Weird trigonometric integral and Simplification question

*To*: mathgroup at smc.vnet.net*Subject*: [mg31777] Weird trigonometric integral and Simplification question*From*: Bruce Atwood <bta at attewode.com>*Date*: Sat, 1 Dec 2001 02:46:00 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Message 1: Weird trigonometric integral The function Sqrt[1-Cos[t]] is continuous for all real t. Hence its integral must be continuous for all real t. In fact there is a general solution that is continuous for all real t. However Mathematica gives only a "particular" solution that is only true on the interval (0, 2 Pi). Is there any way to know in advance when to expect these subtle and difficult problems? Bruce Atwood Message 2: Simplification question If I set lambda=(1+Sqrt[5])/2, and then ask Mathematica to Expand[lambda^7] or ask for any other power of lambda, Mathematica gives a nice result that I can easily rewrite by hand in the form a + b lambda where a and b are integers. Is there any way to get Mathematica to write the result in this form? (I'm not interested in the answer involving the Fibonacci sequence, I'm interested in learning how to manipulate expressions in Mathematica.) Similarly if I ask Mathematica for Inverse[{{a,b},{c,d}}] it gives a nice result, but how do I get it to factor out a d-b c? I apologize that these types of questions have been asked in the past, but I can't remember or find the answers. Bruce Atwood