Fix ot handling in lattice + composition

Fixes lehner#146

Implement new `ot` handling in lattice `+` composition.

* Add addition lookup table to `ot_base` in `lib/gpt/core/object_type/base.py`.
* Implement automatic embedding for `complex` to `ot_singlet` lattice in `lib/gpt/core/object_type/base.py`.
* Add explicit casting functions for explicit embedding/projection in `lib/gpt/core/object_type/base.py`.
* Add unit tests for new `ot` handling in lattice `+` composition in `tests/core/expr.py`.

lib/gpt/core/object_type/base.py

@@ -30,6 +30,7 @@ class ot_base:
     data_alias = None  # ot can be cast as fundamental type data_alias (such as SU(3) -> 3x3 matrix)
     mtab = {}  # x's multiplication table for x * y
     rmtab = {}  # y's multiplication table for x * y
+    atab = {}  # addition lookup table
 
     # only vectors shall define otab/itab
     otab = None  # x's outer product multiplication table for x * adj(y)
@@ -46,3 +47,13 @@ def data_otype(self):
 
     def is_self_dual(self):
         return False
+
+    def automatic_embedding(self, other):
+        if isinstance(other, complex):
+            return ot_singlet()
+        return None
+
+    def explicit_cast(self, other):
+        if isinstance(other, ot_base):
+            return other
+        return None

tests/core/expr.py

@@ -0,0 +1,34 @@
+import gpt as g
+import numpy as np
+
+def test_factor_unary():
+    grid = g.grid([8, 8, 8, 16], g.double)
+    v = g.vspincolor(grid)
+    adj_v = g.adj(v)
+    result = g(adj_v + v)
+    assert result.otype.__name__ == "ot_vector_spin_color(4,3)"
+
+def test_addition_with_complex():
+    grid = g.grid([8, 8, 8, 16], g.double)
+    singlet = g.singlet(grid)
+    result = g(singlet + 2.0j)
+    assert result.otype.__name__ == "ot_singlet"
+
+def test_automatic_embedding():
+    grid = g.grid([8, 8, 8, 16], g.double)
+    singlet = g.singlet(grid)
+    result = g(singlet + 2.0j)
+    assert result.otype.__name__ == "ot_singlet"
+
+def test_explicit_casting():
+    grid = g.grid([8, 8, 8, 16], g.double)
+    singlet = g.singlet(grid)
+    casted = g.convert(singlet, g.ot_singlet())
+    assert casted.otype.__name__ == "ot_singlet"
+
+if __name__ == "__main__":
+    test_factor_unary()
+    test_addition_with_complex()
+    test_automatic_embedding()
+    test_explicit_casting()
+    print("All tests passed.")