add some details to field/group/scalar doc

documentation/aleo/03_language.md

@@ -42,27 +42,35 @@ Higher bit length integers generate more constraints in the circuit, which can s
 
 ### Field Elements
 
-Aleo instructions supports the `field` type for the base field elements of the elliptic curve.
-These are unsigned integers below the modulus of the base field.
+Aleo instructions supports the `field` type for elements of the base field of the elliptic curve.
+These are unsigned integers less than the modulus of the base field, so the largest field element
+is `8444461749428370424248824938781546531375899335154063827935233455917409239040field`.
+
 ```aleo
 function main:
     input r0: field.private;
 ```
 
 ### Group Elements
+
 The set of affine points on the elliptic curve passed into the Aleo instructions compiler forms a group.
-Leo supports a subgroup of this group, generated by a generator point, as a primitive data type.
-Group elements are special since their values can be defined from the x-coordinate of a coordinate pair, such as
-`0group`. The group type keyword `group` must be used when specifying a group value.
+The curve is a Twisted Edwards curve with `a = -1` and `d = 3021`.
+Aleo instructions supports a subgroup of the group, generated by a generator point, as a primitive data type.
+A group element is denoted by the x-coordinate of its point; for example,
+`2group` means the point `(2, 5553594316923449299484601589326170487897520766531075014687114064346375156608)`.
+The generator point is `1540945439182663264862696551825005342995406165131907382295858612069623286213group`.
 
 ```aleo
 function main:
     input r0: group.private;
 ```
 
 ### Scalar Elements
-Aleo instructions supports the `scalar` type for scalar field elements of the elliptic curve subgroup.
-These are unsigned integers below the modulus of the scalar field.
+
+Aleo instructions supports the `scalar` type for elements of the scalar field defined by the elliptic curve subgroup.
+These are unsigned integers less than the modulus of the scalar field, so the largest scalar is
+`2111115437357092606062206234695386632838870926408408195193685246394721360382scalar`.
+
 ```aleo
 function main:
     input r0: scalar.private;

documentation/leo/03_language.md

@@ -57,23 +57,26 @@ let b: u8 = 2; // implicit type -- not supported
 
 ### Field Elements
 
-Leo supports the `field` type for the base field elements of the elliptic curve.
-These are unsigned integers below the modulus of the base field.
+Leo supports the `field` type for elements of the base field of the elliptic curve.
+These are unsigned integers less than the modulus of the base field.  The following are the
+smallest and largest field elements.
 
 ```leo
-let a: field = 1field;
-let b: field = 21888242871839275222246405745257275088548364400416034343698204186575808495617field;
+let a: field = 0field;
+let b: field = 8444461749428370424248824938781546531375899335154063827935233455917409239040field;
 ```
 
 ### Group Elements
 
-The set of affine points on the elliptic curve passed into the Leo compiler forms a group.
-Leo supports a subgroup of this group, generated by a generator point, as a primitive data type.
-Group elements are special since their values can be defined from the x-coordinate of a coordinate pair, such as
-`0group`. The group type keyword `group` must be used when specifying a group value.
+The set of affine points on the elliptic curve forms a group.
+The curve is a Twisted Edwards curve with `a = -1` and `d = 3021`.
+Leo supports a subgroup of the group, generated by a generator point, as a primitive data type.
+A group element is denoted by the x-coordinate of its point; for example,
+`2group` means the point `(2, 5553594316923449299484601589326170487897520766531075014687114064346375156608)`.
 
 ```leo
-let b: group = 0group; // the point with 0 x-coordinate
+let a: group = 0group; // the point with 0 x-coordinate, (0, 1)
+let b: group = 1540945439182663264862696551825005342995406165131907382295858612069623286213group;  // the generator point
 ```
 
 The aforementioned generator point can be obtained via a constant associated to the `group` type.
@@ -84,11 +87,13 @@ let g: group = group::GEN; // the group generator
 
 ### Scalar Elements
 
-Leo supports the `scalar` type for scalar field elements of the elliptic curve subgroup.
-These are unsigned integers below the modulus of the scalar field.
+Leo supports the `scalar` type for elements of the scalar field defined by the elliptic curve subgroup.
+These are unsigned integers less than the modulus of the scalar field.  Showing the smallest and largest
+scalars.
 
 ```leo
-let a: scalar = 1scalar;
+let a: scalar = 0scalar;
+let b: scalar = 2111115437357092606062206234695386632838870926408408195193685246394721360382scalar;
 ```
 
 ### Addresses