small fixes on headlines

A1-Brouwer/Documentation/AnisotropicDimensionDoc.m2

@@ -41,7 +41,7 @@ document{
 
 document{
     Key => {anisotropicDimension, (anisotropicDimension, GrothendieckWittClass), (anisotropicDimension, Matrix)},
-    Headline => "Returns the anisotropic dimension of a symmetric bilinear form",
+    Headline => "returns the anisotropic dimension of a symmetric bilinear form",
     Usage => "anisotropicDimension(beta)",
     Inputs => {
 	GrothendieckWittClass => "beta" => {"over a field ", TEX///$k$///, " where ", TEX///$k$///, " is the complex numbers, reals, rationals, or a finite field."},
@@ -57,7 +57,7 @@ document{
 
 document{
     Key => {WittIndex, (WittIndex, GrothendieckWittClass)},
-    Headline => "Returns the Witt index of a symmetric bilinear form",
+    Headline => "returns the Witt index of a symmetric bilinear form",
     Usage => "WittIndex(beta)",
     Inputs => {
 	GrothendieckWittClass => "beta" => {"denoted by ", TEX///$\beta\in\text{GW}(k)$///, ", where ", TEX///$k$///, " is the complex numbers, reals, rationals, or a finite field"},

A1-Brouwer/Documentation/GWInvariantsDoc.m2

@@ -1,6 +1,6 @@
 document{
     Key => {signature, (signature, GrothendieckWittClass)},
-    Headline => "Outputs the signature of a symmetric bilinear form over the real or rational numbers",
+    Headline => "outputs the signature of a symmetric bilinear form over the real or rational numbers",
     Usage => "signature(beta)",
     Inputs => {
 	GrothendieckWittClass => "beta" => {"a symmetric bilinear form defined over ", TEX///$\mathbb{Q}$///, " or ", TEX///$\mathbb{R}$///},

A1-Brouwer/Documentation/GrothendieckWittClassesDoc.m2

@@ -28,7 +28,7 @@ document{
 
 document {
     Key => {gwClass, (gwClass, Matrix), (matrix, GrothendieckWittClass), (isWellDefined, Matrix)},
-	Headline => "Grothendieck Witt class of a symmetric matrix",
+	Headline => "the Grothendieck Witt class of a symmetric matrix",
 	Usage => "gwClass(M)",
 	Inputs => {
 	    Matrix => "M" => {"a symmetric matrix defined over an arbitrary field"}
@@ -56,7 +56,7 @@ document {
 
 document {
     Key => {baseField, (baseField, GrothendieckWittClass)},
-	Headline => "base field of a Grothendieck Witt class",
+	Headline => "the base field of a Grothendieck Witt class",
 	Usage => "baseField(beta)",
 	Inputs => {
 	    GrothendieckWittClass => "beta" => {"the isomorphism class of a symmetric bilinear form"}
@@ -76,7 +76,7 @@ document {
 
 document {
     Key => {gwAdd, (gwAdd, GrothendieckWittClass, GrothendieckWittClass)},
-    Headline => "The direct sum of two Grothendieck-Witt classes",     
+    Headline => "the direct sum of two Grothendieck-Witt classes",     
     Usage => "gwAdd(beta, gamma)",
 	Inputs => {
 	    GrothendieckWittClass => "beta" => {"the isomorphism class of a non-degenerate symmetric bilinear form represented by a matrix ", TT "M"},
@@ -98,7 +98,7 @@ document {
 
 document {
     Key => {gwMultiply, (gwMultiply, GrothendieckWittClass, GrothendieckWittClass)},
-    Headline => "The tensor product of two Grothendieck-Witt classes",     
+    Headline => "the tensor product of two Grothendieck-Witt classes",     
 	Usage => "gwMultiply(beta, gamma)",
 	Inputs => {
 	    GrothendieckWittClass => "beta" => {"the isomorphism class of a non-degenerate symmetric bilinear form represented by a matrix ", TT "M"},

