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Meaning of 1.name

Posted 10 years ago
 Hi! What does the form 1.number mean? I am getting answers in the form 1.pi or 1.d where d is a variable. There is also just 1. , can someone please explain this? Example: (-0.5 Cos[1. (-3. + 1. a + 1. c - 1. d) pi] + 0.5 Cos[1. (-3. + 1. a - 1. c + 1. d) pi])/((-3. + 1. a) (c - 1. d) pi^2) 
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Posted 10 years ago
 The 1.0 coefficients can be changed to exact 1's in a variety of ways. A simple method is with Rationalize. In[1]:= expr = (-0.5 Cos[1. (-3. + 1. a + 1. c - 1. d) pi] + 0.5 Cos[1. (-3. + 1. a - 1. c + 1. d) pi])/((-3. + 1. a) (c - 1. d) pi^2); In[2]:= rexpr = Rationalize[expr] -Cos[(-3 + a + c - d) pi] Cos[(-3 + a - c + d) pi] ------------------------- + ------------------------ 2 2 Out[2]= ---------------------------------------------------- 2 (-3 + a) (c - d) pi In[3]:= Together[%] -Cos[(-3 + a + c - d) pi] + Cos[(-3 + a - c + d) pi] Out[3]= ---------------------------------------------------- 2 2 (-3 + a) (c - d) pi If by "pi", you mean 3.14159..., this can be simplified further. In[4]:= FullSimplify[rexpr /. pi -> Pi, Element[{a, c, d}, Reals] ] Sin[a Pi] Sin[(c - d) Pi] Out[4]= -(-------------------------) 2 (-3 + a) (c - d) Pi where In[5]:= ? /. expr /.rules applies a rule or list of rules in an attempt to transform each subpart of an expression expr. In[6]:= ? -> lhs -> rhs represents a rule that transforms lhs to rhs. 
Posted 10 years ago
 Thank you! This was extremely helpful!
Posted 10 years ago
 It means there is a coefficient which is the machine double precision 1.0. Since this is not an exact number (such as 1 or Pi or 7/3) it does not get "absorbed" by the rest of the term. This is important since it would be bad to give an exact result for an approximate quantity, even a symbolic one.