mjo/clan: WIP conversion to three coordinates

diff --git a/mjo/clan/clan_element.py b/mjo/clan/clan_element.py
index 30bf82a3c460bf253d53167e064d07c3c2bd5948..4aba6d1fb437b50a61b5f9a1aeaeaa71b134f396 100644 (file)
--- a/mjo/clan/clan_element.py
+++ b/mjo/clan/clan_element.py
@@ -34,7 +34,7 @@ class ClanElement(IndexedFreeModuleElement):
             sage: C = SnClan(3)
             sage: all( e_ii.inner_product(e_ii) == 1/2
             ....:      for i in range(C.rank())
-            ....:      if (e_ii := C.basis()[(i,i)]) )
+            ....:      if (e_ii := C.basis()[(i,i,1)]) )
             True
 
         """
@@ -71,22 +71,27 @@ class NormalDecompositionElement(ClanElement):
 
             sage: C = SnClan(3)
             sage: x = C.an_element(); x
-            2*B(0, 0) + 2*B(1, 0) + 3*B(1, 1)
+            2*B(0, 0, 1) + 2*B(1, 0, 1) + 3*B(1, 1, 1)
             sage: x.tr()
             5
 
         """
         r = self.parent().rank()
-        return sum( self[i,i] for i in range(r) )
+        return sum( self[i,i,1] for i in range(r) )
 
 
-    def elt(self, idx):
+    def elt(self, i, j):
         r"""
-        The algebra component of ``self`` at index ``idx``.
+        The algebra component of ``self`` at position ``i,j``.
 
         This is in contrast with the usual indexing that returns only
         a coefficient.
 
+        .. WARNING:
+
+            This returns zero if you request a component that does
+            not exist (with ``i`` strictly less than ``j``).
+
         SETUP::
 
             sage: from mjo.clan.unital_clan import SnClan
@@ -99,33 +104,36 @@ class NormalDecompositionElement(ClanElement):
             [ 2  6 10]
             [ 6 10 14]
             [10 14 18]
-            sage: X.elt( (0,0) ).lift().lift()
+            sage: X.elt(0,0).lift().lift()
             [2 0 0]
             [0 0 0]
             [0 0 0]
-            sage: X.elt( (1,0) ).lift().lift()
+            sage: X.elt(1,0).lift().lift()
             [0 6 0]
             [6 0 0]
             [0 0 0]
-            sage: X.elt( (1,1) ).lift().lift()
+            sage: X.elt(1,1).lift().lift()
             [ 0  0  0]
             [ 0 10  0]
             [ 0  0  0]
-            sage: X.elt( (2,0) ).lift().lift()
+            sage: X.elt(2,0).lift().lift()
             [ 0  0 10]
             [ 0  0  0]
             [10  0  0]
-            sage: X.elt( (2,1) ).lift().lift()
+            sage: X.elt(2,1).lift().lift()
             [ 0  0  0]
             [ 0  0 14]
             [ 0 14  0]
-            sage: X.elt( (2,2) ).lift().lift()
+            sage: X.elt(2,2).lift().lift()
             [ 0  0  0]
             [ 0  0  0]
             [ 0  0 18]
 
         """
-        return self[idx]*self.parent().monomial(idx)
+        return sum( ( c*self.parent().monomial(idx)
+                      for (idx,c) in self.items()
+                      if (idx[0] == i and idx[1] == j) ),
+                    self.parent().zero() )
 
 
     def seq(self, i):
@@ -179,19 +187,19 @@ class NormalDecompositionElement(ClanElement):
 
         for m in range(i, P.rank()):
             for k in range(i, m+1):
-                a = x_prev.elt( (m, i-1) )
-                b = x_prev.elt( (k, i-1) )
+                a = x_prev.elt(m, i-1)
+                b = x_prev.elt(k, i-1)
 
