leqslant not leq

Author: RobinHankin

man/as.1form.Rd

@@ -45,14 +45,14 @@ The exterior derivative of a \eqn{k}-form \eqn{\phi}{phi} is a
   to calculate differentials  of general \eqn{k}-forms. Specifically, if
 
   \deqn{
-    \phi=\sum_{1\leq i_i < \cdots < i_k\leq n} a_{i_1\ldots
+    \phi=\sum_{1\leqslant i_i < \cdots < i_k\leqslant n} a_{i_1\ldots
       i_k}\mathrm{d}x_{i_1}\wedge\cdots\wedge\mathrm{d}x_{i_k}
   }{omitted; see latex}
 
   then
   \deqn{
     \mathrm{d}\phi=
-    \sum_{1\leq i_i < \cdots < i_k\leq n}
+    \sum_{1\leqslant i_i < \cdots < i_k\leqslant n}
     [\sum_{j=1}^nD_ja_{i_1\ldots
       i_k}\mathrm{d}x_j]\wedge\mathrm{d}x_{i_1}\wedge
     \cdots\wedge\mathrm{d}x_{i_k.}

man/kform.Rd

@@ -81,15 +81,15 @@ e(i,n)
   returns a matrix whose rows constitute a basis for the vector space
   \eqn{\Lambda^k(\mathbb{R}^n)}{L^k(R^n)} of \eqn{k}-forms:
 
-  \deqn{\phi=\sum_{1\leq i_1 < \cdots < i_k\leq n} a_{i_1\ldots
+  \deqn{\phi=\sum_{1\leqslant i_1 < \cdots < i_k\leqslant n} a_{i_1\ldots
       i_k}\mathrm{d}x_{i_1}\wedge\cdots\wedge\mathrm{d}x_{i_k}}{omitted; see latex}
 
   and indeed we have:
 
   \deqn{a_{i_1\ldots i_k}=\phi\left(\mathbf{e}_{i_1},\ldots,\mathbf{e}_{i_k}\right)
   }{omitted; see latex}
 
-  where \eqn{\mathbf{e}_j,1\leq j\leq k}{e_j,1<=j<=k} is a basis for
+  where \eqn{\mathbf{e}_j,1\leqslant j\leqslant k}{e_j,1<=j<=k} is a basis for
   \eqn{V}.
 
 }

man/kinner.Rd

@@ -15,7 +15,7 @@
 
   \deqn{
     \left\langle\alpha,\beta\right\rangle=\det\left(
-    \left\langle\alpha_i,\beta_j\right\rangle_{1\leq i,j\leq n}\right)
+    \left\langle\alpha_i,\beta_j\right\rangle_{1\leqslant i,j\leqslant n}\right)
   }{ omitted}
 
 and secondly, we extend to the whole of \eqn{\Lambda^k(V)}{omitted}