Merge pull request #28 from pnnl/develop

fixed typo in tutorial

tutorials/Tutorial 5 - Homology mod 2 for TriLoop Example.ipynb

@@ -152,12 +152,12 @@
     "\n",
     "We induce a total order on the k-cells. This ordering is somewhat arbitrary but for convenience we define a total ordering on the 0-chains (the nodes in the hypergraph) and use lexicographic ordering to induce an ordering on all of the k-chains. In our example this is just alphabetical order.\n",
     "\n",
-    "With this ordering we define an isomorphism $\\phi : C_k \\rightarrow \\otimes_{i=1}^{|C_k|} \\mathbb{Z}_2$. For any chain, $\\sigma \\in C_k$, $\\phi (\\sigma)$ is a tuple of 0's and 1's with a 1 in the ith position of the tuple if the ith element in the $C_k$ ordering is in $\\sigma$. For our example, the 1-chains in $C_1$ are ordered: [AB,AC,AD,BC,CD]. Using this ordering we find:\n",
+    "With this ordering we define an isomorphism $\\phi : C_k \\rightarrow $\\mathbb{Z}_2^{|C_k|}$. For any chain, $\\sigma \\in C_k$, $\\phi (\\sigma)$ is a tuple of 0's and 1's with a 1 in the ith position of the tuple if the ith element in the $C_k$ ordering is in $\\sigma$. For our example, the 1-chains in $C_1$ are ordered: [AB,AC,AD,BC,CD]. Using this ordering we find:\n",
     "- $\\phi(AB) = (1,0,0,0,0)$\n",
     "- $\\phi(BC+CD) = (0,0,0,1,1)$\n",
     "- $\\phi(AC+AD+CD) = (0,1,1,0,1)$\n",
     "\n",
-    "The isomorphism $\\phi$ induces the structure of $\\mathbb{Z}_2^{n_k}$ onto $C_k$. In particular, we can think of $C_k$ as a vector space over $\\mathbb{Z}_2$. This means:\n",
+    "The isomorphism $\\phi$ induces the structure of $\\mathbb{Z}_2^{|C_k|}$ onto $C_k$. In particular, we can think of $C_k$ as a vector space over $\\mathbb{Z}_2$. This means:\n",
     "- We can add k-chains - vector addition mod 2 - and get another k-chain. This addition is associative and abelian (commutative)\n",
     "- We have a \"0\" chain, the empty chain has tuple (0,0,0,0,0)\n",
     "- We have inverses, $\\sigma + \\sigma = 0$ \n",
@@ -638,27 +638,6 @@
     "        label_alpha=.1)"
    ]
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