-                x_i += x_prev[i-1,i-1]*x_prev.elt( (m,k) )
+                x_i += x_prev[i-1,i-1,1]*x_prev.elt(m,k)
 
                 if k == m:
                     # A special case is needed only for the factor of
                     # two in the inner product.
-                    x_i -= a.inner_product(b) * P.monomial( (m,k) )
+                    x_i -= a.inner_product(b) * P.monomial( (m,k,1) )
                 else:
                     # [m,i]*[k,i] is contained in either [m,k] or [k,m],
                     # whichever makes sense. We've got m>k, so use [m,k].
-                    x_i -= (a*b).elt( (m,k) )
+                    x_i -= (a*b).elt(m,k)
 
         return x_i
 

diff --git a/mjo/clan/unital_clan.py b/mjo/clan/unital_clan.py
index e0a04048f33f11ef2a788c2167a0c6f4094e4ab1..ab601be1c220942e676829ab4cdac356964da3f4 100644 (file)
--- a/mjo/clan/unital_clan.py
+++ b/mjo/clan/unital_clan.py
@@ -154,27 +154,27 @@ class SnClan(NormalDecomposition):
         sage: n = 3
         sage: C = SnClan(n)
         sage: e = C.basis()
-        sage: all( e[i,i]*e[i,i] == e[i,i] for i in range(n) )
+        sage: all( e[i,i,1]*e[i,i,1] == e[i,i,1] for i in range(n) )
         True
-        sage: all( e[i,i]*e[j,i] == e[j,i]/2
+        sage: all( e[i,i,1]*e[j,i,1] == e[j,i,1]/2
         ....:      for i in range(n)
         ....:      for j in range(i+1,n))
         True
-        sage: all( e[i,i]*e[i,k] == e[i,k]/2
+        sage: all( e[i,i,1]*e[i,k,1] == e[i,k,1]/2
         ....:      for i in range(n)
         ....:      for k in range(i))
         True
-        sage: all( (e[i,i]*e[j,k]).is_zero()
+        sage: all( (e[i,i,1]*e[j,k,1]).is_zero()
         ....:      for i in range(n)
         ....:      for j in range(n)
         ....:      for k in range(j+1)
         ....:      if not i in [j,k] )
         True
-        sage: all( (e[i,k]*e[i,i]).is_zero()
+        sage: all( (e[i,k,1]*e[i,i,1]).is_zero()
         ....:      for i in range(n)
         ....:      for k in range(i) )
         True
-        sage: all( (e[j,k]*e[i,i]).is_zero()
+        sage: all( (e[j,k,1]*e[i,i,1]).is_zero()
         ....:      for i in range(n)
         ....:      for j in range(n)
         ....:      for k in range(j)
@@ -186,7 +186,7 @@ class SnClan(NormalDecomposition):
 
         sage: C = SnClan(3)
         sage: x = C.an_element(); x
-        2*B(0, 0) + 2*B(1, 0) + 3*B(1, 1)
+        2*B(0, 0, 1) + 2*B(1, 0, 1) + 3*B(1, 1, 1)
         sage: x.lift().lift()
         [2 2 0]
         [2 3 0]
@@ -199,7 +199,7 @@ class SnClan(NormalDecomposition):
         b = Mn.basis()
 
         from sage.sets.family import Family
-        Sn_basis = Family({ (i,j) :
+        Sn_basis = Family({ (i,j,1) :
             a*(b[(i,j)] + b[(j,i)])
             for i in range(n)
             for j in range(i+1)
@@ -265,7 +265,7 @@ class SnClan(NormalDecomposition):
 
         def ip(x,y):
             p = cp(x,y) / scalar_field(2)
-            return sum( p[(i,i)] for i in range(n) )
+            return sum( p[(i,i,1)] for i in range(n) )
 
         super().__init__(Sn, cp, ip, **kwargs)
 
@@ -300,7 +300,7 @@ class SnClan(NormalDecomposition):
             True
 
         """
-        return sum( self.basis()[i,i] for i in range(self.rank()) )
+        return sum( self.basis()[i,i,1] for i in range(self.rank()) )
 
 
     def from_matrix(self, x):
@@ -323,7 +323,8 @@ class SnClan(NormalDecomposition):
             raise ValueError
         if not self.rank() == x.nrows():
             raise ValueError
-        return self.sum_of_terms( (k, x[k]) for k in self.indices() )
+        return self.sum_of_terms( ((i,j,k), x[i,j])
+                                  for (i,j,k) in self.indices() )
 
 
     def from_list(self, l):