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SandBoxOperatorsAndSqrt

Edit detail for SandBoxOperatorsAndSqrt revision 2 of 2

	1 2
Editor: test1 Time: 2015/06/01 19:17:14 GMT+0
Note:

added:
'f(x)' is computed by 'elt' in ExpressionSpace.  'elt' uses 'belong?' to
check for correct operator and complains otherwise.

AlgebraicNumber defines:

    belong? op           == belong?(op)$ExpressionSpace_&(%) or has?(op, ALGOP)


changed:
-whereas Expression overrides this with::
so 'f' is not among allowed operators, whereas Expression defines::

This fails unexpectedly:

fricas

f:=operator 'f

$\label{eq1}f$

(1)

Type: BasicOperator?

fricas

f(sin(-1))

$\label{eq2}f \left({-{\sin \left({1}\right)}}\right)$

(2)

Type: Expression(Integer)

fricas

f(sqrt(-1))

   >> Error detected within library code:
   Unknown operator 3: f

But this works

fricas

f(sqrt(-1)::Expression(Integer))

$\label{eq3}f \left({\sqrt{- 1}}\right)$

(3)

Type: Expression(Integer)

This happens because sqrt(-1) is interpreted as an AlgebraicNumber? and

fricas

AlgebraicNumber has ExpressionSpace

$\label{eq4} \mbox{\rm true}$

(4)

Type: Boolean

f(x) is computed by elt in ExpressionSpace?. elt uses belong? to check for correct operator and complains otherwise.

AlgebraicNumber? defines:

belong? op == belong?(op)$ExpressionSpace?_&(%) or has?(op, ALGOP)

while ExpressionSpace? exports:

    belong? op   ==
        has?(op, 'any) and (is?(op, PAREN) or is?(op, BOX))

so f is not among allowed operators, whereas Expression defines:

    belong? op == true