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(Default Simplifications, Making Selections, Customizing Calc):

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Clarify associativity of multiplication.
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Jay Belanger 2007-10-25 03:41:31 +00:00
parent 70b8d0a4a3
commit 45b778a677
2 changed files with 31 additions and 23 deletions
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doc/misc/ChangeLog
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@ -1,3 +1,8 @@
2007-10-25 Jay Belanger <jay.p.belanger@gmail.com>
* calc.texi (Default Simplifications, Making Selections)
(Customizing Calc): Clarify associativity of multiplication.
2007-10-23 Michael Albinus <michael.albinus@gmx.de>
* tramp.texi (Traces and Profiles): Simplify loop over

49
doc/misc/calc.texi
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@ -21357,16 +21357,17 @@ entire four-term sum.
@pindex calc-break-selections
The @kbd{j b} (@code{calc-break-selections}) command controls a mode
in which the ``deep structure'' of these associative formulas shows
through. Calc actually stores the above formulas as @samp{((a + b) - c) + d}
and @samp{x * (y * z)}. (Note that for certain obscure reasons, Calc
treats multiplication as right-associative.) Once you have enabled
@kbd{j b} mode, selecting with the cursor on the @samp{-} sign would
only select the @samp{a + b - c} portion, which makes sense when the
deep structure of the sum is considered. There is no way to select
the @samp{b - c + d} portion; although this might initially look
like just as legitimate a sub-formula as @samp{a + b - c}, the deep
structure shows that it isn't. The @kbd{d U} command can be used
to view the deep structure of any formula (@pxref{Normal Language Modes}).
through. Calc actually stores the above formulas as
@samp{((a + b) - c) + d} and @samp{x * (y * z)}. (Note that for certain
obscure reasons, by default Calc treats multiplication as
right-associative.) Once you have enabled @kbd{j b} mode, selecting
with the cursor on the @samp{-} sign would only select the @samp{a + b -
c} portion, which makes sense when the deep structure of the sum is
considered. There is no way to select the @samp{b - c + d} portion;
although this might initially look like just as legitimate a sub-formula
as @samp{a + b - c}, the deep structure shows that it isn't. The @kbd{d
U} command can be used to view the deep structure of any formula
(@pxref{Normal Language Modes}).
When @kbd{j b} mode has not been enabled, the deep structure is
generally hidden by the selection commands---what you see is what
@ -22158,13 +22159,13 @@ Arithmetic operators like @kbd{+} and @kbd{*} always take two
arguments in Calc's internal form. Sums and products of three or
more terms are arranged by the associative law of algebra into
a left-associative form for sums, @expr{((a + b) + c) + d}, and
a right-associative form for products, @expr{a * (b * (c * d))}.
Formulas like @expr{(a + b) + (c + d)} are rearranged to
left-associative form, though this rarely matters since Calc's
algebra commands are designed to hide the inner structure of
sums and products as much as possible. Sums and products in
their proper associative form will be written without parentheses
in the examples below.
(by default) a right-associative form for products,
@expr{a * (b * (c * d))}. Formulas like @expr{(a + b) + (c + d)} are
rearranged to left-associative form, though this rarely matters since
Calc's algebra commands are designed to hide the inner structure of sums
and products as much as possible. Sums and products in their proper
associative form will be written without parentheses in the examples
below.
Sums and products are @emph{not} rearranged according to the
commutative law (@expr{a + b} to @expr{b + a}) except in a few
@ -34868,12 +34869,14 @@ and @code{calc-embedded-open-close-plain-alist}.
@defvar calc-multiplication-has-precedence
The variable @code{calc-multiplication-has-precedence} determines
whether multiplication has precedence over division in algebraic formulas
in normal language modes. If @code{calc-multiplication-has-precedence}
is non-@code{nil}, then multiplication has precedence, and so for
example @samp{a/b*c} will be interpreted as @samp{a/(b*c)}. If
@code{calc-multiplication-has-precedence} is @code{nil}, then
multiplication has the same precedence as division, and so for example
whether multiplication has precedence over division in algebraic
formulas in normal language modes. If
@code{calc-multiplication-has-precedence} is non-@code{nil}, then
multiplication has precedence (and, for certain obscure reasons, is
right associative), and so for example @samp{a/b*c} will be interpreted
as @samp{a/(b*c)}. If @code{calc-multiplication-has-precedence} is
@code{nil}, then multiplication has the same precedence as division
(and, like division, is left associative), and so for example
@samp{a/b*c} will be interpreted as @samp{(a/b)*c}. The default value
of @code{calc-multiplication-has-precedence} is @code{t}.
@end defvar