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[Maxima-commits] [git] Maxima CAS branch rtoy-database-update-examples created. branch-5_48-base-101-gd87816d20
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From: rtoy <rt...@us...> - 2025-08-25 14:45:42
|
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-database-update-examples has been created
at d87816d205054b62dfa566c4950029bb6a182117 (commit)
- Log -----------------------------------------------------------------
commit d87816d205054b62dfa566c4950029bb6a182117
Merge: e8720d15b e9d6f170c
Author: Raymond Toy <toy...@gm...>
Date: Mon Aug 25 07:41:12 2025 -0700
Merge branch 'master' into rtoy-database-update-examples
commit e8720d15b1ef1dca39d6abe61c7cd7f33555da43
Author: Raymond Toy <toy...@gm...>
Date: Sun Aug 24 13:49:52 2025 -0700
Run update_examples to regenerate examples
Also some examples were missing the code to autogenerate them. Add
the code in.
This also allows syntax highlighting if enabled.
diff --git a/doc/info/Database.texi b/doc/info/Database.texi
index 6e4891829..aaf3940ea 100644
--- a/doc/info/Database.texi
+++ b/doc/info/Database.texi
@@ -33,15 +33,23 @@ Example:
@c xx~yy`@ + @yy`xx + `xx@@yy~;
@c listofvars (%);
@c ===end===
-@example
+@example maxima
+@group
(%i1) xx\~yy\`\@@ : 1729;
(%o1) 1729
+@end group
+@group
(%i2) declare ("~`@@", alphabetic);
(%o2) done
+@end group
+@group
(%i3) xx~yy`@@ + @@yy`xx + `xx@@@@yy~;
(%o3) `xx@@@@yy~ + @@yy`xx + 1729
+@end group
+@group
(%i4) listofvars (%);
(%o4) [@@yy`xx, `xx@@@@yy~]
+@end group
@end example
@opencatbox{Categories:}
@@ -63,18 +71,26 @@ when the symbol @var{x} is evaluated unbound.
@c aa : 1234;
@c aa + bb;
@c ===end===
-@example
+evaluation: unbound variable aa
+ -- an error. To debug this try: debugmode(true);
+@example maxima
+@group
(%i1) aa + bb;
(%o1) bb + aa
+@end group
+@group
(%i2) declare (aa, bindtest);
(%o2) done
+@end group
(%i3) aa + bb;
-aa unbound variable
- -- an error. Quitting. To debug this try debugmode(true);
+@group
(%i4) aa : 1234;
(%o4) 1234
+@end group
+@group
(%i5) aa + bb;
(%o5) bb + 1234
+@end group
@end example
@end defvr
@@ -94,15 +110,29 @@ See @mref{constantp} and @mrefdot{declare}
Example:
-@example
+@c ===beg===
+@c declare(c, constant);
+@c constantp(c);
+@c c : x;
+@c constantp(c);
+@c ===end===
+@example maxima
+@group
(%i1) declare(c, constant);
(%o1) done
+@end group
+@group
(%i2) constantp(c);
(%o2) true
+@end group
+@group
(%i3) c : x;
(%o3) x
+@end group
+@group
(%i4) constantp(c);
(%o4) false
+@end group
@end example
@opencatbox{Categories:}
@@ -140,22 +170,35 @@ Examples:
@c constantp (exp (x));
@c constantp (foo (x) + bar (%e) + baz (2));
@c ===end===
-@example
+@example maxima
+@group
(%i1) constantp (7 * sin(2));
-(%o1) true
+(%o1) true
+@end group
+@group
(%i2) constantp (rat (17/29));
-(%o2) true
+(%o2) true
+@end group
+@group
(%i3) constantp (%pi * sin(%e));
-(%o3) true
+(%o3) true
+@end group
+@group
(%i4) constantp (exp (x));
-(%o4) false
+(%o4) false
+@end group
+@group
(%i5) declare (x, constant);
-(%o5) done
+(%o5) done
+@end group
+@group
(%i6) constantp (exp (x));
-(%o6) true
+(%o6) true
+@end group
+@group
(%i7) constantp (foo (x) + bar (%e) + baz (2));
-(%o7) false
-(%i8)
+(%o7) false
+@end group
@end example
@opencatbox{Categories:}
@@ -337,15 +380,29 @@ See also @mref{declare} for more properties.
