diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 32 |
1 files changed, 15 insertions, 17 deletions
diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index df709373..789695d6 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -74,8 +74,9 @@ Integer: IntegerNumberSystem with canonical ++ mathematical equality is data structure equality. == add - ZP ==> SparseUnivariatePolynomial % - ZZP ==> SparseUnivariatePolynomial Integer + macro ZP == SparseUnivariatePolynomial % + macro ZZP == SparseUnivariatePolynomial Integer + macro NNI == NonNegativeInteger import %icst0: % from Foreign Builtin import %icst1: % from Foreign Builtin import %ineg: % -> % from Foreign Builtin @@ -105,20 +106,17 @@ Integer: IntegerNumberSystem with import %i2s: % -> String from Foreign Builtin import %strconc: (String,String) -> String from Foreign Builtin - x,y: % - n: NonNegativeInteger - - zero? x == x = %icst0 - one? x == x = %icst1 + zero? x == x = 0$% + one? x == x = 1$% 0 == %icst0 1 == %icst1 base() == 2 pretend % copy x == x - inc x == x + %icst1 - dec x == x - %icst1 + inc x == x + 1$% + dec x == x - 1$% hash x == %hash x - negative? x == x < %icst0 - positive? x == %icst0 < 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 @@ -132,7 +130,7 @@ Integer: IntegerNumberSystem with latex(x:%):String == s := %i2s x - -%icst1 < x and x < 10 => s + -1$% < x and x < 10 => s %strconc("{", %strconc(s, "}")) positiveRemainder(a, b) == @@ -159,9 +157,9 @@ Integer: IntegerNumberSystem with - x == %ineg x x + y == %iadd(x,y) x - y == %isub(x,y) - x * y == %imul(x,y) + x:% * y:% == %imul(x,y) (m:Integer) * (y:%) == %imul(m,y) -- for subsumption problem - x ** n == %ipow(x,n)$Foreign(Builtin) + x:% ** n:NNI == %ipow(x,n)$Foreign(Builtin) odd? x == %iodd? x even? x == %ieven? x max(x,y) == %imax(x,y) @@ -170,12 +168,12 @@ Integer: IntegerNumberSystem with x quo y == %iquo(x,y) x rem y == %irem(x,y) shift(x, y) == %ilshift(x,y) - recip(x) == if one? x or x=-1 then x else "failed" + recip(x) == if one? x or x=-1$% then x else "failed" gcd(x,y) == %igcd(x,y) UCA ==> Record(unit:%,canonical:%,associate:%) unitNormal x == - negative? x => [-%icst1,-x,-%icst1]$UCA - [%icst1,x,%icst1]$UCA + negative? x => [-1$%,-x,-1$%]$UCA + [1$%,x,1$%]$UCA unitCanonical x == abs x solveLinearPolynomialEquation(lp:List ZP,p:ZP):Union(List ZP,"failed") == solveLinearPolynomialEquation(lp pretend List ZZP, |