Description
Pretty-prints the matrix as the GL-equivariant map it represents on the labeled bases. Each row of the netList corresponds to a source basis element (a tableau, or a (tableau, monomial) pair, etc.) and lists the image as a sum over target basis elements with their coefficients. Rows where the image is identically zero appear with an empty list.
After
symbolicForm M is called once, the rule is cached on
M.cache#"rule" so subsequent calls reuse it. For interactive exploration, you can also evaluate the rule on a single basis element directly via
(M.cache#"rule")(label).
i1 : P = QQ[a,b,c];
|
i2 : M = pieri({2,1}, {1}, P);
3 8
o2 : Matrix P <-- P
|
i3 : symbolicForm M
+-----+----------+
|+-+-+| +-+|
o3 = ||0|0||2a * |0||
||1| || |1||
|+-+-+| +-+|
+-----+----------+
|+-+-+| +-+|
||0|0||2a * |0||
||2| || |2||
|+-+-+| +-+|
+-----+----------+
|+-+-+| +-+ |
||0|1||b * |0| |
||1| || |1| |
|+-+-+| +-+ |
+-----+----------+
|+-+-+| +-+ |
||0|1||b * |0| |
||2| || |2| |
|+-+-+| +-+ |
| | +-+ |
| |a * |1| |
| | |2| |
| | +-+ |
+-----+----------+
|+-+-+| +-+ |
||0|2||c * |0| |
||1| || |1| |
|+-+-+| +-+ |
| | +-+|
| |-a * |1||
| | |2||
| | +-+|
+-----+----------+
|+-+-+| +-+ |
||0|2||c * |0| |
||2| || |2| |
|+-+-+| +-+ |
+-----+----------+
|+-+-+| +-+|
||1|1||2b * |1||
||2| || |2||
|+-+-+| +-+|
+-----+----------+
|+-+-+| +-+ |
||1|2||c * |1| |
||2| || |2| |
|+-+-+| +-+ |
+-----+----------+
|
i4 : shapes = ({2,1}, {1}, {1,1});
|
i5 : Q = (lrTableaux shapes)#0;
|
i6 : N = lrMap(shapes, Q, 3);
9 8
o6 : Matrix QQ <-- QQ
|
i7 : symbolicForm N
+-----+-------------------+
|+-+-+| +-+ +-+ |
o7 = ||0|0||3 * |0| ⊗ |0| |
||1| || |1| +-+ |
|+-+-+| +-+ |
+-----+-------------------+
|+-+-+| +-+ +-+ |
||0|0||3 * |0| ⊗ |0| |
||2| || |2| +-+ |
|+-+-+| +-+ |
+-----+-------------------+
|+-+-+|3 +-+ +-+ |
||0|1||- * |0| ⊗ |1| |
||1| ||2 |1| +-+ |
|+-+-+| +-+ |
+-----+-------------------+
|+-+-+|3 +-+ +-+ |
||0|1||- * |0| ⊗ |1| |
||2| ||2 |2| +-+ |
|+-+-+| +-+ |
| |3 +-+ +-+ |
| |- * |1| ⊗ |0| |
| |2 |2| +-+ |
| | +-+ |
+-----+-------------------+
|+-+-+|3 +-+ +-+ |
||0|2||- * |0| ⊗ |2| |
||1| ||2 |1| +-+ |
|+-+-+| +-+ |
| | 3 +-+ +-+|
| |- - * |1| ⊗ |0||
| | 2 |2| +-+|
| | +-+ |
+-----+-------------------+
|+-+-+|3 +-+ +-+ |
||0|2||- * |0| ⊗ |2| |
||2| ||2 |2| +-+ |
|+-+-+| +-+ |
+-----+-------------------+
|+-+-+| +-+ +-+ |
||1|1||3 * |1| ⊗ |1| |
||2| || |2| +-+ |
|+-+-+| +-+ |
+-----+-------------------+
|+-+-+|3 +-+ +-+ |
||1|2||- * |1| ⊗ |2| |
||2| ||2 |2| +-+ |
|+-+-+| +-+ |
+-----+-------------------+
|