diff options
Diffstat (limited to 'src/algebra/si.spad.pamphlet')
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 70 |
1 files changed, 44 insertions, 26 deletions
diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index b62da15a..ee43e1dc 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -217,8 +217,26 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM MULTIPLIER ==> 314159269$Lisp -- from Knuth's table MODULUS ==> 2147483647$Lisp -- 2**31-1 + import %icst0: % from Foreign Builtin + import %icst1: % from Foreign Builtin + import %iadd: (%,%) -> % from Foreign Builtin + import %isub: (%,%) -> % from Foreign Builtin + import %imul: (%,%) -> % from Foreign Builtin + import %ineg: % -> % from Foreign Builtin + import %iabs: % -> % from Foreign Builtin + import %imax: (%,%) -> % from Foreign Builtin + import %imin: (%,%) -> % from Foreign Builtin + import %igcd: (%,%) -> % from Foreign Builtin + import %hash: % -> SingleInteger from Foreign Builtin + import %iodd?: % -> Boolean from Foreign Builtin + import %ieq: (%,%) -> Boolean from Foreign Builtin + import %ilt: (%,%) -> Boolean from Foreign Builtin + import %ile: (%,%) -> Boolean from Foreign Builtin + import %igt: (%,%) -> Boolean from Foreign Builtin + import %ige: (%,%) -> Boolean from Foreign Builtin + writeOMSingleInt(dev: OpenMathDevice, x: %): Void == - if x < 0 then + if negative? x then OMputApp(dev) OMputSymbol(dev, "arith1", "unary_minus") OMputInteger(dev, convert(-x)) @@ -265,13 +283,13 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM reducedSystem(m: Matrix %) == m pretend Matrix(Integer) coerce(x):OutputForm == rep(x)::OutputForm convert(x:%):Integer == rep x - i:Integer * y:% == i::% * y - 0 == 0$Lisp - 1 == 1$Lisp - base() == 2$Lisp + i:Integer * y:% == %imul(i::%,y) + 0 == %icst0 + 1 == %icst1 + base() == per 2 max() == MAXINT min() == MININT - x = y == %ieq(x,y)$Foreign(Builtin) + x = y == %ieq(x,y) ~ x == LOGNOT(x)$Lisp not(x) == LOGNOT(x)$Lisp x /\ y == LOGAND(x,y)$Lisp @@ -282,29 +300,29 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM Or(x,y) == LOGIOR(x,y)$Lisp x or y == Or(x,y) xor(x,y) == LOGXOR(x,y)$Lisp - x < y == QSLESSP(x,y)$Lisp - x > y == QSGREATERP(x,y)$Lisp - x <= y == %ile(x,y)$Foreign(Builtin) - x >= y == %ige(x,y)$Foreign(Builtin) + x < y == %ilt(x,y) + x > y == %igt(x,y) + x <= y == %ile(x,y) + x >= y == %ige(x,y) inc x == QSADD1(x)$Lisp dec x == QSSUB1(x)$Lisp - - x == QSMINUS(x)$Lisp - x + y == QSPLUS(x,y)$Lisp - x:% - y:% == QSDIFFERENCE(x,y)$Lisp - x:% * y:% == QSTIMES(x,y)$Lisp + - x == %ineg x + x + y == %iadd(x,y) + x:% - y:% == %isub(x,y) + x:% * y:% == %imul(x,y) x:% ** n:NonNegativeInteger == (%ipow(x, n)$Foreign(Builtin) pretend Integer)::% x quo y == QSQUOTIENT(x,y)$Lisp x rem y == QSREMAINDER(x,y)$Lisp divide(x, y) == CONS(QSQUOTIENT(x,y)$Lisp,QSREMAINDER(x,y)$Lisp)$Lisp - gcd(x,y) == %igcd(x,y)$Foreign(Builtin) - abs(x) == QSABSVAL(x)$Lisp - odd?(x) == QSODDP(x)$Lisp + gcd(x,y) == %igcd(x,y) + abs(x) == %iabs x + odd?(x) == %iodd? x zero?(x) == QSZEROP(x)$Lisp - one?(x) == x = 1 - max(x,y) == QSMAX(x,y)$Lisp - min(x,y) == QSMIN(x,y)$Lisp - hash(x) == HASHEQ(x)$Lisp + one?(x) == x = 1@% + max(x,y) == %imax(x,y) + min(x,y) == %imin(x,y) + hash(x) == %hash x length(x) == INTEGER_-LENGTH(x)$Lisp shift(x,n) == QSLEFTSHIFT(x,n)$Lisp mulmod(a,b,p) == QSMULTMOD(a,b,p)$Lisp @@ -322,9 +340,9 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM positiveRemainder(x,n) == r := QSREMAINDER(x,n)$Lisp - QSMINUSP(r)$Lisp => - QSMINUSP(n)$Lisp => QSDIFFERENCE(x, n)$Lisp - QSPLUS(r, n)$Lisp + negative? r => + negative? n => x - n + r + n r coerce(x:Integer):% == per x @@ -337,8 +355,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM UCA ==> Record(unit:%,canonical:%,associate:%) unitNormal x == - x < 0 => [-1,-x,-1]$UCA - [1,x,1]$UCA + negative? x => [-1@%,-x,-1@%]$UCA + [1@%,x,1@%]$UCA @ |