12.12 Evaluating a String in SAGE

Module: sage.misc.sage_eval

Evaluating a String in SAGE

Module-level Functions

sage_eval( source, [locals=])

Obtain a Sage object from the input string by evaluate it using SAGE. This means calling eval after preparsing and with globals equal to everything included in the scope of from sage.all import *.).

If the object has an _sage_ method it is called and the value is returned. Otherwise str is called on the object, and all preparsing is applied and the resulting expression is evaluated in the context of from sage.all import *. To evaluate the expression with certain variables set, use the locals argument, which should be a dictionary.

This example illustrates that preparsing is applied.

sage: eval('2^3')
1
sage: sage_eval('2^3')
8

Note that you have explicitly define variables and pass them as the second option:

sage: x = PolynomialRing(RationalField(),"x").gen()
sage: sage_eval('x^2+1', locals={'x':x})
x^2 + 1

This illustrates interfaces:

sage: f = gp('2/3')
sage: type(f)
<class 'sage.interfaces.gp.GpElement'>
sage: f._sage_()
2/3
sage: type(f._sage_())
<type 'sage.rings.rational.Rational'>
sage: a = gap(939393/2433)
sage: a._sage_()
313131/811
sage: type(a._sage_())
<type 'sage.rings.rational.Rational'>

This example illustrates that evaluation occurs in the context of from sage.all import *. Even though bernoulli has been redefined in the local scope, when calling sage_eval the default value meaning of bernoulli is used. Likewise for QQ below.

sage: bernoulli = lambda x : x^2
sage: bernoulli(6)
36
sage: eval('bernoulli(6)')
36
sage: sage_eval('bernoulli(6)')
1/42

sage: QQ = lambda x : x^2
sage: QQ(2)
4
sage: sage_eval('QQ(2)')
2
sage: parent(sage_eval('QQ(2)'))
Rational Field

This example illustrates setting a variable for use in evaluation.

sage: x = 5
sage: eval('4/3 + x', {'x':25})
26
sage: sage_eval('4/3 + x',  locals={'x':25})
79/3

This example illustrates how sage_eval can be useful when evaluating the output of other computer algebra systems.

sage: R.<x> = PolynomialRing(RationalField())
sage: gap.eval('R:=PolynomialRing(Rationals,["x"]);')
'PolynomialRing(..., [ x ])'
sage: ff = gap.eval('x:=IndeterminatesOfPolynomialRing(R);; f:=x^2+1;'); ff
'x^2+1'
sage: sage_eval(ff, locals={'x':x})
x^2 + 1
sage: eval(ff)
Traceback (most recent call last):
...
RuntimeError: Use ** for exponentiation, not '^', which means xor
in Python, and has the wrong precedence.

Here you can see eval simply will not work but sage_eval will.

sageobj( x, [vars=None])

Return a native SAGE object associated to x, if possible and implemented.

If x is a string it is evaluated with SAGE preparsing.

sage: type(sageobj(gp('34/56')))
<type 'sage.rings.rational.Rational'>
sage: n = 5/2
sage: sageobj(n) is n
True
sage: k = sageobj('Z(8^3/1)', {'Z':ZZ}); k
512
sage: type(k)
<type 'sage.rings.integer.Integer'>

See About this document... for information on suggesting changes.