Example:
-@example
+@c ===beg===
+@c assume(a > b);
+@c is(f(a) > f(b));
+@c declare(f, increasing);
+@c is(f(a) > f(b));
+@c ===end===
+@example maxima
+@group
(%i1) assume(a > b);
(%o1) [a > b]
+@end group
+@group
(%i2) is(f(a) > f(b));
(%o2) unknown
+@end group
+@group
(%i3) declare(f, increasing);
(%o3) done
+@end group
+@group
(%i4) is(f(a) > f(b));
(%o4) true
+@end group
@end example
@opencatbox{Categories:}
@@ -368,15 +425,29 @@ See also @mref{declare} and @mrefdot{askinteger}
Example:
-@example
+@c ===beg===
+@c declare(n, even);
+@c askinteger(n, even);
+@c askinteger(n);
+@c evenp(n);
+@c ===end===
+@example maxima
+@group
(%i1) declare(n, even);
(%o1) done
+@end group
+@group
(%i2) askinteger(n, even);
(%o2) yes
+@end group
+@group
(%i3) askinteger(n);
(%o3) yes
+@end group
+@group
(%i4) evenp(n);
(%o4) false
+@end group
@end example
@opencatbox{Categories:}
@@ -418,10 +489,16 @@ nor the negation of @var{f} can be established.
See also @mref{declare} and @mrefdot{features}
-@example
+@c ===beg===
+@c declare (j, even)$
+@c featurep (j, integer);
+@c ===end===
+@example maxima
(%i1) declare (j, even)$
+@group
(%i2) featurep (j, integer);
-(%o2) true
+(%o2) true
+@end group
@end example
@opencatbox{Categories:}
@@ -474,13 +551,19 @@ Example:
@c declare (x, FOO);
@c featurep (x, FOO);
@c ===end===
-@example
+@example maxima
+@group
(%i1) declare (FOO, feature);
(%o1) done
+@end group
+@group
(%i2) declare (x, FOO);
(%o2) done
+@end group
+@group
(%i3) featurep (x, FOO);
(%o3) true
+@end group
@end example
@opencatbox{Categories:}
@@ -514,11 +597,14 @@ See also @mref{put} and @mrefdot{qput}
@c typeof (2*%e + x*%pi);
@c typeof (2*%e + %pi);
@c ===end===
-@example
+@example maxima
+@group
(%i1) put (%e, 'transcendental, 'type);
(%o1) transcendental
+@end group
(%i2) put (%pi, 'transcendental, 'type)$
(%i3) put (%i, 'algebraic, 'type)$
+@group
(%i4) typeof (expr) := block ([q],
if numberp (expr)
then return ('algebraic),
@@ -527,11 +613,16 @@ See also @mref{put} and @mrefdot{qput}
q: get (expr, 'type),
if q=false
then errcatch (error(expr,"is not numeric.")) else q)$
+@end group
+@group
(%i5) typeof (2*%e + x*%pi);
x is not numeric.
