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(Embedded Mode, Algebraic-Style Calculations): Make Calc the subject

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of sentences.
(Rearranging Formulas using Selections): Discuss new options for `j *'.
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Jay Belanger 2009-01-27 01:55:20 +00:00
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7
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@ -1,3 +1,10 @@
2009-01-27 Jay Belanger <jay.p.belanger@gmail.com>
* calc.texi (Embedded Mode, Algebraic-Style Calculations):
Make Calc the subject of sentences.
(Rearranging Formulas using Selections): Discuss new options
for `j *'.
2009-01-26 Michael Albinus <michael.albinus@gmx.de>
* dbus.texi (Errors and Events): New variable dbus-event-error-hooks.

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doc/misc/calc.texi
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@ -913,8 +913,8 @@ is
@end group
@end smallexample
(Note that by default division had lower precedence than multiplication
in Calc, so that @samp{1 / ln(x) x} is equivalent to @samp{1 / (ln(x) x)}.)
(Note that by default, Calc gives division lower precedence than multiplication,
so that @samp{1 / ln(x) x} is equivalent to @samp{1 / (ln(x) x)}.)
To make this look nicer, you might want to press @kbd{d =} to center
the formula, and even @kbd{d B} to use Big display mode.
@ -1758,9 +1758,9 @@ Calculator in Algebraic mode, which is closer to the way
non-RPN calculators work. In Algebraic mode, you enter formulas
in traditional @expr{2+3} notation.
@strong{Warning:} Note that @samp{/} has lower precedence than
@samp{*}, so that @samp{a/b*c} is interpreted as @samp{a/(b*c)}. See
below for details.
@strong{Notice:} Calc gives @samp{/} lower precedence than @samp{*}, so
that @samp{a/b*c} is interpreted as @samp{a/(b*c)}; this is not
standard across all computer languages. See below for details.
You don't really need any special ``mode'' to enter algebraic formulas.
You can enter a formula at any time by pressing the apostrophe (@kbd{'})
@ -21921,24 +21921,33 @@ formula using algebraic entry, then multiplies both sides of the
selected quotient or equation by that formula. It simplifies each
side with @kbd{a s} (@code{calc-simplify}) before re-forming the
quotient or equation. You can suppress this simplification by
providing any numeric prefix argument. There is also a @kbd{j /}
providing a prefix argument: @kbd{C-u j *}. There is also a @kbd{j /}
(@code{calc-sel-div-both-sides}) which is similar to @kbd{j *} but
dividing instead of multiplying by the factor you enter.
As a special feature, if the numerator of the quotient is 1, then
the denominator is expanded at the top level using the distributive
law (i.e., using the @kbd{C-u -1 a x} command). Suppose the
formula on the stack is @samp{1 / (sqrt(a) + 1)}, and you wish
to eliminate the square root in the denominator by multiplying both
sides by @samp{sqrt(a) - 1}. Calc's default simplifications would
change the result @samp{(sqrt(a) - 1) / (sqrt(a) - 1) (sqrt(a) + 1)}
right back to the original form by cancellation; Calc expands the
denominator to @samp{sqrt(a) (sqrt(a) - 1) + sqrt(a) - 1} to prevent
this. (You would now want to use an @kbd{a x} command to expand
the rest of the way, whereupon the denominator would cancel out to
the desired form, @samp{a - 1}.) When the numerator is not 1, this
initial expansion is not necessary because Calc's default
simplifications will not notice the potential cancellation.
If the selection is a quotient with numerator 1, then Calc's default
simplifications would normally cancel the new factors. To prevent
this, when the @kbd{j *} command is used on a selection whose numerator is
1 or -1, the denominator is expanded at the top level using the
distributive law (as if using the @kbd{C-u 1 a x} command). Suppose the
formula on the stack is @samp{1 / (a + 1)} and you wish to multiplying the
top and bottom by @samp{a - 1}. Calc's default simplifications would
normally change the result @samp{(a - 1) /(a + 1) (a - 1)} back
to the original form by cancellation; when @kbd{j *} is used, Calc
expands the denominator to @samp{a (a - 1) + a - 1} to prevent this.
If you wish the @kbd{j *} command to completely expand the denominator
of a quotient you can call it with a zero prefix: @kbd{C-u 0 j *}. For
example, if the formula on the stack is @samp{1 / (sqrt(a) + 1)}, you may
wish to eliminate the square root in the denominator by multiplying
the top and bottom by @samp{sqrt(a) - 1}. If you did this simply by using
a simple @kbd{j *} command, you would get
@samp{(sqrt(a)-1)/ (sqrt(a) (sqrt(a) - 1) + sqrt(a) - 1)}. Instead,
you would probably want to use @kbd{C-u 0 j *}, which would expand the
bottom and give you the desired result @samp{(sqrt(a)-1)/(a-1)}. More
generally, if @kbd{j *} is called with an argument of a positive
integer @var{n}, then the denominator of the expression will be
expanded @var{n} times (as if with the @kbd{C-u @var{n} a x} command).
If the selection is an inequality, @kbd{j *} and @kbd{j /} will
accept any factor, but will warn unless they can prove the factor