* algebra/si.spad.pamphlet (IntegerNumberSystem) [positive?]:

	Remove definition.
	(SingleInteger): Simplify implementation of random.
	* algebra/sf.spad.pamphlet (DoubleFloat): Likewise.  
	[positive?]: Define.
	* algebra/integer.spad.pamphlet (Integer): Tidy.

3 files changed, 16 insertions, 27 deletions

diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet
index 0b70def4..ac09f419 100644
--- a/src/algebra/integer.spad.pamphlet
+++ b/src/algebra/integer.spad.pamphlet
@@ -86,6 +86,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with
       import %icst1: %                 from Foreign Builtin
       import %ineg: % -> %             from Foreign Builtin
       import %iabs: % -> %             from Foreign Builtin
+      import %irandom: % -> %          from Foreign Builtin
       import %iodd?: % -> Boolean      from Foreign Builtin
       import %hash: % -> SingleInteger from Foreign Builtin
       import %iadd: (%,%) -> %         from Foreign Builtin
@@ -161,6 +162,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with
       dec  x  == x - 1@%
       hash x == %hash x
       negative? x == x < 0@%
+      positive? x == 0 < x
       coerce(x):OutputForm == outputForm(x pretend Integer)
       coerce(m:Integer):% == m pretend %
       convert(x:%):Integer == x pretend Integer
@@ -199,7 +201,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with
 
       abs(x) == %iabs x
       random() == random()$Lisp
-      random(x) == RANDOM(x)$Lisp
+      random(x) == %irandom x
       x = y == %ieq(x,y)
       x < y == %ilt(x,y)
       x > y == %igt(x,y)
diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet
index 1a6f8266..bfd30d62 100644
--- a/src/algebra/sf.spad.pamphlet
+++ b/src/algebra/sf.spad.pamphlet
@@ -473,9 +473,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath,
 
    sign(x) == retract FLOAT_-SIGN(x,1)$Lisp
    abs x   == %fabs x
-
-
-   
+   positive? x == 0 < x
    manexp(x) ==
       zero? x => [0,0]
       s := sign x
diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet
index 085cc0fe..ad162629 100644
--- a/src/algebra/si.spad.pamphlet
+++ b/src/algebra/si.spad.pamphlet
@@ -84,7 +84,6 @@ IntegerNumberSystem(): Category ==
    characteristic == 0
    differentiate x          == 0
    even? x                  == not odd? x
-   positive? x              == x > 0
    copy x                   == x
    bit?(x, i)               == odd? shift(x, -i)
    mask n                   == dec shift(1, n)
@@ -181,10 +180,7 @@ IntegerNumberSystem(): Category ==
 
 
 -- Lisp dependencies
--- ABSVAL, TIMES,
--- QSLESSP, QSGREATERP, QSDIFFERENCE
--- QSNOT, QSAND
--- QSOR, QSXOR, QSLEFTSHIFT, QSADDMOD, QSDIFMOD, QSMULTMOD
+-- QSLEFTSHIFT, QSADDMOD, QSDIFMOD, QSMULTMOD
 
 
 SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) with
@@ -212,6 +208,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w
 
    import %icst0: %                 from Foreign Builtin
    import %icst1: %                 from Foreign Builtin
+   import %icstmin: %               from Foreign Builtin
+   import %icstmax: %               from Foreign Builtin
    import %iadd: (%,%) -> %         from Foreign Builtin
    import %isub: (%,%) -> %         from Foreign Builtin
    import %imul: (%,%) -> %         from Foreign Builtin
@@ -221,6 +219,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w
    import %iinc: % -> %             from Foreign Builtin
    import %idec: % -> %             from Foreign Builtin
    import %iabs: % -> %             from Foreign Builtin
+   import %irandom: % -> %          from Foreign Builtin
    import %imax: (%,%) -> %         from Foreign Builtin
    import %imin: (%,%) -> %         from Foreign Builtin
    import %igcd: (%,%) -> %         from Foreign Builtin
@@ -237,13 +236,6 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w
    import %bitior: (%,%) -> %       from Foreign Builtin
    import %bitxor: (%,%) -> %       from Foreign Builtin
 
-   seed : % := %icst1               -- for random()
-   MAXINT ==> _$ShortMaximum$Lisp
-   MININT ==> _$ShortMinimum$Lisp
-   BASE ==> 67108864$Lisp           -- 2**26
-   MULTIPLIER ==> 314159269$Lisp    -- from Knuth's table
-   MODULUS ==> 2147483647$Lisp      -- 2**31-1
-
    writeOMSingleInt(dev: OpenMathDevice, x: %): Void ==
     if negative? x then
       OMputApp(dev)
@@ -296,8 +288,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w
    0         == %icst0
    1         == %icst1
    base()    == per 2
-   max()     == MAXINT
-   min()     == MININT
+   max()     == %icstmax
+   min()     == %icstmin
    x = y     == %ieq(x,y)
    ~ x       == %bitnot x
    not(x)    == %bitnot x
@@ -339,10 +331,10 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w
    submod(a,b,p) == QSDIFMOD(a,b,p)$Lisp
    negative?(x)  == %ilt(x,%icst0)
    size() ==
-     (MAXINT - MININT + 1)  pretend NonNegativeInteger
-   index i == per(i + MININT - 1)
+     (%icstmax - %icstmin + %icst1)  pretend NonNegativeInteger
+   index i == per(i + rep %icstmin - rep %icst1)
    lookup x ==
-     (x - MININT + 1) pretend PositiveInteger
+     (x - %icstmin + %icst1) pretend PositiveInteger
 
 
    reducedSystem(m: Matrix %, v: Vector %) ==
@@ -356,17 +348,14 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w
       r
 
    coerce(x:Integer):% == per x
-
-   random() ==
-      seed := TIMES(MULTIPLIER,seed)$Lisp rem MODULUS
-      seed rem BASE
-
-   random(n) == RANDOM(n)$Lisp
+   random() == random %icstmax
+   random(n) == %irandom n
 
    UCA ==> Record(unit:%,canonical:%,associate:%)
    unitNormal x ==
       negative? x => [-1@%,-x,-1@%]$UCA
       [1@%,x,1@%]$UCA
+   positive? x == 0 < x
 
 @