fixing a few typos in kernel/ (#116)

kernel/addl_code/change_peripheral_curves_nonorientable.c

@@ -144,7 +144,7 @@ FuncResult change_peripheral_curves_nonorientable(
 
             /*
              * Adjust the cusp_shape.
-             * We need to apply complex conjugation because we transfered
+             * We need to apply complex conjugation because we transferred
              * the curves to a different sheet.
              * We need to negate because we flipped the meridian.
              * So, the net effect is to flip the sign of the meridian.

kernel/addl_code/dilog.c

@@ -96,7 +96,7 @@
  * a floating-point number.
  *
  * For the remaining case (1/3 <= |z| <= 3 and Re(z) < 1/2), we use the following
- * identity and then use (3) to compute dilog(1-z) (implemented in dialog_left):
+ * identity and then use (3) to compute dilog(1-z) (implemented in dilog_left):
  *                               2
  *                             pi
  *    dilog(z) + dilog(1-z) = ----- - log(z) * log(1-z)                     (6)

kernel/addl_code/gluing_equations_pgl.c

@@ -426,7 +426,7 @@ void get_internal_gluing_equations_pgl(Triangulation *manifold,
    
    Proof:
 
-   FLOW has the properites that it picks the coefficient of A, B, and C
+   FLOW has the properties that it picks the coefficient of A, B, and C
    are minimal, so in particular, you cannot have a cycle such as taking 
    (1,1,1) as coefficients of A, B, and C.
    This means that we can (non-canonically) lift the homological description

kernel/addl_code/old_link_code/CLinkProjectionPanorama.cc

@@ -733,8 +733,8 @@ void CLinkProjectionPanorama::MaybeCreateOneCrossing(
 	q2 = e2->forwardVertex ->position;
 
 	//	Recall that the coordinates of the vertices will lie (approximately)
-	//	in the range 0 to 1000.  The following comparisions all involve
-	//	binominal expressions in the original coordinates, so there is no
+	//	in the range 0 to 1000.  The following comparisons all involve
+	//	binomial expressions in the original coordinates, so there is no
 	//	danger of overflowing the 32-bit integer arithmetic.
 
 	if
@@ -781,7 +781,7 @@ void CLinkProjectionPanorama::MaybeCreateOneCrossing(
 	//	fear of overflowing the 32-bit integer arithmetic.
 	theDet = (double) (e1->a * e2->b  -  e1->b * e2->a);
 
-	//	Now we swtich over to floating point arithmetic, to avoid computing
+	//	Now we switch over to floating point arithmetic, to avoid computing
 	//	trinomials which might overflow the 32-bit integer arithmetic.
 	theNewCrossing->position.h =
 		(	((double) e2->b * (double) e1->c)

kernel/headers/SnapPea.h

@@ -744,7 +744,7 @@ extern void canonical_retriangulation_with_opacities( Triangulation *manifold,
 /**<
  * Similar to canonical_retriangulation, replaces the given triangulation
  * (which has to be a subdivision of the canonical cell decomposition) with
- * the canonical retriangulation of the canonical cell decompositon.
+ * the canonical retriangulation of the canonical cell decomposition.
  * However, instead of doing numerical comparisons of tilt, it takes an array
  * of booleans indicating which faces are opaque. Four consecutive entries
  * correspond to the four faces of one tetrahedron. Thus, the length has to

kernel/headers/tersest_triangulation.h

@@ -71,8 +71,8 @@
  *      if (CS_is_present == TRUE)
  *          bytes 10 through 17 hold the CS_value, encoded as follows.
  *          First add a multiple of 1/2, if necessary, so that the CS_value
- *          lies in the range [-1/4, 1/4)  Then mulitply by 2 and add 1/2
- *          so that it lies in the ragne [0, 1).  The CS_value is a
+ *          lies in the range [-1/4, 1/4)  Then multiply by 2 and add 1/2
+ *          so that it lies in the range [0, 1).  The CS_value is a
  *          double which on some machines (e.g. the Mac) has an 8-btye
  *          mantissa.  In binary, this is a number like 0.100101000..., with
  *          64 meaningful binary digits after the decimal point (the "binary

kernel/kernel_code/fundamental_group.c

@@ -196,7 +196,7 @@
  *  Conventions.
  *
  *  (1) The generators of an abstract group presentation are represented
- *      by lowercase letters.  Their inverses are respresented by the
+ *      by lowercase letters.  Their inverses are represented by the
  *      corresponding uppercase letters.  For example, "A" is the inverse
  *      of "a".
  *
@@ -344,7 +344,7 @@ struct GroupPresentation
      *  occasionally the user may want access to the unsimplified
      *  presentation.  For example, you can pass an unsimplified
      *  presentation of a lens space to John Berge's program Heegaard,
-     *  and it will most likley be able to recognize the exact lens space.
+     *  and it will most likely be able to recognize the exact lens space.
      *  Yes, it distinguishes L(5,1) from L(5,2), but only if it
      *  begins with a sufficiently complicated presentation.
      *  Passing it the presentation < a | a^5 = 1 > isn't good enough!

kernel/kernel_code/hyperbolic_structure.c

@@ -73,7 +73,7 @@
  *
  *  [One could of course use real equations for oriented manifolds as
  *  well, but the speed suffers.  The arithmetic involved in the row
- *  operations (mulitplying an entry in one row by a constant and adding
+ *  operations (multiplying an entry in one row by a constant and adding
  *  it to the corresponding entry in another row) is four times faster
  *  for real numbers than for complex numbers, but a 2n x 2m real system
  *  requires eight times as many such steps as does an n x m complex system.

kernel/kernel_code/symmetry_group_cusped.c

@@ -163,7 +163,7 @@ FuncResult compute_cusped_symmetry_group(
 /*
  *  symmetry_list_to_group() converts a SymmetryList to a SymmetryGroup.
  *  The SymmetryGroup subsumes the SymmetryList, and adds additional
- *  information, namely a mulitplication table for the group, the orders
+ *  information, namely a multiplication table for the group, the orders
  *  and inverses of the elements, and whether the group is abelian, cyclic,
  *  dihedral and/or a spherical triangle group.
  *

kernel/kernel_code/symmetry_group_info.c

@@ -934,9 +934,9 @@ static void assign_generators(
         elements_remaining--;
 
         /*
-         *  Use the symmetry group's mulitplication table to deduce the
+         *  Use the symmetry group's multiplication table to deduce the
          *  assignments of words to as many other group elements as possible.
-         *  The symmetry group's mulitplication table composes symmetries
+         *  The symmetry group's multiplication table composes symmetries
          *  right-to-left:  product[i][j] is obtained by doing symmetry j,
          *  followed by symmetry i.
          */