(%o5) [[transcendental, []], [algebraic, transcendental]]
+@end group
+@group
(%i6) typeof (2*%e + %pi);
(%o6) [transcendental, [algebraic, transcendental]]
+@end group
@end example
@opencatbox{Categories:}
@@ -552,13 +643,24 @@ See also @mrefdot{declare}
Example:
-@example
+@c ===beg===
+@c declare(n, integer, x, noninteger);
+@c askinteger(n);
+@c askinteger(x);
+@c ===end===
+@example maxima
+@group
(%i1) declare(n, integer, x, noninteger);
(%o1) done
+@end group
+@group
(%i2) askinteger(n);
(%o2) yes
+@end group
+@group
(%i3) askinteger(x);
(%o3) no
+@end group
@end example
@opencatbox{Categories:}
@@ -577,15 +679,26 @@ See also @mrefdot{declare}
Example:
-@example
+@c ===beg===
+@c exp(%i)^f(x);
+@c declare(f, integervalued);
+@c exp(%i)^f(x);
+@c ===end===
+@example maxima
+@group
(%i1) exp(%i)^f(x);
%i f(x)
-(%o1) (%e )
+(%o1) %e
+@end group
+@group
(%i2) declare(f, integervalued);
(%o2) done
+@end group
+@group
(%i3) exp(%i)^f(x);
%i f(x)
(%o3) %e
+@end group
@end example
@opencatbox{Categories:}
@@ -611,17 +724,22 @@ Example:
@c declare(a, nonarray);
@c a[x];
@c ===end===
-@example
+@example maxima
(%i1) a:'b$ b:'c$ c:'d$
-
+@group
(%i4) a[x];
(%o4) d
x
+@end group
+@group
(%i5) declare(a, nonarray);
(%o5) done
+@end group
+@group
(%i6) a[x];
(%o6) a
x
+@end group
@end example
@opencatbox{Categories:}
@@ -775,19 +893,36 @@ See also @mref{qput} and @mrefdot{get}
Examples:
-@example
+@c ===beg===
+@c put (foo, (a+b)^5, expr);
+@c put (foo, "Hello", str);
+@c properties (foo);
+@c get (foo, expr);
+@c get (foo, str);
+@c ===end===
+@example maxima
+@group
(%i1) put (foo, (a+b)^5, expr);
5
(%o1) (b + a)
+@end group
+@group
(%i2) put (foo, "Hello", str);
(%o2) Hello
+@end group
+@group
(%i3) properties (foo);
(%o3) [[user properties, str, expr]]
+@end group
+@group
(%i4) get (foo, expr);
5
(%o4) (b + a)
+@end group
+@group
(%i5) get (foo, str);
(%o5) Hello
+@end group
@end example
@opencatbox{Categories:}
@@ -807,22 +942,45 @@ See also @mrefdot{get}
Example:
-@example
-(%i1) foo: aa$
+@c ===beg===
+@c foo: aa$
+@c bar: bb$
+@c baz: cc$
+@c put (foo, bar, baz);
+@c properties (aa);
+@c get (aa, cc);
+@c qput (foo, bar, baz);
+@c properties (foo);
+@c get ('foo, 'baz);
+@c ===end===
+@example maxima
+(%i1) foo: aa$
(%i2) bar: bb$
(%i3) baz: cc$
+@group
(%i4) put (foo, bar, baz);
(%o4) bb
+@end group
+@group
(%i5) properties (aa);
(%o5) [[user properties, cc]]
+@end group
+@group
(%i6) get (aa, cc);
(%o6) bb
+@end group
+@group
(%i7) qput (foo, bar, baz);
(%o7) bar
+@end group
+@group
(%i8) properties (foo);
(%o8) [value, [user properties, baz]]
+@end group
+@group
(%i9) get ('foo, 'baz);
(%o9) bar
+@end group
@end example
@opencatbox{Categories:}
@@ -1136,27 +1294,47 @@ Examples:
