A tensor can be built like a matrix, by entering a rectangular nested list of its entries,
i1 : makeTensor{{{1,2},{3,4}},{{5,6},{7,8}}}
+------+------+
o1 = |{1, 2}|{3, 4}|
+------+------+
|{5, 6}|{7, 8}|
+------+------+
8
o1 : ZZ {2x2x2}
|
or by entering its dimensions followed by a non-nested visible list of entries
i2 : makeTensor({2,2,2},{1,2,3,4,5,6,7,8})
+------+------+
o2 = |{1, 2}|{3, 4}|
+------+------+
|{5, 6}|{7, 8}|
+------+------+
8
o2 : ZZ {2x2x2}
|
i3 : makeTensor({3,3,3},1..27)
+------------+------------+------------+
o3 = |{1 , 2 , 3 }|{4 , 5 , 6 }|{7 , 8 , 9 }|
+------------+------------+------------+
|{10, 11, 12}|{13, 14, 15}|{16, 17, 18}|
+------------+------------+------------+
|{19, 20, 21}|{22, 23, 24}|{25, 26, 27}|
+------------+------------+------------+
27
o3 : ZZ {3x3x3}
|
or by entering its dimenions followed by a function which gives the entries of tensor as a function of their position keys,
i4 : R=QQ[x,y,z] o4 = R o4 : PolynomialRing |
i5 : T=makeTensor({3,3,3},(i,j,k)->x^i*y^j*z^k)
+---------------+--------------------+---------------------+
| 2 | 2 | 2 2 2 2 |
o5 = |{1 , z , z }|{y , y*z , y*z }|{y , y z , y z }|
+---------------+--------------------+---------------------+
| 2 | 2 | 2 2 2 2 |
|{x , x*z, x*z }|{x*y, x*y*z, x*y*z }|{x*y , x*y z, x*y z }|
+---------------+--------------------+---------------------+
| 2 2 2 2 | 2 2 2 2 | 2 2 2 2 2 2 2 |
|{x , x z, x z }|{x y, x y*z, x y*z }|{x y , x y z, x y z }|
+---------------+--------------------+---------------------+
27
o5 : R {3x3x3}
|
i6 : T_(1,2,2)==x^1*y^2*z^2 o6 = true |
The constructor tensor is used to return tensors from tensor-related types defined in the Tensors package.