/usr/share/axiom-20170501/src/algebra/INTCAT.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | )abbrev category INTCAT IntervalCategory
++ Author: Mike Dewar
++ Date Created: November 1996
++ Description:
++ This category implements of interval arithmetic and transcendental
++ functions over intervals.
IntervalCategory(R) : Category == SIG where
R : Join(FloatingPointSystem,TranscendentalFunctionCategory)
GD ==> GcdDomain
OS ==> OrderedSet
TFC ==> TranscendentalFunctionCategory
RC ==> RadicalCategory
RI ==> RetractableTo(Integer)
SIG ==> Join(GD,OS,TFC,RC,RI) with
approximate
interval : (R,R) -> %
++ interval(inf,sup) creates a new interval, either \axiom{[inf,sup]} if
++ \axiom{inf <= sup} or \axiom{[sup,in]} otherwise.
qinterval : (R,R) -> %
++ qinterval(inf,sup) creates a new interval \axiom{[inf,sup]}, without
++ checking the ordering on the elements.
interval : R -> %
++ interval(f) creates a new interval around f.
interval : Fraction Integer -> %
++ interval(f) creates a new interval around f.
inf : % -> R
++ inf(u) returns the infinum of \axiom{u}.
sup : % -> R
++ sup(u) returns the supremum of \axiom{u}.
width : % -> R
++ width(u) returns \axiom{sup(u) - inf(u)}.
positive? : % -> Boolean
++ positive?(u) returns \axiom{true} if every element of u is positive,
++ \axiom{false} otherwise.
negative? : % -> Boolean
++ negative?(u) returns \axiom{true} if every element of u is negative,
++ \axiom{false} otherwise.
contains? : (%,R) -> Boolean
++ contains?(i,f) returns true if \axiom{f} is contained within the
++ interval \axiom{i}, false otherwise.
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