A number of methods are especially useful when working with polynomials. Let's see how they work:
var('x')
exp1 = (x + 3)^3 == (x - 1)^2
show(exp1)
print("Expanded expression:")
exp2 = exp1.expand()
show(exp2)
print("Expand left-hand side only:")
show(exp1.expand('left'))
lhs = exp1.expand('left').lhs()
print("Factor LHS:")
show(lhs.factor())
print("Information about the expanded LHS:")
print(" Highest degree of x on LHS: {0}".format(lhs.degree(x)))
print(" Coefficients: {0}".format(lhs.coeffs(x)))
print(" Coefficient of x^2: {0}".format(lhs.coeff(x,2)))
print(" Trailing coefficient of LHS: {0}".format
(lhs.trailing_coefficient(x)))The output is shown in the following screenshot:
