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Add Vector == ZZ method #3606

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Add Vector == ZZ method #3606

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f0815b9
Add +, -, and == methods for Vector and Number/RingElement/ZZ
d-torrance Dec 4, 2024
0aba649
Add == methods for Matrix/Vector
d-torrance Dec 5, 2024
07cf2da
Document +/- methods for Vector & Number/RingElement
d-torrance Dec 8, 2024
6f014fd
Preserve source when using Number/RingElement +/- Matrix
d-torrance Dec 9, 2024
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30 changes: 20 additions & 10 deletions M2/Macaulay2/m2/matrix.m2
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Expand Up @@ -102,8 +102,10 @@ Matrix _ Sequence := RingElement => (m,ind) -> (
else error "expected a sequence of length two"
)

Number == Matrix :=
RingElement == Matrix := (r,m) -> m == r
Number == Matrix :=
RingElement == Matrix :=
Number == Vector :=
RingElement == Vector := (r,m) -> m == r
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I get that this is necessary but looking at it I realized I hate the way things are, so opened #3608.


Matrix == Matrix := (f,g) -> (
if source f === source g
Expand All @@ -115,26 +117,34 @@ Matrix == Matrix := (f,g) -> (
target f == target g and
raw(super f * inducedMap(source f, source g)) === raw super g
)
Vector == Matrix := (v,m) -> matrix v == m
Matrix == Vector := (m,v) -> m == matrix v

Matrix == Number :=
Matrix == RingElement := (m,f) -> m - f == 0 -- slow!
Vector == Number :=
Vector == RingElement := (v,f) -> matrix v == f
Matrix == ZZ := (m,i) -> if i === 0 then rawIsZero m.RawMatrix else m - i == 0

Matrix + Matrix := Matrix => (
(f,g) -> map(target f, source f, reduce(target f, raw f + raw g))
) @@ toSameRing
Matrix + RingElement := (f,r) -> if r == 0 then f else f + r*id_(target f)
RingElement + Matrix := (r,f) -> if r == 0 then f else r*id_(target f) + f
Number + Matrix := (i,f) -> if i === 0 then f else i*id_(target f) + f
Matrix + Number := (f,i) -> if i === 0 then f else f + i*id_(target f)
Matrix + RingElement :=
Matrix + Number := (f,r) -> if r == 0 then f else f + r*id_(target f)
RingElement + Matrix :=
Number + Matrix := (r,f) -> f + r
Vector + Number := Vector + RingElement := (v,r) -> vector(matrix v + r)
Number + Vector := RingElement + Vector := (r,v) -> vector(r + matrix v)
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i1 : Number + Vector := RingElement + Vector := (r,v) -> vector(r + matrix v);

i2 : 1 + (coker matrix {{ 10 }})_0
stdio:1:58:(3):[1]: error: expected source to be free with rank 1

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This is coming from vector(Matrix):

i1 : code (vector, Matrix)

o1 = -- code for method: vector(Matrix)
     M2/Macaulay2/m2/modules.m2:66:17-69:5: --source code:
     vector Matrix := f -> (
          if not isFreeModule source f or numgens source f =!= 1 then error "expected source to be free with rank 1";
          new target f from {f}
         )

Should Vector objects be elements of free modules? Or arbitrary modules?

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That's not the problem. Single generators of any module whatsoever are vectors. The implementation of Number + Vector isn't correct because it uses the identity matrix on the target.

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Hmm, this seems to be a problem with matrix addition:

i1 : M = coker matrix 10;

i2 : A = map(M, ZZ^1, 1)

o2 = | 1 |

                    1
o2 : Matrix M <-- ZZ

i3 : 1 + A

o3 = | 2 |

o3 : Matrix M <-- M

i4 : A + 1

o4 = | 2 |

                    1
o4 : Matrix M <-- ZZ

Shouldn't they both have ZZ^1 as their source?

