Method on @sym: rewrite (f, how) ¶

Rewrite a symbolic expression.

Attempts to rewrite an expression f in terms of functions indicated by the case-sensitive string how.

Examples using trigonometry:

syms x
rewrite(exp(x), 'sin')
  ⇒ ans = (sym) sinh(x) + cosh(x)
rewrite(sin(x), 'exp')
  ⇒ ans = (sym)
         ⎛ ⅈ⋅x    -ⅈ⋅x⎞
      -ⅈ⋅⎝ℯ    - ℯ    ⎠
      ──────────────────
              2

Often sincos is more useful than sin or cos:

rewrite(tan(x), 'sin')
  ⇒ (sym)
           2
      2⋅sin (x)
      ─────────
       sin(2⋅x)
rewrite(tan(x), 'sincos')
  ⇒ (sym)
      sin(x)
      ──────
      cos(x)

The argument f can be a matrix:

rewrite([exp(x) cos(x) asin(x)], 'log')
  ⇒ ans = (sym 1×3 matrix)
      ⎡                  ⎛         ________⎞⎤
      ⎢ x                ⎜        ╱      2 ⎟⎥
      ⎣ℯ   cos(x)  -ⅈ⋅log⎝ⅈ⋅x + ╲╱  1 - x  ⎠⎦

(and note that some elements of f might be unchanged.)

Example using integrals:

syms f(t) s
G = laplace(f)
  ⇒ G = (sym) LaplaceTransform(f(t), t, s)
rewrite(G, 'Integral')
  ⇒ ans = (sym)
      ∞
      ⌠
      ⎮       -s⋅t
      ⎮ f(t)⋅ℯ     dt
      ⌡
      0

Note the case-sensitivity of how: use Integral not integral.

Further examples:

syms n r
rewrite(factorial(n), 'gamma')
  ⇒ ans = (sym) Γ(n + 1)

nCr = nchoosek(n, r)
  ⇒ nCr = (sym)
      ⎛n⎞
      ⎜ ⎟
      ⎝r⎠
rewrite(nCr, 'factorial')
  ⇒ ans = (sym)
           n!
      ───────────
      r!⋅(n - r)!

See also: @@sym/simplify, @@sym/expand, @@sym/factor.

Package: symbolic