$SPAD/src/input defintrf.input

Timothy Daly December 3, 2016

Abstract

Contents

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1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

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— * —

)set break resume
)spool defintrf.output
)set message test on
)set message auto off
)clear all

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This is a difficult example from Kahan. Most symbolic indefinite integrals for f will have a pole between 1 and 2. Note that f is positive on [1..2] so we expect the integral to be positive

— * —

--S 1 of 3
f := (x**4 - 3*x**2 + 6)/(x**6-5*x**4+5*x**2+4)
--R
--R
--R            4     2
--R           x  - 3x  + 6
--R   (1)  ------------------
--R         6     4     2
--R        x  - 5x  + 5x  + 4
--R                                          Type: Fraction(Polynomial(Integer))
--E 1
--S 2 of 3
integrate(f, x = 1..2)
--R
--R
--R                                               1
--R        2atan(8) + 2atan(5) + 2atan(2) + 2atan(-) - %pi
--R                                               2
--R   (2)  -----------------------------------------------
--R                               2
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 2
--S 3 of 3
numeric %
--R

--R
--R   (3)  2.8198420991 931510451
--R                                                                  Type: Float
--E 3
)spool
)lisp (bye)

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References^{[1] nothing}

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