Let's express some simple inequalities as relational expressions to see how they work:
exp1 = SR(-5) < SR(-3) # use the symbolic ring print("Expression {0} is {1}".format(exp1, bool(exp1))) exp2 = exp1^2 print("Expression {0} is {1}".format(exp2, bool(exp2))) forget() exp3 = x^2 + 2 >= -3 * x^2 print("Expression {0} is {1}".format(exp3, bool(exp3))) p1 = plot(exp3.lhs(), (x, -5, 5), legend_label='lhs') # also lhs() or left_hand_side() p2 = plot(exp3.rhs(), (x, -5, 5), color='red', legend_label='rhs') # also rhs() or right_hand_side() show(p1 + p2)
The output is shown in the following screenshot:
We defined a simple relational expression that expresses an inequality between two integers. We used the SR
function to create symbolic objects, rather than integer objects, that represent the values -5 and -3. This is important because we need to give Sage a symbolic expression to work with. To evaluate the truth of...