author | paulson |
Thu, 01 Jul 2004 12:29:53 +0200 | |
changeset 15013 | 34264f5e4691 |
parent 13958 | c1c67582c9b5 |
child 15077 | 89840837108e |
permissions | -rw-r--r-- |
12196 | 1 |
(* Title : Transcendental.thy |
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Author : Jacques D. Fleuriot |
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Copyright : 1998,1999 University of Cambridge |
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New material on integration, etc. Moving Hyperreal/ex
paulson
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12196
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changeset
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1999,2001 University of Edinburgh |
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Description : Power Series, transcendental functions etc. |
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*) |
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Transcendental = NthRoot + Fact + HSeries + EvenOdd + Lim + |
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constdefs |
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root :: "[nat,real] => real" |
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"root n x == (@u. ((0::real) < x --> 0 < u) & (u ^ n = x))" |
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sqrt :: "real => real" |
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"sqrt x == root 2 x" |
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exp :: "real => real" |
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"exp x == suminf(%n. inverse(real (fact n)) * (x ^ n))" |
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sin :: "real => real" |
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"sin x == suminf(%n. (if even(n) then 0 else |
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((- 1) ^ ((n - Suc 0) div 2))/(real (fact n))) * x ^ n)" |
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diffs :: "(nat => real) => nat => real" |
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"diffs c == (%n. real (Suc n) * c(Suc n))" |
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cos :: "real => real" |
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"cos x == suminf(%n. (if even(n) then ((- 1) ^ (n div 2))/(real (fact n)) |
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else 0) * x ^ n)" |
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ln :: "real => real" |
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"ln x == (@u. exp u = x)" |
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pi :: "real" |
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"pi == 2 * (@x. 0 <= (x::real) & x <= 2 & cos x = 0)" |
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tan :: "real => real" |
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"tan x == (sin x)/(cos x)" |
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arcsin :: "real => real" |
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"arcsin y == (@x. -(pi/2) <= x & x <= pi/2 & sin x = y)" |
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arcos :: "real => real" |
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"arcos y == (@x. 0 <= x & x <= pi & cos x = y)" |
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arctan :: "real => real" |
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"arctan y == (@x. -(pi/2) < x & x < pi/2 & tan x = y)" |
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end |