@c is (sinh (bb - aa) > 0);
@c is (bb^2 < cc^2);
@c ===end===
-@example
+@example maxima
+@group
(%i1) assume (xx > 0, yy < -1, zz >= 0);
(%o1) [xx > 0, yy < - 1, zz >= 0]
+@end group
+@group
(%i2) assume (aa < bb and bb < cc);
(%o2) [bb > aa, cc > bb]
+@end group
+@group
(%i3) facts ();
(%o3) [xx > 0, - 1 > yy, zz >= 0, bb > aa, cc > bb]
+@end group
+@group
(%i4) is (xx > yy);
(%o4) true
+@end group
+@group
(%i5) is (yy < -yy);
(%o5) true
+@end group
+@group
(%i6) is (sinh (bb - aa) > 0);
(%o6) true
+@end group
+@group
(%i7) forget (bb > aa);
(%o7) [bb > aa]
+@end group
+@group
(%i8) prederror : false;
(%o8) false
+@end group
+@group
(%i9) is (sinh (bb - aa) > 0);
(%o9) unknown
+@end group
+@group
(%i10) is (bb^2 < cc^2);
(%o10) unknown
+@end group
@end example
@opencatbox{Categories:}
@@ -1270,40 +1448,72 @@ Examples:
@c asksign (a - b);
@c input:p;
@c ===end===
-@example
+@example maxima
(%i1) assume_pos: true$
(%i2) assume_pos_pred: symbolp$
+@group
(%i3) sign (a);
(%o3) pos
+@end group
+@group
(%i4) sign (a[1]);
(%o4) pnz
+@end group
(%i5) assume_pos_pred: lambda ([x], display (x), true)$
+@group
(%i6) asksign (a);
x = a
(%o6) pos
+@end group
+@group
(%i7) asksign (a[1]);
x = a
1
(%o7) pos
+@end group
+@group
(%i8) asksign (foo (a));
x = foo(a)
(%o8) pos
+@end group
+@group
(%i9) asksign (foo (a) + bar (b));
x = foo(a)
x = bar(b)
(%o9) pos
+@end group
+@group
(%i10) asksign (log (a));
x = a
-Is a - 1 positive, negative, or zero?
+ x = a
+
+ x = a
+
+ x = a
+
+ x = a
+ x = a
+
+ x = a
+
+ x = a
+
+ x = a
+
+@end group
+@group
+Is a - 1 positive, negative or zero?
p;
(%o10) pos
+@end group
+@group
(%i11) asksign (a - b);
x = a
@@ -1313,10 +1523,12 @@ p;
x = b
-Is b - a positive, negative, or zero?
-
+@end group
+@group
+Is b - a positive, negative or zero?
p;
(%o11) neg
+@end group
@end example
@opencatbox{Categories:}
@@ -1486,11 +1698,15 @@ Examples:
@c %pi > %e;
@c is (%pi > %e);
@c ===end===
-@example
+@example maxima
+@group
(%i1) %pi > %e;
(%o1) %pi > %e
+@end group
+@group
(%i2) is (%pi > %e);
(%o2) true
+@end group
@end example
@code{is} attempts to derive predicates from the @code{assume} database.
@@ -1502,17 +1718,27 @@ Examples:
@c is (a > c);
@c is (equal (a, c));
@c ===end===
-@example
+@example maxima
+@group
(%i1) assume (a > b);
(%o1) [a > b]
+@end group
+@group
(%i2) assume (b > c);
(%o2) [b > c]
+@end group
+@group
(%i3) is (a < b);
(%o3) false
+@end group
+@group
(%i4) is (a > c);
(%o4) true
+@end group
+@group
(%i5) is (equal (a, c));
(%o5) false
+@end group
@end example
If @code{is} can neither prove nor disprove a predicate from the @code{assume}
@@ -1525,17 +1751,20 @@ database, the global flag @code{prederror} governs the behavior of @code{is}.
