Allow negative indices when getting matrix entries

Also support using Matrix_Sequence to get submatrices, just like we've
been doing with MutableMatrix_Sequence.

Author: d-torrance

M2/Macaulay2/m2/engine.m2

@@ -323,13 +323,23 @@ RawMatrix.synonym = "raw matrix"
 setAttribute(RawMutableMatrix,ReverseDictionary,symbol RawMutableMatrix)
 RawMutableMatrix.synonym = "raw mutable matrix"
 
+-- helper functions for negative indices
+adjustIndex = (i, n) -> if i < 0 then n + i else i
+adjustIndices = (I, n) -> apply(I, i -> adjustIndex(i, n))
+
 rawExtract = method()
 
 rawExtract(RawMatrix,ZZ,ZZ) := 
-rawExtract(RawMutableMatrix,ZZ,ZZ) := (m,r,c) -> rawMatrixEntry(m,r,c)
+rawExtract(RawMutableMatrix,ZZ,ZZ) := (m,r,c) -> (
+    r = adjustIndex(r, rawNumberOfRows m);
+    c = adjustIndex(c, rawNumberOfColumns m);
+    rawMatrixEntry(m, r, c))
 
 rawExtract(RawMatrix,Sequence,Sequence) := 
-rawExtract(RawMutableMatrix,Sequence,Sequence) := (m,r,c) -> rawSubmatrix(m,spliceInside r,spliceInside c)
+rawExtract(RawMutableMatrix,Sequence,Sequence) := (m,r,c) -> (
+    r = adjustIndices(spliceInside r, rawNumberOfRows m);
+    c = adjustIndices(spliceInside c, rawNumberOfColumns m);
+    rawSubmatrix(m,spliceInside r,spliceInside c))
 
 RawMatrix _ Sequence := 
 RawMutableMatrix _ Sequence := (m,rc) -> ((r,c) -> rawExtract(m,r,c)) rc
@@ -364,7 +374,13 @@ new RawMatrix from RawRingElement := (RawMatrix,f) -> rawMatrix1(rawFreeModule(r
 new RawMatrix from RawMutableMatrix := rawMatrix
 new RawMutableMatrix from RawMatrix := rawMutableMatrix
 
-RawMutableMatrix _ Sequence = (M,ij,val) -> ((i,j) -> (rawSetMatrixEntry(M,i,j,val); val)) ij
+RawMutableMatrix _ Sequence = (M,ij,val) -> ((i,j) -> (
+	rawSetMatrixEntry(
+	    M,
+	    adjustIndex(i, rawNumberOfRows M),
+	    adjustIndex(j, rawNumberOfColumns M),
+	    val);
+	val)) ij
 
 degree RawMatrix := rawMultiDegree
 degrees RawMatrix :=f -> {rawMultiDegree rawTarget f,rawMultiDegree rawSource f}

M2/Macaulay2/m2/matrix.m2

@@ -97,10 +97,10 @@ toSameRing = (m,n) -> (
      else (m,n))
 
 Matrix _ Sequence := RingElement => (m,ind) -> (
-     if # ind === 2
-     then promote(rawMatrixEntry(m.RawMatrix, ind#0, ind#1), ring m)
-     else error "expected a sequence of length two"
-     )
+    n := (raw m)_ind;
+    if instance(n, RawRingElement) then promote(n, ring m)
+    else if instance(n, RawMatrix) then map(ring m, n)
+    else error "internal error")
 
 Number      == Matrix :=
 RingElement == Matrix :=
@@ -442,10 +442,9 @@ Matrix _ ZZ := Vector => (m,i) -> (
      new target h from {h})
 
 -- given a map of free modules, find a submatrix of it
-adjustindex := (I, n) -> apply(I, i -> if i < 0 then n + i else i)
 submatrixFree = (m, rows, cols) -> (
-    if rows =!= null then rows = adjustindex(listZZ rows, numRows m);
-    if cols =!= null then cols = adjustindex(listZZ cols, numColumns m);
+    if rows =!= null then rows = adjustIndices(listZZ rows, numRows m);
+    if cols =!= null then cols = adjustIndices(listZZ cols, numColumns m);
     map(ring m, if rows === null
     then rawSubmatrix(raw cover m, cols)
     else rawSubmatrix(raw cover m, rows,

M2/Macaulay2/tests/normal/mutmat.m2

@@ -2,7 +2,8 @@ R = QQ
 M = mutableMatrix(QQ,3,5)
 M_(0,0) = 1_QQ
 M_(2,4) = 3/4
-M
+M_(-1,-2) = 7
+assert(M == mutableMatrix {{1,0,0,0,0}, {0,0,0,0,0}, {0,0,0,7,3/4}})
 debug Core
 rawSubmatrix(raw M,(0,1),(0,1))
 
@@ -18,6 +19,7 @@ m
 assert(m_(0,2) == z)
 m_(1,2) = x+y
 assert(m_(1,2) == x+y)
+assert(m_(-1,-1) == z)
 assert(not (m == mutableMatrix f))
 m
 rowSwap(m,0,1)

M2/Macaulay2/tests/normal/submatrix.m2

@@ -23,6 +23,7 @@ assert(m^{-1} == map(R^1, N++R^1, {{c, d}}))
 assert(m_{0} == map(N++R^1, N, {{a}, {c}}))
 assert(m_{1} == map(N++R^1, R^1, {{b}, {d}}))
 assert(m_{-1} == map(N++R^1, R^1, {{b}, {d}}))
+assert(m_(-1,-2) == c)
 
 R = QQ[a..d];
 M = image vars R ++ coker vars R