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[Maxima-commits] CVS: maxima/doc/info Operators.texi,1.17,1.18 Program.texi,1.17,1.18
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From: Robert D. <rob...@us...> - 2005-05-23 05:43:42
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Update of /cvsroot/maxima/maxima/doc/info In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv18309 Modified Files: Operators.texi Program.texi Log Message: New items maybe and notequal. Revision of =, #, equal, is, prederror, and if, including examples for # and is. Index: Operators.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Operators.texi,v retrieving revision 1.17 retrieving revision 1.18 diff -u -d -r1.17 -r1.18 --- Operators.texi 21 Apr 2005 04:58:34 -0000 1.17 +++ Operators.texi 23 May 2005 05:43:28 -0000 1.18 @@ -152,7 +152,35 @@ @end deffn @deffn operator "#" -The logical operator "Not equals". +Represents the negation of syntactic equality @code{=}. + +Note that because of the rules for evaluation of predicate expressions +(in particular because @code{not @var{expr}} causes evaluation of @var{expr}), +@code{not @var{a} = @var{b}} is not equivalent to @code{@var{a} # @var{b}} in some cases. + +Examples: +@c GENERATED FROM: +@c a = b; +@c is (a = b); +@c a # b; +@c not a = b; +@c is (a # b); +@c is (not a = b); + +@example +(%i1) a = b; +(%o1) a = b +(%i2) is (a = b); +(%o2) false +(%i3) a # b; +(%o3) a # b +(%i4) not a = b; +(%o4) true +(%i5) is (a # b); +(%o5) true +(%i6) is (not a = b); +(%o6) true +@end example @end deffn @@ -207,6 +235,11 @@ Maxima it denotes a total relation that holds between two expressions if and only if the expressions are syntactically identical. +The negation of @code{=} is represented by @code{#}. +Note that because of the rules for evaluation of predicate expressions +(in particular because @code{not @var{expr}} causes evaluation of @var{expr}), +@code{not @var{a} = @var{b}} is not equivalent to @code{@var{a} # @var{b}} in some cases. + @end deffn @c NEEDS EXAMPLES @@ -366,6 +399,11 @@ All variables occurring in @var{expr_1} and @var{expr_2} are presumed to be real valued. +The negation of @code{equal} is @code{notequal}. +Note that because of the rules for evaluation of predicate expressions +(in particular because @code{not @var{expr}} causes evaluation of @var{expr}), +@code{notequal} is not equivalent to @code{not equal} in some cases. + @c COPY THIS TO DESCRIPTION OF is @code{ev (@var{expr}, pred)} is equivalent to @code{is (@var{expr})}. @@ -380,6 +418,62 @@ @end deffn +@deffn {Function} notequal (@var{expr_1}, @var{expr_2}) +Represents the negation of @code{equal (@var{expr_1}, @var{expr_2})}. + +Note that because of the rules for evaluation of predicate expressions +(in particular because @code{not @var{expr}} causes evaluation of @var{expr}), +@code{notequal} is not equivalent to @code{not equal} in some cases. + +Examples: +@c GENERATED FROM: +@c equal (a, b); +@c maybe (equal (a, b)); +@c notequal (a, b); +@c not equal (a, b); +@c maybe (notequal (a, b)); +@c maybe (not equal (a, b)); +@c assume (a > b); +@c equal (a, b); +@c maybe (equal (a, b)); +@c notequal (a, b); +@c not equal (a, b); +@c maybe (notequal (a, b)); +@c maybe (not equal (a, b)); + +@example +(%i1) equal (a, b); +(%o1) equal(a, b) +(%i2) maybe (equal (a, b)); +(%o2) unknown +(%i3) notequal (a, b); +(%o3) notequal(a, b) +(%i4) not equal (a, b); +`macsyma' was unable to evaluate the predicate: +equal(a, b) + -- an error. Quitting. To debug this try debugmode(true); +(%i5) maybe (notequal (a, b)); +(%o5) unknown +(%i6) maybe (not equal (a, b)); +(%o6) unknown +(%i7) assume (a > b); +(%o7) [a > b] +(%i8) equal (a, b); +(%o8) equal(a, b) +(%i9) maybe (equal (a, b)); +(%o9) false +(%i10) notequal (a, b); +(%o10) notequal(a, b) +(%i11) not equal (a, b); +(%o11) true +(%i12) maybe (notequal (a, b)); +(%o12) true +(%i13) maybe (not equal (a, b)); +(%o13) true +@end example + +@end deffn + @c NEEDS EXPANSION, CLARIFICATION, AND EXAMPLES @c NOTE THAT eval IS RECOGNIZED ONLY AS AN ARGUMENT TO ev, @c BUT FOR SOME REASON eval DOES NOT HAVE THE evflag PROPERTY @@ -433,15 +527,105 @@ @end deffn -@c NEEDS CLARIFICATION AND EXAMPLES @deffn {Function} is (@var{expr}) -Attempts to determine whether @var{expr} (which must evaluate to a -predicate) is provable from the facts in the current data base. @code{is} -returns @code{true} if the predicate is true for all values of its variables -consistent with the data base and returns @code{false} if it is false for all -such values. Otherwise, its action depends on the setting of the -switch @code{prederror}. @code{is} errs out if the value of -@code{prederror} is @code{true} and returns @code{unknown} if @code{prederror} is @code{false}. +Attempts to determine whether the predicate @var{expr} +is provable from the facts in the @code{assume} database. + +If the predicate is provably @code{true} or @code{false}, +@code{is} returns @code{true} or @code{false}, respectively. +Otherwise, the return value is controlled by the global flag @code{prederror}. +When @code{prederror} is @code{false}, @code{is} returns @code{unknown} for +a predicate which cannot be proven nor disproven, +and reports an error otherwise. + +See also @code{assume}, @code{facts}, and @code{maybe}. + +Examples: + +@code{is} causes evaluation of predicates. +@c GENERATED FROM: +@c %pi > %e; +@c is (%pi > %e); + +@example +(%i1) %pi > %e; +(%o1) %pi > %e +(%i2) is (%pi > %e); +(%o2) true +@end example + +@code{is} attempts to derive predicates from the @code{assume} database. +@c GENERATED FROM: +@c assume (a > b); +@c assume (b > c); +@c is (a < b); +@c is (a > c); +@c is (equal (a, c)); + +@example +(%i1) assume (a > b); +(%o1) [a > b] +(%i2) assume (b > c); +(%o2) [b > c] +(%i3) is (a < b); +(%o3) false +(%i4) is (a > c); +(%o4) true +(%i5) is (equal (a, c)); +(%o5) false +@end example + +If @code{is} can neither prove nor disprove a predicate from the @code{assume} database, +the global flag @code{prederror} governs the behavior of @code{is}. +@c GENERATED FROM: +@c assume (a > b); +@c prederror: true$ +@c is (a > 0); +@c prederror: false$ +@c is (a > 0); + +@example +(%i1) assume (a > b); +(%o1) [a > b] +(%i2) prederror: true$ +(%i3) is (a > 0); +`macsyma' was unable to evaluate the predicate: +a > 0 + -- an error. Quitting. To debug this try debugmode(true); +(%i4) prederror: false$ +(%i5) is (a > 0); +(%o5) unknown +@end example + +@end deffn + +@deffn {Function} maybe (@var{expr}) +Attempts to determine whether the predicate @var{expr} +is provable from the facts in the @code{assume} database. + +If the predicate is provably @code{true} or @code{false}, +@code{maybe} returns @code{true} or @code{false}, respectively. +Otherwise, @code{maybe} returns @code{unknown}. + +@code{maybe} is functionally equivalent to @code{is} with @code{prederror: false}, +but the result is computed without actually assigning a value to @code{prederror}. + +See also @code{assume}, @code{facts}, and @code{is}. + +Examples: +@c GENERATED FROM: +@c maybe (x > 0); +@c assume (x > 1); +@c maybe (x > 0); + +@example +(%i1) maybe (x > 0); +(%o1) unknown +(%i2) assume (x > 1); +(%o2) [x > 1] +(%i3) maybe (x > 0); +(%o3) true +@end example @end deffn Index: Program.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Program.texi,v retrieving revision 1.17 retrieving revision 1.18 diff -u -d -r1.17 -r1.18 --- Program.texi 18 May 2005 05:12:49 -0000 1.17 +++ Program.texi 23 May 2005 05:43:28 -0000 1.18 @@ -359,25 +359,24 @@ an expression which evaluates to @code{true} or @code{false} and is composed of relational and logical operators which are as follows: -@c - SEEMS LIKE THIS TABLE REALLY WANTS TO BE IN A DISCUSSION OF PREDICATE FUNCTIONS; THIS IS OK I GUESS -@c - NEED TO FIGURE OUT WHETHER # IS "not =" OR "not equal" -@c WHEN WE HAVE AN ANSWER, MAKE A NOTE HERE AND ALSO IN DESCRIPTIONS OF = AND equal -@c - REFORMAT THIS TABLE USING TEXINFO MARKUP +@c - SEEMS LIKE THIS TABLE WANTS TO BE IN A DISCUSSION OF PREDICATE FUNCTIONS; PRESENT LOCATION IS OK I GUESS +@c - REFORMAT THIS TABLE USING TEXINFO MARKUP (MAYBE) @example -Operation Symbol Type +Operation Symbol Type -less than < relational infix -less than <= - or equal to relational infix -syntactic equality = relational infix -equivalence equal relational function -not equal to # relational infix -greater than >= - or equal to relational infix -greater than > relational infix -and and logical infix -or or logical infix -not not logical prefix +less than < relational infix +less than <= + or equal to relational infix +equality (syntactic) = relational infix +negation of = # relational infix +equality (value) equal relational function +negation of equal notequal relational function +greater than >= + or equal to relational infix +greater than > relational infix +and and logical infix +or or logical infix +not not logical prefix @end example @end deffn @@ -473,8 +472,11 @@ evaluate to either @code{true} or @code{false}. If @code{false}, @code{unknown} is returned -instead in this case. The @code{prederror:false} mode is not supported in -translated code. +instead in this case. The @code{prederror: false} mode is not supported in +translated code; +however, @code{maybe} is supported in translated code. + +See also @code{is} and @code{maybe}. @end defvr |