use @samp{[[-inf .. 0), (0 .. inf]]}. (There is no way in the
current notation to say that @code{x} is nonzero but not necessarily
real.) The @kbd{a e} command does ``unsafe'' simplifications,
-including cancelling @samp{x} from the equation when @samp{x} is
+including canceling @samp{x} from the equation when @samp{x} is
not known to be nonzero.
Another set of type symbols distinguish between scalars and vectors.
@end smallexample
Unselecting the sub-formula reveals that the minus sign, which would
-normally have cancelled out with the subtraction automatically, has
+normally have canceled out with the subtraction automatically, has
not been able to do so because the subtraction was not part of the
selected portion. Pressing @kbd{=} (@code{calc-evaluate}) or doing
any other mathematical operation on the whole formula will cause it
Quotients of products cancel only in the leading terms of the
numerator and denominator. In other words, @expr{a x b / a y b}
-is cancelled to @expr{x b / y b} but not to @expr{x / y}. Once
+is canceled to @expr{x b / y b} but not to @expr{x / y}. Once
again this is because full cancellation can be slow; use @kbd{a s}
to cancel all terms of the quotient.
cancel @expr{x^2} from the top and bottom to get @expr{a b / c x d}.
(The terms in the denominator will then be rearranged to @expr{c d x}
as described above.) If there is any common integer or fractional
-factor in the numerator and denominator, it is cancelled out;
+factor in the numerator and denominator, it is canceled out;
for example, @expr{(4 x + 6) / 8 x} simplifies to @expr{(2 x + 3) / 4 x}.
Non-constant common factors are not found even by @kbd{a s}. To
If the argument is multiplied by a constant, and this constant
has a common integer divisor with the modulus, then this factor is
-cancelled out. For example, @samp{12 x % 15} is changed to
+canceled out. For example, @samp{12 x % 15} is changed to
@samp{3 (4 x % 5)} by factoring out 3. Also, @samp{(12 x + 1) % 15}
is changed to @samp{3 ((4 x + 1:3) % 5)}. While these forms may
not seem ``simpler,'' they allow Calc to discover useful information
\bigskip
@end tex
-Equations and inequalities are simplified by cancelling factors
+Equations and inequalities are simplified by canceling factors
of products, quotients, or sums on both sides. Inequalities
-change sign if a negative multiplicative factor is cancelled.
+change sign if a negative multiplicative factor is canceled.
Non-constant multiplicative factors as in @expr{a b = a c} are
-cancelled from equations only if they are provably nonzero (generally
+canceled from equations only if they are provably nonzero (generally
because they were declared so; @pxref{Declarations}). Factors
-are cancelled from inequalities only if they are nonzero and their
+are canceled from inequalities only if they are nonzero and their
sign is known.
Simplification also replaces an equation or inequality with
unsafe because of problems with principal values (although these
simplifications are safe if @expr{x} is known to be real).
-Common factors are cancelled from products on both sides of an
+Common factors are canceled from products on both sides of an
equation, even if those factors may be zero: @expr{a x / b x}
-to @expr{a / b}. Such factors are never cancelled from
+to @expr{a / b}. Such factors are never canceled from
inequalities: Even @kbd{a e} is not bold enough to reduce
@expr{a x < b x} to @expr{a < b} (or @expr{a > b}, depending
on whether you believe @expr{x} is positive or negative).
which the first argument is a number which is out of range for the
leading unit are modified accordingly.
-When cancelling and combining units in products and quotients,
+When canceling and combining units in products and quotients,
Calc accounts for unit names that differ only in the prefix letter.
For example, @samp{2 km m} is simplified to @samp{2000 m^2}.
However, compatible but different units like @code{ft} and @code{in}
of @samp{<} and @samp{<=} are allowed, or any of the four combinations
of @samp{>} and @samp{>=}. Four-argument constructions like
@samp{a < b < c < d}, and mixtures like @w{@samp{a < b = c}} that
-involve both equalities and inequalities, are not allowed.
+involve both equations and inequalities, are not allowed.
@kindex a .
@pindex calc-remove-equal
derivative is left in terms of @var{var}. If the expression contains
functions for which no derivative formula is known, new derivative
functions are invented by adding primes to the names; @pxref{Calculus}.
-However, if @var{symb} is non-@code{nil}, the presence of undifferentiable
+However, if @var{symb} is non-@code{nil}, the presence of nondifferentiable
functions in @var{expr} instead cancels the whole differentiation, and
@code{deriv} returns @code{nil} instead.
HCoop / bpt / emacs.git / blobdiff