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In Python (which is the base language of Sage), the call of a == b is supposed to return the boolean True whenever a is equal to b, and False otherwise.

In mathematics, when $x$ is a symbol or an un determinate, you want to be able to deal with expressions such as $2x+4 = 3*x+3$ or $2x+4 < 42$ (e.g. in order to solve them as equations, or to simplify them, etc).

To be able to construct such expressions in Sage, we break the promise that a == b will return a boolean, so that 2*x+4 == 3x+3 and 2*x+4 < 42 will return symbolic expressions.

For this, the __eq__ method that is called when testing for equality between 2 objects is overriden so that instead of returning a boolean, it returns an expression. Hence, if a and b are symbolic expressions, then a == b is a symbolic expression as well, not a boolean as it should be [1].

If you want to test whether the symbolic expression a is equal to the symbolic expression b, you have to type bool(a == b).

Note however that, since a boolean is either True or False, but not Unknown, when Sage is not able to prove that a is equal to b, it will return False even if the two expressions are equal.

Note [1] : i omit the coercion layer to make the answer understandable.

In Python (which is the base language of Sage), the call of a == b is supposed to return the boolean True whenever a is equal to b, and False otherwise.

In mathematics, when $x$ is a symbol or an un determinate, indeterminate, you want to be able to deal with expressions such as $2x+4 = 3*x+3$ or $2x+4 < 42$ (e.g. in order to solve them as equations, or to simplify them, etc).

To be able to construct such expressions in Sage, we break the promise that a == b will return a boolean, so that 2*x+4 == 3x+3 and 2*x+4 < 42 will return symbolic expressions.

For this, the __eq__ method that is called when testing for equality between 2 objects is overriden so that instead of returning a boolean, it returns an expression. Hence, if a and b are symbolic expressions, then a == b is a symbolic expression as well, not a boolean as it should be [1].

If you want to test whether the symbolic expression a is equal to the symbolic expression b, you have to type bool(a == b).

Note however that, since a boolean is either True or False, but not Unknown, when Sage is not able to prove that a is equal to b, it will return False even if the two expressions are equal.

Note [1] : i omit the coercion layer to make the answer understandable.

In Python (which is the base programmng language on top of Sage), which Sage is built), the call of a == b is supposed to return the boolean True whenever a is equal to b, and False otherwise.

In mathematics, when $x$ is a symbol or an indeterminate, you want to be able to deal with expressions such as $2x+4 = 3*x+3$ or $2x+4 < 42$ (e.g. in order to solve them as equations, or to simplify them, etc).

To be able to construct such expressions in Sage, we break the promise that a == b will return a boolean, so that 2*x+4 == 3x+3 and 2*x+4 < 42 will return symbolic expressions.

For this, the __eq__ method that is called when testing for equality between 2 objects is overriden so that instead of returning a boolean, it returns an expression. Hence, if a and b are symbolic expressions, then a == b is a symbolic expression as well, not a boolean as it should be [1].

If you want to test whether the symbolic expression a is equal to the symbolic expression b, you have to type bool(a == b).

Note however that, since a boolean is either True or False, but not Unknown, when Sage is not able to prove that a is equal to b, it will return False even if the two expressions are equal.

Note [1] : i omit the coercion layer to make the answer understandable.

In Python (which is the programmng language on top of which Sage is built), the call of a == b is supposed to return the boolean True whenever a is equal to b, and False otherwise.

In mathematics, when $x$ is a symbol or an indeterminate, you want to be able to deal with expressions such as $2x+4 = 3*x+3$ 3x+3$ or $2x+4 < 42$ (e.g. in order to solve them as equations, or to simplify them, etc).

To be able to construct such expressions in Sage, we break the promise that a == b will return a boolean, so that 2*x+4 == 3x+33*x+3 and 2*x+4 < 42 will return symbolic expressions.

For this, the __eq__ method that is called when testing for equality between 2 objects is overriden so that instead of returning a boolean, it returns an expression. Hence, if a and b are symbolic expressions, then a == b is a symbolic expression as well, not a boolean as it should be [1].

If you want to test whether the symbolic expression a is equal to the symbolic expression b, you have to type bool(a == b).

Note however that, since a boolean is either True or False, but not Unknown, when Sage is not able to prove that a is equal to b, it will return False even if the two expressions are equal.

Note [1] : i omit the coercion layer to make the answer understandable.