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Define gcd & lcm of single element #3595

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Define gcd & lcm of single element #3595

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2 changes: 2 additions & 0 deletions M2/Macaulay2/m2/factor.m2
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Original file line number Diff line number Diff line change
Expand Up @@ -37,6 +37,7 @@ gcd(RingElement,RingElement) := RingElement => (r,s) -> (
if s%a != 0 then error "can't find gcd in this ring";
s // a))
else notImplemented()))
gcd RingElement := identity

gcdCoefficients(RingElement,RingElement) := (f,g) -> ( -- ??
R := ring f;
Expand All @@ -52,6 +53,7 @@ lcm(RingElement,RingElement) := (f,g) -> (
d := gcd(f, g);
if d == 0 then d
else f * (g // d))
lcm RingElement := identity

-----------------------------------------------------------------------------

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2 changes: 2 additions & 0 deletions M2/Macaulay2/m2/integers.m2
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Expand Up @@ -51,6 +51,7 @@ gcd(QQ,ZZ) := QQ => (y,x) -> gcd(x * denominator y, numerator y) / denominator y
gcd(QQ,QQ) := QQ => (x,y) -> (
d := denominator x * (denominator y // gcd(denominator x, denominator y));
gcd(numerator (x * d), numerator (y * d)) / d)
gcd ZZ := gcd QQ := identity

abs = method()
abs ZZ := abs RR := abs RRi := abs CC := abs QQ := abs0
Expand All @@ -68,6 +69,7 @@ lcm(QQ,QQ) := (f,g) -> (
d := gcd(f, g);
if d == 0 then 0_QQ
else abs f * (abs g / d))
lcm ZZ := lcm QQ := identity
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Number, perhaps?

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I thought about that. I stuck with ZZ and QQ since those are the ones we have binary methods for. It seems like it might be a bit strange if, say, gcd(3.0) worked but gcd(3.0, 6.0) didn't.


odd = x -> 1 === x%2
even = x -> 0 === x%2
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9 changes: 8 additions & 1 deletion M2/Macaulay2/packages/Macaulay2Doc/operators.m2
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Expand Up @@ -148,7 +148,11 @@ document {
(gcd, QQ, ZZ),
(gcd, ZZ, ZZ),
(gcd,RingElement,ZZ),
(gcd,ZZ,RingElement)},
(gcd,ZZ,RingElement),
(gcd, ZZ),
(gcd, QQ),
(gcd, RingElement)
},
Headline => "greatest common divisor",
Usage => "gcd(x,y,...)",
Inputs => { "x" => ZZ, ", or ", ofClass QQ, ", or ",ofClass RingElement },
Expand All @@ -175,6 +179,9 @@ doc ///
(lcm, ZZ, ZZ)
(lcm,RingElement,ZZ)
(lcm,ZZ,RingElement)
(lcm, ZZ)
(lcm, QQ)
(lcm, RingElement)
Headline
least common multiple
Usage
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4 changes: 4 additions & 0 deletions M2/Macaulay2/tests/normal/gcd.m2
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Expand Up @@ -3,17 +3,21 @@ assert( gcd(2*3*5,2*3*7,2*5*7,3*5*7) == 1 )
assert( gcd(1000:2) == 2 )
assert( gcd splice(1000:2,3) == 1 )
assert( gcd {} == 0 )
assert( gcd 2 == 2 )
assert( lcm(2,3,5,7) == 210 )
assert( lcm(1000:2) == 2 )
assert( lcm(0, 0) == 0 )
assert( lcm(0/1, 0/1) == 0 )
assert( lcm {} == 1 )
assert( lcm 2 == 2 )

R = ZZ/32003[x,y]
f = (x+y)^3*(x-y^2)
g = (x+y)^2*(x^3-x*y+y^3)^4
assert ( gcd(f,g) == (x+y)^2 )
assert ( lcm(0_R, 0_R) == 0 )
assert ( gcd f == f )
assert ( lcm f == f )

GF 729[x, y, z]
assert( gcd((x^5+y^3+a+1)*(y-1),(x^5+y^3+a+1)*(z+1)) == x^5+y^3+a+1 )
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