diff options
Diffstat (limited to 'src/algebra/intfact.spad.pamphlet')
| -rw-r--r-- | src/algebra/intfact.spad.pamphlet | 38 |
1 files changed, 19 insertions, 19 deletions
diff --git a/src/algebra/intfact.spad.pamphlet b/src/algebra/intfact.spad.pamphlet index a1e08c3b..f12bf58f 100644 --- a/src/algebra/intfact.spad.pamphlet +++ b/src/algebra/intfact.spad.pamphlet @@ -101,7 +101,7 @@ IntegerPrimesPackage(I:IntegerNumberSystem): with if even? m then m := m + 1 ll:List(I) := [k::I for k in convert(m)@Integer..convert(n)@Integer by 2 | prime?(k::I)] - reverse_! concat_!(ll, l) + reverse! concat!(ll, l) rabinProvesComposite : (I,I,I,I,NonNegativeInteger) -> Boolean rabinProvesCompositeSmall : (I,I,I,I,NonNegativeInteger) -> Boolean @@ -383,8 +383,8 @@ IntegerFactorizationPackage(I): Exports == Implementation where y := one?(m:= unit x) => factorList x (v := perfectSqrt m) case I => - concat_!(factorList x, ["sqfr",v,2]$FFE) - concat_!(factorList x, ["sqfr",m,1]$FFE) + concat!(factorList x, ["sqfr",v,2]$FFE) + concat!(factorList x, ["sqfr",m,1]$FFE) makeFR(u, y) -- Pfun(y: I,n: I): I == (y**2 + 5) rem n @@ -447,18 +447,18 @@ IntegerFactorizationPackage(I): Exports == Implementation where BasicSieve(r, lim) == l:List(I) := [1::I,2::I,2::I,4::I,2::I,4::I,2::I,4::I,6::I,2::I,6::I] - concat_!(l, rest(l, 3)) + concat!(l, rest(l, 3)) d := 2::I n := r ls := empty()$List(FFE) for s in l repeat d > lim => return makeFR(n, ls) if n<d*d then - if n>1 then ls := concat_!(ls, ["prime",n,1]$FFE) + if n>1 then ls := concat!(ls, ["prime",n,1]$FFE) return makeFR(1, ls) m : Integer for m in 0.. while zero?(n rem d) repeat n := n quo d - if m>0 then ls := concat_!(ls, ["prime",d,convert m]$FFE) + if m>0 then ls := concat!(ls, ["prime",d,convert m]$FFE) d := d+s BasicMethod n == @@ -479,36 +479,36 @@ IntegerFactorizationPackage(I): Exports == Implementation where a:LMI := dictionary() -- numbers yet to be factored b:LMI := dictionary() -- prime factors found f:LMI := dictionary() -- number which could not be factored - insert_!(n, a) + insert!(n, a) while not empty? a repeat n := inspect a; c := count(n, a); - remove_!(n, a) - prime?(n)$IntegerPrimesPackage(I) => insert_!(n, b, c) + remove!(n, a) + prime?(n)$IntegerPrimesPackage(I) => insert!(n, b, c) -- test for a perfect power (s := perfectNthRoot n).exponent > 1 => - insert_!(s.base, a, c * s.exponent) + insert!(s.base, a, c * s.exponent) -- test for a difference of square x:=approxSqrt n; if (x**2<n) then x:=x+1 (y:=perfectSqrt (x**2-n)) case I => - insert_!(x+y,a,c) - insert_!(x-y,a,c) + insert!(x+y,a,c) + insert!(x-y,a,c) (d := PollardSmallFactor20 n) case I => m' : NonNegativeInteger for m' in 0.. while zero?(n rem d) repeat n := n quo d - insert_!(d, a, m' * c) - if n > 1 then insert_!(n, a, c) + insert!(d, a, m' * c) + if n > 1 then insert!(n, a, c) -- an elliptic curve factorization attempt should be made here - insert_!(n, f, c) + insert!(n, f, c) -- insert prime factors found while not empty? b repeat - n := inspect b; c := count(n, b); remove_!(n, b) - flb := concat_!(flb, ["prime",n,convert c]$FFE) + n := inspect b; c := count(n, b); remove!(n, b) + flb := concat!(flb, ["prime",n,convert c]$FFE) -- insert non-prime factors found while not empty? f repeat - n := inspect f; c := count(n, f); remove_!(n, f) - flb := concat_!(flb, ["nil",n,convert c]$FFE) + n := inspect f; c := count(n, f); remove!(n, f) + flb := concat!(flb, ["nil",n,convert c]$FFE) makeFR(u, flb) @ |