| 1 | #-----------------------------------------------------------------------------
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| 2 | #
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| 3 | # Hermite polynomial
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| 4 | #
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| 5 | # Input: tos-2 x (can be a symbol or expr)
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| 6 | #
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| 7 | # tos-1 n
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| 8 | #
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| 9 | # Output: Result on stack
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| 10 | #
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| 11 | #-----------------------------------------------------------------------------
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| 12 |
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| 13 |
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| 14 |
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| 15 | hermite = ->
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| 16 | save()
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| 17 | yyhermite()
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| 18 | restore()
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| 19 |
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| 20 | # uses the recurrence relation H(x,n+1)=2*x*H(x,n)-2*n*H(x,n-1)
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| 21 |
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| 22 | #define X p1
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| 23 | #define N p2
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| 24 | #define Y p3
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| 25 | #define Y1 p4
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| 26 | #define Y0 p5
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| 27 |
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| 28 | yyhermite = ->
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| 29 |
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| 30 | n = 0
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| 31 |
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| 32 | p2 = pop()
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| 33 | p1 = pop()
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| 34 |
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| 35 | push(p2)
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| 36 | n = pop_integer()
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| 37 |
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| 38 | if (n < 0 || isNaN(n))
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| 39 | push_symbol(HERMITE)
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| 40 | push(p1)
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| 41 | push(p2)
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| 42 | list(3)
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| 43 | return
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| 44 |
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| 45 | if (issymbol(p1))
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| 46 | yyhermite2(n)
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| 47 | else
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| 48 | p3 = p1; # do this when X is an expr
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| 49 | p1 = symbol(SECRETX)
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| 50 | yyhermite2(n)
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| 51 | p1 = p3
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| 52 | push(symbol(SECRETX))
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| 53 | push(p1)
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| 54 | subst()
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| 55 | Eval()
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| 56 |
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| 57 | yyhermite2 = (n) ->
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| 58 | i = 0
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| 59 |
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| 60 | push_integer(1)
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| 61 | push_integer(0)
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| 62 |
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| 63 | p4 = pop()
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| 64 |
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| 65 | for i in [0...n]
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| 66 |
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| 67 | p5 = p4
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| 68 |
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| 69 | p4 = pop()
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| 70 |
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| 71 | push(p1)
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| 72 | push(p4)
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| 73 | multiply()
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| 74 |
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| 75 | push_integer(i)
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| 76 | push(p5)
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| 77 | multiply()
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| 78 |
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| 79 | subtract()
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| 80 |
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| 81 | push_integer(2)
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| 82 | multiply()
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| 83 |
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