexpand} is @code{true},
@c ===beg===
@c log(n^2), logexpand=true;
@c ===end===
-@example
+@example maxima
@group
(%i1) log(n^2), logexpand=true;
(%o1) 2 log(n)
@@ -2075,7 +2053,7 @@ When @code{logexpand} is @code{all},
@c ===beg===
@c log(10*x), logexpand=all;
@c ===end===
-@example
+@example maxima
@group
(%i1) log(10*x), logexpand=all;
(%o1) log(x) + log(10)
@@ -2089,7 +2067,7 @@ for rational numbers @code{a/b} with @code{a#1}.
@c ===beg===
@c log(a/(n + 1)), logexpand=super;
@c ===end===
-@example
+@example maxima
@group
(%i1) log(a/(n + 1)), logexpand=super;
(%o1) log(a) - log(n + 1)
@@ -2104,7 +2082,7 @@ the logarithm of a product expression simplifies to a summation of logarithms.
@c log(my_product), logexpand=all;
@c log(my_product), logexpand=super;
@c ===end===
-@example
+@example maxima
@group
(%i1) my_product : product (X(i), i, 1, n);
n
@@ -2146,7 +2124,7 @@ these simplifications are disabled.
@c log(a/(n + 1));
@c log ('product (X(i), i, 1, n));
@c ===end===
-@example
+@example maxima
(%i1) logexpand : false $
@group
(%i2) log(n^2);
@@ -2681,7 +2659,7 @@ Examples:
@c [cos (%pi/3), cos (10*%pi/3), tan (10*%pi/3),
@c cos (sqrt(2)*%pi/3)];
@c ===end===
-@example
+@example maxima
(%i1) %piargs : false$
@group
(%i2) [sin (%pi), sin (%pi/2), sin (%pi/3)];
@@ -2737,7 +2715,7 @@ multiplied by an integer variable.
@c [sin (%pi * n), cos (%pi * m), sin (%pi/2 * m),
@c cos (%pi/2 * m)];
@c ===end===
-@example
+@example maxima
(%i1) declare (n, integer, m, even)$
@group
(%i2) [sin (%pi * n), cos (%pi * m), sin (%pi/2 * m),
@@ -2789,7 +2767,7 @@ Examples:
@c %iargs : true$
@c [sin (%i * x), cos (%i * x), tan (%i * x)];
@c ===end===
-@example
+@example maxima
(%i1) %iargs : false$
@group
(%i2) [sin (%i * x), cos (%i * x), tan (%i * x)];
@@ -2809,7 +2787,7 @@ Even when the argument is demonstrably real, the simplification is applied.
@c [featurep (x, imaginary), featurep (x, real)];
@c sin (%i * x);
@c ===end===
-@example
+@example maxima
(%i1) declare (x, imaginary)$
@group
(%i2) [featurep (x, imaginary), featurep (x, real)];
@@ -2879,7 +2857,7 @@ Examples:
@c assume(x>0, x<2*%pi)$
@c sin(x / 2);
@c ===end===
-@example
+@example maxima
(%i1) halfangles : false$
@group
(%i2) sin (x / 2);
@@ -2972,7 +2950,7 @@ Examples:
@c x+sin(3*x)/sin(x),trigexpand=true,expand;
@c trigexpand(sin(10*x+y));
@c ===end===
-@example
+@example maxima
@group
(%i1) x+sin(3*x)/sin(x),trigexpand=true,expand;
2 2
@@ -3065,7 +3043,7 @@ See also @mref{poissimp}.
@c ===beg===
@c trigreduce(-sin(x)^2+3*cos(x)^2+x);
@c ===end===
-@example
+@example maxima
@group
(%i1) trigreduce(-sin(x)^2+3*cos(x)^2+x);
cos(2 x) cos(2 x) 1 1
@@ -3161,7 +3139,7 @@ possible.
@c ===beg===
@c trigrat(sin(3*a)/sin(a+%pi/3));
@c ===end===
-@example
+@example maxima
@group
(%i1) trigrat(sin(3*a)/sin(a+%pi/3));
(%o1) sqrt(3) sin(2 a) + cos(2 a) - 1
@@ -3179,7 +3157,7 @@ Addison-Wesley), section 1.5.5, Morley theorem.
@c ac2 : ba^2 + bc^2 - 2*bc*ba*cos(b);
@c trigrat (ac2);
@c ===end===
-@example
+@example maxima
(%i1) c : %pi/3 - a - b$
@group
(%i2) bc : sin(a)*sin(3*c)/sin(a+b);
@@ -3374,7 +3352,7 @@ Examples:
@c random (10.0);
@c random (100.0);
@c ===end===
-@example
+@example maxima
(%i1) s1: make_random_state (654321)$
@group
(%i2) set_random_state (s1);
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