# Symbolic Equation 0=0

What's the "correct" way to create the symbolic equation $0=0$ in Sage?

(In particular, 0==0 returns True, so that's a non-starter.)

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The value of 0 == 0 is True because 0 is an Integer and equality of Integers is defined that way. To construct the symbolic equation $0=0$, you need the value 0 as a symbolic expression, so that == will construct a symbolic equation:

sage: SR.zero() == SR.zero()
0 == 0


Here SR is the name of the Symbolic Ring, and the zero() method of any ring returns its zero. You can also convert the integer 0 to a symbolic expression:

sage: SR(0) == 0
0 == 0

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Awesome, thank you! The key insight I lacked was how to create a "symbolic zero", and various permutations of Google searches never sent me here: https://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/ring.html (https://doc.sagemath.org/html/en/refe...)

( 2020-08-02 00:01:52 +0200 )edit

you can get the same result with:

sage: SR(0)==0
0 == 0

( 2020-08-02 15:15:47 +0200 )edit