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-rw-r--r--src/algebra/integer.spad.pamphlet32
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,