Commit 5fafc247 by Jay Belanger

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

```of sentences.
(Rearranging Formulas using Selections): Discuss new options for `j *'.```
parent d22546d5
 2009-01-27 Jay Belanger * 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 * dbus.texi (Errors and Events): New variable dbus-event-error-hooks. ... ...
 ... ... @@ -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
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