@c prederror: false$
@c is (a > 0);
@c ===end===
-@example
+Unable to evaluate predicate a > 0
+ -- an error. To debug this try: debugmode(true);
+@example maxima
+@group
(%i1) assume (a > b);
(%o1) [a > b]
+@end group
(%i2) prederror: true$
(%i3) is (a > 0);
-Maxima was unable to evaluate the predicate:
-a > 0
- -- an error. Quitting. To debug this try debugmode(true);
(%i4) prederror: false$
+@group
(%i5) is (a > 0);
(%o5) unknown
+@end group
@end example
@opencatbox{Categories:}
@@ -1592,13 +1821,19 @@ Examples:
@c assume (x > 1);
@c maybe (x > 0);
@c ===end===
-@example
+@example maxima
+@group
(%i1) maybe (x > 0);
(%o1) unknown
+@end group
+@group
(%i2) assume (x > 1);
(%o2) [x > 1]
+@end group
+@group
(%i3) maybe (x > 0);
(%o3) true
+@end group
@end example
@opencatbox{Categories:}
@@ -1691,14 +1926,21 @@ Examples:
@c e : charfun ('"and" (-1 < x, x < 1))$
@c [subst (x = -1, e), subst (x = 0, e), subst (x = 1, e)];
@c ===end===
-@example
+@example maxima
+@group
(%i1) charfun (x < 1);
(%o1) charfun(x < 1)
+@end group
+@group
(%i2) subst (x = -1, %);
(%o2) 1
+@end group
(%i3) e : charfun ('"and" (-1 < x, x < 1))$
+@group
(%i4) [subst (x = -1, e), subst (x = 0, e), subst (x = 1, e)];
-(%o4) [0, 1, 0]
+(%o4) [charfun((- 1 < - 1) and (- 1 < 1)),
+ charfun((- 1 < 0) and (0 < 1)), charfun((- 1 < 1) and (1 < 1))]
+@end group
@end example
@opencatbox{Categories:}
@@ -1726,19 +1968,31 @@ Examples:
@c compare (1/x, 0);
@c compare (x, abs(x));
@c ===end===
-@example
+@example maxima
+@group
(%i1) compare (1, 2);
(%o1) <
+@end group
+@group
(%i2) compare (1, x);
(%o2) unknown
+@end group
+@group
(%i3) compare (%i, %i);
(%o3) =
+@end group
+@group
(%i4) compare (%i, %i + 1);
(%o4) notcomparable
+@end group
+@group
(%i5) compare (1/x, 0);
(%o5) #
+@end group
+@group
(%i6) compare (x, abs(x));
(%o6) <=
+@end group
@end example
The function @code{compare} doesn't try to determine whether the real domains of
@@ -1747,9 +2001,11 @@ its arguments are nonempty; thus
@c ===beg===
@c compare (acos (x^2 + 1), acos (x^2 + 1) + 1);
@c ===end===
-@example
+@example maxima
+@group
(%i1) compare (acos (x^2 + 1), acos (x^2 + 1) + 1);
(%o1) <
+@end group
@end example
@c IT IS NOT QUITE TRUE, WHAT ABOUT x=0 ?
@@ -1800,14 +2056,20 @@ By itself, @code{equal} does not evaluate or simplify.
@c equal (x, x + 1);
@c equal (x, y);
@c ===end===
-@example
+@example maxima
+@group
(%i1) equal (x^2 - 1, (x + 1) * (x - 1));
2
(%o1) equal(x - 1, (x - 1) (x + 1))
+@end group
+@group
(%i2) equal (x, x + 1);
(%o2) equal(x, x + 1)
+@end group
+@group
(%i3) equal (x, y);
(%o3) equal(x, y)
+@end group
@end example
The function @code{is} attempts to evaluate @code{equal} to a Boolean value.
@@ -1826,25 +2088,43 @@ even if they are not syntactically equal (i.e., identical).
@c is (equal (x, y));
@c is (x = y);
@c ===end===
-@example
+@example maxima
+@group
(%i1) ratsimp (x^2 - 1 - (x + 1) * (x - 1));
(%o1) 0
+@end group
+@group
(%i2) is (equal (x^2 - 1, (x + 1) * (x - 1)));
(%o2) true
+@end group
+@group
(%i3) is (x^2 - 1 = (x + 1) * (x - 1));
(%o3) false
+@end group
+@group
(%i4) ratsimp (x - (x + 1));
(%o4) - 1
+@end group
+@group
(%i5) is (equal (x, x + 1));
(%o5) false
+@end group
+@group
(%i6) is (x = x + 1);
(%o6) false
+@end group
+@group
(%i7) ratsimp (x - y);
(%o7) x - y
+@end group
+@group
(%i8) is (equal (x, y));
(%o8) unknown
+@end group
+@group
(%i9) is (x = y);
(%o9) false
+@end group
@end example
When @code{is} fails to reduce @code{equal} to @code{true} or @code{false},
@@ -1858,23 +2138,32 @@ the result is governed by the global flag @code{prederror}.
