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| It's an output form you would choose for certain kinds of expressions. I have monsters containing lots of `Root` constants in mind. If not appropriate for your expression, don't choose it. |
| Please post the actual Mathematica code you attempted to use to solve this. |
| **FullSimplify** works, but it is much slower: Timing[mkAlgebraic[thing]] (* {0.052406, Root[1 - 10 #1 + 5 #1^3 &, 2] + Sin[1]} *) Timing[FullSimplify[Re[thing]] + FullSimplify[Im[thing]]] (* {3.76156, Root[1 - 10 #1 + 5 #1^3 &,... |
| That one doesn't depend on x either. Did you forget to put a space between **b** and **x**? |
| A 19th order polynomial expressed as a power series with approximate numerical coefficients is not an object from which I would expect to extract any mathematical sense. |
| **RotationMatrix** rotates the vectors, not the coordinate system. Either change the sign of your angle or transpose your matrix if you want to rotate the coordinates. |
| Mathematica has a rigorous, general way to deal with this. roots = x /. Solve[x^3 - 3 x - 1 == 0, x, Cubics -> False] {Root[-1 - 3 #1 + #1^3 &, 1], Root[-1 - 3 #1 + #1^3 &, 2], Root[-1 - 3 #1 + #1^3 &, 3]} Now, that looks like it... |
| RealDigits[N[Sqrt[2] - 1, 6], 2] yields {{1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1}, -1} |
| To use pattern matching to turn an enumeration into a function, define your "plus" function as follows: plus[a,a]=a plus[a,b]=b plus[b,a]=b ... When the left hand side matches, the right hand side replaces it. Note that `a`... |
| Your code exactly evaluates "nc" already: 77/51 is an exact rational number. It has no exact, finite decimal representation: 77/51 is the best you can have. If you want to see lots of digits, try something like N[nc,1000]. |