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-rw-r--r--src/algebra/interval.spad.pamphlet26
1 files changed, 13 insertions, 13 deletions
diff --git a/src/algebra/interval.spad.pamphlet b/src/algebra/interval.spad.pamphlet
index a15715c9..db070f59 100644
--- a/src/algebra/interval.spad.pamphlet
+++ b/src/algebra/interval.spad.pamphlet
@@ -131,7 +131,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
positive?(u:%):Boolean == inf(u) > 0
negative?(u:%):Boolean == sup(u) < 0
- _< (a:%,b:%):Boolean ==
+ a:% < b:% ==
if inf(a) < inf(b) then
true
else if inf(a) > inf(b) then
@@ -139,19 +139,19 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
else
sup(a) < sup(b)
- _+ (a:%,b:%):% ==
+ a:% + b:% ==
-- A couple of blatent hacks to preserve the Ring Axioms!
if zero?(a) then return(b) else if zero?(b) then return(a)
if a = b then return qinterval(2*inf(a),2*sup(a))
qinterval(inf(a) + inf(b), sup(a) + sup(b))
- _- (a:%,b:%):% ==
+ a:% - b:% ==
if zero?(a) then return(-b) else if zero?(b) then return(a)
if a = b then 0 else qinterval(inf(a) - sup(b), sup(a) - inf(b))
- _* (a:%,b:%):% ==
+ a:% * b:% ==
-- A couple of blatent hacks to preserve the Ring Axioms!
if one?(a) then return(b) else if one?(b) then return(a)
if zero?(a) then return(0) else if zero?(b) then return(0)
@@ -160,7 +160,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
qinterval(first prods, last prods)
- _* (a:Integer,b:%):% ==
+ a:Integer * b:% ==
if (a > 0) then
qinterval(a*inf(b),a*sup(b))
else if (a < 0) then
@@ -168,18 +168,18 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
else
0
- _* (a:PositiveInteger,b:%):% == qinterval(a*inf(b),a*sup(b))
+ a:PositiveInteger * b:% == qinterval(a*inf(b),a*sup(b))
- _*_* (a:%,n:PositiveInteger):% ==
+ a:% ** n:PositiveInteger ==
contains?(a,0) and zero?((n pretend Integer) rem 2) =>
interval(0,max(inf(a)**n,sup(a)**n))
interval(inf(a)**n,sup(a)**n)
- _- (a:%):% == exactInterval(-sup(a),-inf(a))
+ -(a:%) == exactInterval(-sup(a),-inf(a))
- _= (a:%,b:%):Boolean == (inf(a)=inf(b)) and (sup(a)=sup(b))
- _~_= (a:%,b:%):Boolean == (inf(a)~=inf(b)) or (sup(a)~=sup(b))
+ a:% = b:% == (inf(a)=inf(b)) and (sup(a)=sup(b))
+ a:% ~= b:% == (inf(a)~=inf(b)) or (sup(a)~=sup(b))
1 ==
one : R := normaliseFloat 1
@@ -195,7 +195,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
unit?(u:%):Boolean == contains?(u,0)
- _exquo(u:%,v:%):Union(%,"failed") ==
+ (u:% exquo v:%): Union(%,"failed") ==
contains?(v,0) => "failed"
one?(v) => u
u=v => 1
@@ -256,7 +256,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
exp(u:%):% == qinterval(exp inf u, exp sup u)
- _*_* (u:%,v:%):% ==
+ u:% ** v:% ==
zero?(v) => if zero?(u) then error "0**0 is undefined" else 1
one?(u) => 1
expts : List R := sort [inf(u)**inf(v),sup(u)**sup(v),
@@ -490,7 +490,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa
-- From RadicalCategory
- _*_* (u:%,n:Fraction Integer):% == interval(inf(u)**n,sup(u)**n)
+ u:% ** n:Fraction Integer == interval(inf(u)**n,sup(u)**n)
@
\section{License}