Le vendredi 21 juin 2013 07:00:54 UTC+2, rjf a écrit :
>
> Yes, I wrote radcan. The full source of it is available. I think it is in
> file rat3e.lisp. Look for
> (defun $radcan
> or perhaps (defmfun $radcan
>
> I think that if you wish to modify it to make a function with another
> name, you will first
> have to specify what that function should do. It can then be read in to
> the maxima
> image. (you can presumably prod maxima to do so by having it execute
> "load("yourfilename.lisp") " from Sage).
>
> Radcan was written sometime before 1971. Other people have thought about
> what might be "better" for 40+ years. If you come up with a truly 100%
> satisfactory replacement, more power to you. ")
> RJF
>
>
>
Thanks for your answer.
I will have to remember my lisp courses then...
Meanwhile, I've written the following workaround in python: basically, it
scans all the sqrt's in a given symbolic expression, send them to radcan,
takes the absolute value of the output and then calls simplify(). It is not
optimal but it works:
sage: assume(x<0)
sage: simplify_sqrt_real( sqrt(x^2) )
-x
sage: simplify_sqrt_real( sqrt(x^2-2*x+1) )
-x + 1
sage: simplify_sqrt_real( sqrt(x^2) + sqrt(x^2-2*x+1) )
-2*x + 1
Here is the source code:
def simplify_sqrt_real(expr):
r"""
Simplify sqrt in symbolic expressions in the real domain.
EXAMPLES:
Simplifications of basic expressions::
sage: assume(x<0)
sage: simplify_sqrt_real( sqrt(x^2) )
-x
sage: simplify_sqrt_real( sqrt(x^2-2*x+1) )
-x + 1
sage: simplify_sqrt_real( sqrt(x^2) + sqrt(x^2-2*x+1) )
-2*x + 1
"""
from sage.symbolic.ring import SR
from sage.calculus.calculus import maxima
# 1/ Search for the sqrt's in expr
sexpr = str(expr)
if 'sqrt(' not in sexpr: # no sqrt to simplify
return expr
pos_sqrts = [] # positions of the sqrt's in sexpr
the_sqrts = [] # the sqrt sub-expressions in sexpr
for pos in range(len(sexpr)):
if sexpr[pos:pos+5] == 'sqrt(':
pos_sqrts.append(pos)
parenth = 1
scan = pos+5
while parenth != 0:
if sexpr[scan] == '(': parenth += 1
if sexpr[scan] == ')': parenth -= 1
scan += 1
the_sqrts.append( sexpr[pos:scan] )
# 2/ Simplifications of the sqrt's
new_expr = "" # will contain the result
pos0 = 0
for i, pos in enumerate(pos_sqrts):
# radcan is called on each sqrt:
x = SR(the_sqrts[i])
simpl = SR(x._maxima_().radcan())
# the absolute value of radcan's output is taken, the call to
simplify()
# taking into account possible assumptions regarding the sign of
simpl:
new_expr += sexpr[pos0:pos] + '(' + str(abs(simpl).simplify()) + ')'
pos0 = pos + len(the_sqrts[i])
new_expr += sexpr[pos0:]
return SR(new_expr)
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