[GiNaC-devel] About a (poor) parity in expressions.

[Francois Maltey]

Hello,

I'm a ginac user because I use Sage, and I work around expressions.

I discover that ginac remains function arguments (more than the other 
computer algebra system).
So sin(x)+sin(-x) remains sin(x)+sin(-x), and I don't get 0.

The only automatic rewrite rules I discover around signs and integers are :
1 / exp(x) ==> exp(-x) 
exp(x)^2 ==> exp(2*x)

I don't speak about exp(log(x)) ==> x, sin(atan(x)) ==> x/sqrt(x^2+1), ...

Are there other rewrite rules ?

After some computations, I offen get a result as sin(x)+sin(-x) or 
cos(x)-cos(-x).

I know it's almost impossible to choose between cos(a-b) and cos(b-a).
But it's possible to choose only one expression between a-b and b-a :
  1/ Look at the only numeric constant in a product, and test if it's a 
positive one.
  2/ Look at the first term in a sum, and test this first term.

Can I find it in ginac or must I use this sage function :

def pseudoPositive (expr) :
  if expr._is_real() : return bool (RR(expr) >= 0)
  if expr._is_numeric () :
    return bool ((expr.real() > 0) or (expr.real() == 0 and expr.imag() 
 > 0))
  if expr._is_symbol() : return True
  opor = expr.operator()
  opands = expr.operands()
  if opor == operator.mul : 
    return pseudoPositive (opands[-1])
  if opor == operator.add : 
    return pseudoPositive (opands[0])
  return True

Then I redefine the usual functions as sin by :

def rewSin (expr) :
  if pseudoPositive (expr) : return sin (expr)
  else : return -sin(-expr)

By this way I get all the easy simplifications.

Where do ginac developpers see these rules ? inside-ginac or outside-ginac ?
It's not a good idea to (re-)code these rules inside sage if I can get 
them by ginac.

Many thanks for your advices.

Francois (in France)