A1-Brouwer/Documentation/HilbertSymbolsDoc.m2

@@ -1,6 +1,6 @@
 document{
     Key => {HilbertSymbol, (HilbertSymbol, ZZ, ZZ, ZZ),  (HilbertSymbol, QQ, QQ, ZZ),  (HilbertSymbol, ZZ, QQ, ZZ),  (HilbertSymbol, QQ, ZZ, ZZ)},
-    Headline => "Computes the Hilbert symbol of two integers or rational numbers at a prime",
+    Headline => "computes the Hilbert symbol of two integers or rational numbers at a prime",
     Usage => "HilbertSymbol(a,b,p)",
     Inputs => {
 	QQ => "a" => {"any integer or rational number, considered as an element of ", TEX///$\mathbb{Q}_p$///},
@@ -27,7 +27,7 @@ document{
 
 document{
     Key => {HilbertSymbolReal, (HilbertSymbolReal, QQ, QQ),  (HilbertSymbolReal, ZZ, ZZ),  (HilbertSymbolReal, ZZ, QQ),  (HilbertSymbolReal, QQ, ZZ)},
-    Headline => "Computes the Hilbert symbol of two rational numbers over the reals",
+    Headline => "computes the Hilbert symbol of two rational numbers over the reals",
     Usage => "HilbertSymbolReal(a,b,p)",
     Inputs => {
 	QQ => "a" => {"any non-zero integer or rational number, considered as an element of ", TEX///$\mathbb{Q}_p$///},

A1-Brouwer/Documentation/IsomorphismOfFormsDoc.m2

@@ -1,6 +1,6 @@
 document{
     Key => {gwIsomorphic, (gwIsomorphic, GrothendieckWittClass, GrothendieckWittClass)},
-    Headline => "Determines whether two Grothendieck Witt classes are isomorphic over CC, RR, QQ, or a finite field.",
+    Headline => "determines whether two Grothendieck Witt classes are isomorphic over CC, RR, QQ, or a finite field.",
     Usage => "gwIsomorphic(alpha,beta)",
     Inputs => {
 	GrothendieckWittClass => "alpha" => {"denoted by ",TEX///$\alpha$///},

A1-Brouwer/Documentation/IsotropyDoc.m2

@@ -1,6 +1,6 @@
 document{
     Key => {isIsotropic, (isIsotropic, GrothendieckWittClass), (isIsotropic, Matrix)},
-    Headline => "Determines whether a Grothendieck-Witt class is isotropic",
+    Headline => "determines whether a Grothendieck-Witt class is isotropic",
     Usage => "isIsotropic(beta)",
     Inputs => {
 	GrothendieckWittClass => "beta" => {"denoted by ", TEX///$\beta\in\text{GW}(k)$///, ", where ", TEX///$k$///, " is the rationals, reals, complex numbers, or a finite field."},
@@ -15,7 +15,7 @@ document{
 
 document{
     Key => {isAnisotropic, (isAnisotropic, GrothendieckWittClass), (isAnisotropic, Matrix)},
-    Headline => "Determines whether a Grothendieck-Witt class is anisotropic",
+    Headline => "determines whether a Grothendieck-Witt class is anisotropic",
     Usage => "isAnisotropic(beta)",
     Inputs => {
 	GrothendieckWittClass => "beta" => {"denoted by ", TEX///$\beta\in\text{GW}(k)$///, ", where ", TEX///$k$///, " is the rationals, reals, complex numbers, or a finite field"},

A1-Brouwer/Documentation/LocalGlobalDegreesDoc.m2

@@ -1,6 +1,6 @@
 document {
     Key => {globalA1Degree, (globalA1Degree, List)},
-    Headline => "Computes a global A1-Brouwer degree of a list of n polynomials in n variables over a field k",
+    Headline => "computes a global A1-Brouwer degree of a list of n polynomials in n variables over a field k",
     Usage => "globalA1Degree(L)",
     Inputs => {
 	List => "L" => {"of polynomials ", TEX///$f = (f_1, \ldots, f_n)$///, " in the polynomial ring ", TEX///$k[x_1,\ldots,x_n]$///, " over a field ", TEX///$k$///}
@@ -60,7 +60,7 @@ document {
 
 document {
     Key => {localA1Degree, (localA1Degree, List, Ideal)},
-    Headline => "Computes a local A1-Brouwer degree of a list of n polynomials in n variables over a field k at a prime ideal in the zero locus",
+    Headline => "computes a local A1-Brouwer degree of a list of n polynomials in n variables over a field k at a prime ideal in the zero locus",
     Usage => "locallA1Degree(L,p)",
     Inputs => {
 	List => "L" => {"of polynomials ", TEX///$f = (f_1, \ldots, f_n)$///, " in the polynomial ring ", TEX///$k[x_1,\ldots,x_n]$///, " over a field ", TEX///$k$///},