I was musing about formal symbolic expressions on sage support:
http://groups.google.com/group/sage-support/browse_thread/thread/78dc8d2d476acc46
but thought it was time to move it over to devel. The motivation is
to have a nice notation for formal integrals and derivatives:
sage: integral(sin(x),x).formal()
integral(sin(x),x)
If this is a good idea, then maybe it's a good idea to have a formal
method for all symbolic expressions.
sage: (x - x).formal()
x - x
Here's a monkeypatch that makes this work(ish)
from sage.calculus.calculus import SymbolicExpression
class FormalSymbolicExpression(SymbolicExpression):
def __init__(self,expr):
self.expr = expr
# just delegate everything to the input expression
for m in dir(expr):
self.m = m
def _repr_(self,simplify=False):
return self.expr._repr_(simplify=False)
# implement a _latex_ method
SymbolicExpression.formal = lambda self:
FormalSymbolicExpression(self)
def formal(expr):
try:
return expr.formal()
except AttributeError:
return expr
Let's see it in action
sage: x - x
0
sage: (x - x).formal()
x - x
sage: formal(x - x)
x - x
sage: simplify(formal(x - x))
0
sage: exp(i*pi)
-1
sage: formal(exp(i*pi))
exp(I*pi)
This won't work on integral or derivative yet because they aren't lazy
enough. But it seems like they could be made to behave like the
Function_* classes, for instance Function_exp above.
Cheers,
JM
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