If you want a Sage number X of n (binary) bits precision to be converted to
a Maxima bigfloat of n bits,
then you can do this.
First in Sage compute Xrat which is an exact rational that is equal to X.
It could be computed
by something like (some integer) times 2^(some power):
then in maxima, you utter the program fragment:
block([?fpprec:n], bfloat(Xrat))
note ?fpprec is the BINARY version of fpprec.
On Wednesday, June 13, 2012 4:44:28 PM UTC-7, Eviatar wrote:
>
> Here's a possible way to solve the precision problems with Maxima. This
> replaces RealNumbers and RealLiterals with variables before simplifying an
> Expression.
>
> from sage.symbolic.expression_conversions import Converter
>
> class DoNothing(Converter):
> def arithmetic(self, ex, operator):
> return reduce(operator, map(self, ex.operands()))
> def pyobject(self, ex, obj):
> return ex
> def symbol(self, ex):
> return ex
> def relation(self, ex, operator):
> return operator(*map(self, ex.operands()))
> def derivative(self, ex, operator):
> #We'll just ignore this for now
> return ex
> def composition(self, ex, operator):
> return operator(*map(self, ex.operands()))
>
> class MaintainPrec(DoNothing):
> def __init__(self):
> self.repl_dict = {}
> self.counter = 1
> def pyobject(self, ex, obj):
> if isinstance(obj, sage.rings.real_mpfr.RealLiteral) or
> isinstance(obj, sage.rings.real_mpfr.RealNumber):
> newvar = var('repl%s' % self.counter)
> self.repl_dict[newvar] = obj
> self.counter += 1
> return newvar
> else:
> return obj
>
> def safe_simplify(expr):
> replacer = MaintainPrec()
> return replacer(expr).simplify_full().subs(replacer.repl_dict)
>
> Now:
>
> sage: a = RealField(200)(8.987551787368175506591796875e9)
> sage: var('y')
> y
> sage: b = (a * x).mul(y, hold=True)
> sage: (b / (x * y)).simplify()
> 8987551787.37
> sage: safe_simplify(b / (x * y))
> 8.9875517873681755065917968750000000000000000000000000000000e9
>
> Does this look like a good solution? It should be done before sending any
> Expression to Maxima, because Maxima itself does not try to preserve
> precision at all with its
> bigfloats<http://trac.sagemath.org/sage_trac/ticket/11643#comment:3>
> .
>
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