@c prederror : false;
@c is (equal (aa, bb));
@c ===end===
-@example
+ 2 2
+Unable to evaluate predicate equal(x + 2 x + 1, x - 2 x - 1)
+ -- an error. To debug this try: debugmode(true);
+@example maxima
+@group
(%i1) [aa : x^2 + 2*x + 1, bb : x^2 - 2*x - 1];
2 2
(%o1) [x + 2 x + 1, x - 2 x - 1]
+@end group
+@group
(%i2) ratsimp (aa - bb);
(%o2) 4 x + 2
+@end group
+@group
(%i3) prederror : true;
(%o3) true
+@end group
(%i4) is (equal (aa, bb));
-Maxima was unable to evaluate the predicate:
- 2 2
-equal(x + 2 x + 1, x - 2 x - 1)
- -- an error. Quitting. To debug this try debugmode(true);
+@group
(%i5) prederror : false;
(%o5) false
+@end group
+@group
(%i6) is (equal (aa, bb));
(%o6) unknown
+@end group
@end example
Some operators evaluate @code{equal} and @code{notequal} to @code{true} or
@@ -1886,16 +2175,24 @@ Some operators evaluate @code{equal} and @code{notequal} to @code{true} or
@c eq_2 : equal (y^2 + 2*y + 1, (y + 1)^2);
@c [eq_1 and eq_2, eq_1 or eq_2, not eq_1];
@c ===end===
-@example
+@example maxima
+@group
(%i1) if equal (y, y - 1) then FOO else BAR;
(%o1) BAR
+@end group
+@group
(%i2) eq_1 : equal (x, x + 1);
(%o2) equal(x, x + 1)
+@end group
+@group
(%i3) eq_2 : equal (y^2 + 2*y + 1, (y + 1)^2);
2 2
(%o3) equal(y + 2 y + 1, (y + 1) )
+@end group
+@group
(%i4) [eq_1 and eq_2, eq_1 or eq_2, not eq_1];
(%o4) [false, true, true]
+@end group
@end example
Because @code{not @var{expr}} causes evaluation of @var{expr},
@@ -1906,11 +2203,15 @@ Because @code{not @var{expr}} causes evaluation of @var{expr},
@c [notequal (2*z, 2*z - 1), not equal (2*z, 2*z - 1)];
@c is (notequal (2*z, 2*z - 1));
@c ===end===
-@example
+@example maxima
+@group
(%i1) [notequal (2*z, 2*z - 1), not equal (2*z, 2*z - 1)];
(%o1) [notequal(2 z, 2 z - 1), true]
+@end group
+@group
(%i2) is (notequal (2*z, 2*z - 1));
(%o2) true
+@end group
@end example
@opencatbox{Categories:}
@@ -1938,27 +2239,47 @@ Examples:
@c notequal (a, b);
@c maybe (notequal (a, b));
@c ===end===
-@example
+@example maxima
+@group
(%i1) equal (a, b);
(%o1) equal(a, b)
+@end group
+@group
(%i2) maybe (equal (a, b));
(%o2) unknown
+@end group
+@group
(%i3) notequal (a, b);
(%o3) notequal(a, b)
+@end group
+@group
(%i4) not equal (a, b);
(%o4) notequal(a, b)
+@end group
+@group
(%i5) maybe (notequal (a, b));
(%o5) unknown
+@end group
+@group
(%i6) assume (a > b);
(%o6) [a > b]
+@end group
+@group
(%i7) equal (a, b);
(%o7) equal(a, b)
+@end group
+@group
(%i8) maybe (equal (a, b));
(%o8) false
+@end group
+@group
(%i9) notequal (a, b);
(%o9) notequal(a, b)
+@end group
+@group
(%i10) maybe (notequal (a, b));
(%o10) true
+@end group
@end example
@opencatbox{Categories:}
-----------------------------------------------------------------------
hooks/post-receive
--
Maxima CAS
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