precision, but it doesn't always bump the precision up enough.
In each case, Calc added about two digits of precision during
its calculation and then rounded back down to 12 digits
-afterward. In one case, it was enough; in the the other, it
+afterward. In one case, it was enough; in the other, it
wasn't. If you really need @var{x} digits of precision, it
never hurts to do the calculation with a few extra guard digits.
@kindex v p (complex)
@pindex calc-pack
The @kbd{v p} (@code{calc-pack}) command can pack the top two numbers on
-the the stack into a composite object such as a complex number. With
+the stack into a composite object such as a complex number. With
a prefix argument of @i{-1}, it produces a rectangular complex number;
with an argument of @i{-2}, it produces a polar complex number.
(Also, @pxref{Building Vectors}.)
@noindent
The portion selected is always large enough to be considered a complete
formula all by itself, so selecting the parenthesis selects the whole
-formula that it encloses. Putting the cursor on the the @samp{+} sign
+formula that it encloses. Putting the cursor on the @samp{+} sign
would have had the same effect.
(Strictly speaking, the Emacs cursor is really the manifestation of
guess on the stack, and are prompted for the name of a variable. The guess
may be either a number near the desired minimum, or an interval enclosing
the desired minimum. The function returns a vector containing the
-value of the the variable which minimizes the formula's value, along
+value of the variable which minimizes the formula's value, along
with the minimum value itself.
Note that this command looks for a @emph{local} minimum. Many functions
@defun format-value a width
Convert the Calc number or formula @var{a} to string form, using the
-format seen in the stack buffer. Beware the the string returned may
+format seen in the stack buffer. Beware the string returned may
not be re-readable by @code{read-expr}, for example, because of digit
grouping. Multi-line objects like matrices produce strings that
contain newline characters to separate the lines. The @var{w}
@cindex buffer definitions index
@cindex tags
- The Imenu facility offers a way to find the the major definitions in
+ The Imenu facility offers a way to find the major definitions in
a file by name. It is also useful in text formatter major modes,
where it treats each chapter, section, etc., as a definition.
(@xref{Tags}, for a more powerful feature that handles multiple files
@vindex lisp-body-indent
Certain functions override the standard pattern. Functions whose
-names start with @code{def} treat the the second lines as the start of
+names start with @code{def} treat the second lines as the start of
a @dfn{body}, by indenting the second line @code{lisp-body-indent}
additional columns beyond the open-parenthesis that starts the
expression.
4. `:height HEIGHT' specifies that the height of the stretch produced
should be HEIGHT, measured in canonical character units.
- 5. `:relative-height FACTOR' specifies that the height of the the
+ 5. `:relative-height FACTOR' specifies that the height of the
stretch should be FACTOR times the height of the characters having
the glyph property.
#endif /* not 0 */
-/* Find the position of the the glyph for position POS in OBJECT in
+/* Find the position of the glyph for position POS in OBJECT in
window W's current matrix, and return in *X/*Y the pixel
coordinates, and return in *HPOS/*VPOS the column/row of the glyph.
4. `:height HEIGHT' specifies that the height of the stretch produced
should be HEIGHT, measured in canonical character units.
- 5. `:relative-height FACTOR' specifies that the height of the the
+ 5. `:relative-height FACTOR' specifies that the height of the
stretch should be FACTOR times the height of the characters having
the glyph property.
#endif /* not 0 */
-/* Find the position of the the glyph for position POS in OBJECT in
+/* Find the position of the glyph for position POS in OBJECT in
window W's current matrix, and return in *X/*Y the pixel
coordinates, and return in *HPOS/*VPOS the column/row of the glyph.