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I just pushed a new commit that should fix this


Matrix - Matrix := Matrix => (
(f,g) -> map(target f, source f, reduce(target f, raw f - raw g))
) @@ toSameRing
Matrix - RingElement := (f,r) -> if r == 0 then f else f - r*id_(target f)
RingElement - Matrix := (r,f) -> if r == 0 then -f else r*id_(target f) - f
Number - Matrix := (i,f) -> if i === 0 then -f else i*id_(target f) - f
Matrix - Number := (f,i) -> if i === 0 then f else f - i*id_(target f)
Matrix - RingElement :=
Matrix - Number := (f,r) -> if r == 0 then f else f - r*id_(target f)
RingElement - Matrix :=
Number - Matrix := (r,f) -> -f + r
Vector - Number := Vector - RingElement := (v,r) -> vector(matrix v - r)
Number - Vector := RingElement - Vector := (r,v) -> vector(r - matrix v)

- Matrix := Matrix => f -> new Matrix from {
symbol ring => ring f,
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4 changes: 4 additions & 0 deletions M2/Macaulay2/packages/Macaulay2Doc/operators/minus.m2
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Expand Up @@ -82,14 +82,18 @@ document {
(symbol -, Number, InfiniteNumber),
(symbol -, Number, Matrix),
(symbol -, Number, RingElement),
(symbol -, Number, Vector),
(symbol -, RingElement),
(symbol -, RingElement, Constant),
(symbol -, RingElement, InexactNumber),
(symbol -, RingElement, Matrix),
(symbol -, RingElement, Number),
(symbol -, RingElement, RingElement),
(symbol -, RingElement, Vector),
(symbol -, Tally),
(symbol -, Vector),
(symbol -, Vector, Number),
(symbol -, Vector, RingElement),
(symbol -, Vector, Vector),
},
Headline => "a unary or binary operator, usually used for negation or subtraction",
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4 changes: 4 additions & 0 deletions M2/Macaulay2/packages/Macaulay2Doc/operators/plus.m2
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Expand Up @@ -72,16 +72,20 @@ document {
(symbol +, Number, InfiniteNumber),
(symbol +, Number, Matrix),
(symbol +, Number, RingElement),
(symbol +, Number, Vector),
(symbol +, RingElement),
(symbol +, RingElement, Constant),
(symbol +, RingElement, Ideal),
(symbol +, RingElement, InexactNumber),
(symbol +, RingElement, Matrix),
(symbol +, RingElement, Number),
(symbol +, RingElement, RingElement),
(symbol +, RingElement, Vector),
(symbol +, Ideal, Number),
(symbol +, Ideal, RingElement),
(symbol +, Vector),
(symbol +, Vector, Number),
(symbol +, Vector, RingElement),
(symbol +, Vector, Vector),
},
Headline => "a unary or binary operator, usually used for addition",
Expand Down
1 change: 1 addition & 0 deletions M2/Macaulay2/tests/normal/matrix.m2
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Expand Up @@ -363,6 +363,7 @@ A = map(M, ZZ^1, {{1}})
assert Equation(A + A, 0)
assert Equation(A - A, 0)
assert Equation(A, -A)
assert Equation(A + 1, 1 + A)

-- empty matrix
scan({matrix {}, matrix(ZZ, {}), map(ZZ^0, ZZ^0, {}), map(ZZ^0,, {})}, A -> (
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4 changes: 4 additions & 0 deletions M2/Macaulay2/tests/normal/vector.m2
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Expand Up @@ -19,6 +19,10 @@ N = image vars R
v = vector(N, {1, 2, 3})
w = vector(N, {4, 5, 6})
assert Equation(v, vector map(N,, {{1}, {2}, {3}}))
assert Equation(v, matrix v)
assert Equation(matrix v, v)

assert zero vector {0, 0, 0}

-- module operations
assert Equation(+v, v)
Expand Down
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