Evaluating a String in Sage¶

sage.misc.sage_eval.
sage_eval
(source, locals=None, cmds='', preparse=True)¶ Obtain a Sage object from the input string by evaluating it using Sage. This means calling eval after preparsing and with globals equal to everything included in the scope of
from sage.all import *
.).INPUT:
source
 a string or object with a _sage_ methodlocals
 evaluate in namespace of sage.all plus the locals dictionarycmds
 string; sequence of commands to be run before source is evaluated.preparse
 (default: True) if True, preparse the string expression.
EXAMPLES: This example illustrates that preparsing is applied.
sage: eval('2^3') 1 sage: sage_eval('2^3') 8
However, preparsing can be turned off.
sage: sage_eval('2^3', preparse=False) 1
Note that you can 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 example illustrates that evaluation occurs in the context of
from sage.all import *
. Even though bernoulli has been redefined in the local scope, when callingsage_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}) # py2 26 sage: eval('4//3 + x', {'x': 25}) # py3 26 sage: sage_eval('4/3 + x', locals={'x': 25}) 79/3
You can also specify a sequence of commands to be run before the expression is evaluated:
sage: sage_eval('p', cmds='K.<x> = QQ[]\np = x^2 + 1') x^2 + 1
If you give commands to execute and a dictionary of variables, then the dictionary will be modified by assignments in the commands:
sage: vars = {} sage: sage_eval('None', cmds='y = 3', locals=vars) sage: vars['y'], parent(vars['y']) (3, Integer Ring)
You can also specify the object to evaluate as a tuple. A 2tuple is assumed to be a pair of a command sequence and an expression; a 3tuple is assumed to be a triple of a command sequence, an expression, and a dictionary holding local variables. (In this case, the given dictionary will not be modified by assignments in the commands.)
sage: sage_eval(('f(x) = x^2', 'f(3)')) 9 sage: vars = {'rt2': sqrt(2.0)} sage: sage_eval(('rt2 += 1', 'rt2', vars)) 2.41421356237309 sage: vars['rt2'] 1.41421356237310
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"]);') 'Rationals[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.sage: sage_eval('None', cmds='$x = $y[3] # Does Perl syntax work?') Traceback (most recent call last): ... File "<string>", line 1 $x = $y[Integer(3)] # Does Perl syntax work? ^ SyntaxError: invalid syntax

sage.misc.sage_eval.
sageobj
(x, vars=None)¶ Return a native Sage object associated to x, if possible and implemented.
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 vars argument, which should be a dictionary.EXAMPLES:
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'>
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'>