Re: [Maxima-discuss] how to simplify integrate(sqrt(x) * sqrt(x + 1), x)

[Barton W. <wi...@un...>]

>> Substituting a lambda form for a function has been called my favorite trick. It is.

>Thank you very much! I will try to understand this trick.

Maybe I shouldn't call it a trick--substitution of one function for another is  a fairly natural operation.

Often it is convenient for the substituted function to be a lambda form (anonymous function), but
it doesn't have to be.  If the substituted function isn't a lambda form, it might be necessary to call
ev on the result:

   (%i36) f(x,y) := max(x,y)$

   (%i37) subst(g = f, g(2,4));
   (%o37) f(2,4)

   (%i38) ev(%);
    (%o38) 4

When substituting a lambda form for a function, the lambda form is automatically evaluated. This is
inconsistent--maybe soon this behavior will be changed.

To substitute for +, *, ^, ^^, enclose the operator in double quotes; for example to convert from
non-commutative multiplication to commutative multiplication,  use

   (%i49) subst("." = "*",a.b.a);
   (%o49) a^2*b

Internally, a-b is a + (-1 * b), so substitution for "-" might not work as expected:

  (%i54) subst("-" = f,a-b);
  (%o54) a-b

  (%i55) subst("+" = f,a-b);
  (%o55) f(a,-b)

One thing that consistently trips me up is substitution for  noun form. Substitution for integrate
doesn't seem to work

  (%i67) subst('integrate = lambda([e,x,a,b], quad_qag(e,x,a,b,6)), integrate(x^x,x,0,1));
  (%o67) integrate(x^x,x,0,1)

But substitution for the noun form of integrate does

  (%i68) subst(nounify('integrate) = lambda([e,x,a,b], quad_qag(e,x,a,b,6)), integrate(x^x,x,0,1));
 (%o68) [0.78343051069213,2.1976896391359236*10^-9,549,0]

--Barton