rewrite
-- rewrite an
expressionrewrite
(f, target)
transforms an
expression f
to a mathematically equivalent form, trying
to express f
in terms of the specified target
function.
rewrite(f, target)
f |
- | an arithmetical expression |
target |
- | the target function to be used in the representation:
one of cot , coth , diff , exp , fact , gamma , heaviside , ln , piecewise , sign , sincos , sinhcosh , tan , or tanh |
an arithmetical expression.
f
Chapter ``Manipulating Expressions'' of the Tutorial.
collect
, combine
, expand
, factor
, normal
, partfrac
, rationalize
, rectform
, simplify
f
are
replaced by the target function if this is mathematically valid.exp
, all trigonometric and hyperbolic
functions are rewritten in terms of exp
. Further, the
inverse functions as well as arg
are rewritten in terms of
ln
.tan
, cot
, exp
,
sinh
, cosh
, tanh
, and
coth
are rewritten in terms of sin
and
cos
.exp
, tanh
, coth
,
sin
, cos
, tan
, and
cot
are rewritten in terms of sinh
and
cosh
.This examples demonstrates the use of
rewrite
:
>> rewrite(D(D(y))(x), diff)
diff(y(x), x, x)
>> rewrite(fact(n), gamma), rewrite(gamma(n), fact);
gamma(n + 1), fact(n - 1)
>> rewrite(sign(x), heaviside), rewrite(heaviside(x), sign);
sign(x) 2 heaviside(x) - 1, ------- + 1/2 2
>> rewrite(heaviside(x), piecewise)
piecewise(1 if 0 < x, heaviside(0) if x = 0, -1 if x < 0)
Trigonometric functions can be rewritten in terms of
exp
, sin
, cos
etc.:
>> rewrite(tan(x), exp), rewrite(cot(x), sincos), rewrite(sin(x), tan)
/ x \ 2 2 tan| - | I exp(I x) - I cos(x) \ 2 / - ---------------, ------, ------------- 2 sin(x) / x \2 exp(I x) + 1 tan| - | + 1 \ 2 /
>> rewrite(arcsinh(x), ln)
2 1/2 ln(x + (x + 1) )
cot
, coth
, tanh
,
and piecewise
were
added.