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2016-02-19 21:38:45 -0500 commented answer Specifying names of variables in output of self.coordinate_ring()

@tmonteil I un-accepted this answer since it didn't seem to actually change the names. But if I should accept the answer based on the unedited question and ask a new question, please let me know (or whatever the correct thing to do is).

2016-02-19 20:47:20 -0500 commented answer convert polynomial rings from Sage to Singular

how to I find functions like self._singular_() (also self._name? (they don't seem to come up in a google search of the documentation)

2016-02-19 12:03:01 -0500 asked a question convert polynomial rings from Sage to Singular

Suppose I have a ring R in sage (I have in mind a polynomial ring modulo some ideal). Is there a way to convert it into a ring in Singular?

I want to use the tensor product function (which singular provides) on two rings (and then convert back to sage) but singular doesn't have (natural) constructors for the rings I'd like to tensor.

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2016-02-11 09:34:35 -0500 asked a question Specifying names of variables in output of self.coordinate_ring()

Let

E = EllipticCurve([1,2,3,4,5])

Then E.coordinate_ring() outputs a ring with generators.

E.coordinate_ring().gens()

yields

(xbar,ybar,zbar)

Is there a way to change the names of these variables at any point in this process?

EDIT The goal is to have sage treat the underlying rings to be treated as unique objects. Currently if I execute

E1 = EllipticCurve([1,2,3,4,5]).coordinate_ring() 
E1._names = ('a','b','c')
E2 = EllipticCurve([1,2,3,4,5]).coordinate_ring() 
E2._names =('l','m','n')
E1;E2

I get

Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - 2*x^2*z + x*y*z + y^2*z - 4*x*z^2 + 3*y*z^2 - 5*z^3)
Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - 2*x^2*z + x*y*z + y^2*z - 4*x*z^2 + 3*y*z^2 - 5*z^3)

(An indication that the rings are "the same":

E1sing = E1._singular_()
E2sing = E2._singular_()

ProdE1E2sing = singular.ringtensor(E1sing,E2sing);
ProdE1E2.sage()

gives

Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - 2*x^2*z + x*y*z + y^2*z - 4*x*z^2 + 3*y*z^2 - 5*z^3)

whereas there should be 6 variables if the two rings were unique.)


Note: I have also tried to change the _gens, as well as injecting variables at every stage, but all with the same outcome.