# Sage is refusing to simplify an element of the symbolic ring to an integer

 1 For example: How can I get sage to simplify ( sqrt(2) + sqrt(3) ) * ( sqrt(2) - sqrt(3) ) to -1? I've tried simplify() but it wont do it. Thanks. asked Jan 29 '12 Zaubertrank 23 ● 2 ● 6 DSM 4882 ● 12 ● 65 ● 105

 6 Not every method -- i.e. a function which lives inside an object -- has a function form. What I mean is that you can write sqrt(2), because sqrt is a function, and you could also write 2.sqrt(), but not everything is paired up like that. This holds for simplify too. There is a simplify function, but you can get much tighter control by calling the simplify methods. You can usually look inside an object by hitting TAB. For example: sage: q = ( sqrt(2) + sqrt(3) ) * ( sqrt(2) - sqrt(3) ) sage: q.[HERE I HIT TAB] q.N q.exp_simplify q.leading_coeff q.reduce_trig q.Order q.expand q.leading_coefficient q.rename q.abs q.expand_log q.left q.reset_name q.add q.expand_rational q.left_hand_side q.rhs q.add_to_both_sides q.expand_trig q.lgamma q.right q.additive_order q.factor q.lhs q.right_hand_side [etc..]  In sage, lots of functionality lives inside objects like this. If you type sage: q.simp[TAB] q.simplify q.simplify_factorial q.simplify_log q.simplify_rational q.simplify_exp q.simplify_full q.simplify_radical q.simplify_trig  you'll see a bunch of possibilities. If you type sage: q.simplify_radical?  you can see the docs for it (and two ?? show the code.) All of that is a long-winded way to bring us here: sage: q = ( sqrt(2) + sqrt(3) ) * ( sqrt(2) - sqrt(3) ) sage: q.simplify_radical() -1 sage: q.simplify_full() -1  posted Jan 29 '12 DSM 4882 ● 12 ● 65 ● 105 oh man great answer, I didn't even know about all that functionality, thanks.Zaubertrank (Jan 29 '12)

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