Larger Finite Fields, take 2

doc/ref/fieldfin.xml

@@ -178,8 +178,8 @@ Finally note that elements of large prime fields are stored and
 displayed as residue class objects. So
 <P/>
 <Example><![CDATA[
-gap> Z(65537);
-ZmodpZObj( 3, 65537 )
+gap> Z(NextPrimeInt(2^30));
+ZmodpZObj( 2, 1073741827 )
 ]]></Example>
 </Description>
 </ManSection>

etc/ffgen.c

@@ -6,8 +6,13 @@
 #include <stdlib.h>
 #include <string.h>
 
-
-#define MAX_FF 65536
+/* These next lines control the size of internal finite field elements
+   in GAP. Changes here will propagate as needed */
+#if (SIZEOF_VOID_P == 8)
+#define MAX_FF (1 << 24)
+#else
+#define MAX_FF (1 << 16)
+#endif
 
 unsigned char is_prime[MAX_FF + 1];
 unsigned char is_ff[MAX_FF + 1];

etc/gen_conway.g

@@ -48,7 +48,7 @@ ConwayPolForCCodeNice := function(p,h,align)
     return Concatenation(substring);
 end;
 
-MAX := 2^16;
+MAX := 2^24;
 align := 4 + LogInt(MAX, 10);
 
 polynomials_as_strings_of_numbers := [];

lib/ffe.gd

@@ -18,6 +18,7 @@
 ##  <ManSection>
 ##  <Func Name="Z" Arg='p^d' Label="for field size"/>
 ##  <Func Name="Z" Arg='p, d' Label="for prime and degree"/>
+##  <Var Name="MAXSIZE_GF_INTERNAL"/>
 ##
 ##  <Description>
 ##  For creating elements of a finite field,
@@ -30,15 +31,20 @@
 ##  <P/>
 ##  &GAP; can represent elements of all finite fields
 ##  <C>GF(<A>p^d</A>)</C> such that either
-##  (1) <A>p^d</A> <M>&lt;= 65536</M> (in which case an extremely efficient
-##      internal representation is used);
+##  (1) <A>p^d</A> <M>&lt;=</M> <C>MAXSIZE_GF_INTERNAL</C> (in which case an 
+##      efficient internal representation is used);
 ##  (2) d = 1, (in which case, for large <A>p</A>, the field is represented
 ##      using the machinery of residue class rings
 ##      (see section&nbsp;<Ref Sect="Residue Class Rings"/>) or
 ##  (3) if the Conway polynomial of degree <A>d</A> over the field with
 ##      <A>p</A> elements is known, or can be computed
 ##      (see <Ref Func="ConwayPolynomial"/>).
 ##  <P/>
+##
+##  <C>MAXSIZE_GF_INTERNAL</C> may depend on the word size of your computer
+##  and the version of &GAP; but will typically be either <M>2^{16}</M> or
+##  <M>2^{24}</M>.<P/>
+##  
 ##  If you attempt to construct an element of <C>GF(<A>p^d</A>)</C> for which
 ##  <A>d</A> <M>> 1</M> and the relevant Conway polynomial is not known,
 ##  and not necessarily easy to find
@@ -107,14 +113,15 @@
 ##  0*Z(2)
 ##  gap> a*a;
 ##  Z(2^5)^2
-##  gap> b := Z(3,12);
+##  gap> b := Z(3,20);
 ##  z
 ##  gap> b*b;
 ##  z2
 ##  gap> b+b;
 ##  2z
 ##  gap> Print(b^100,"\n");
-##  Z(3)^0+Z(3,12)^5+Z(3,12)^6+2*Z(3,12)^8+Z(3,12)^10+Z(3,12)^11
+##  2*Z(3,20)^2+Z(3,20)^4+Z(3,20)^6+Z(3,20)^7+2*Z(3,20)^9+2*Z(3,20)^10+2*Z\
+##  (3,20)^12+2*Z(3,20)^15+2*Z(3,20)^17+Z(3,20)^18+Z(3,20)^19
 ##  ]]></Example>
 ##  <Log><![CDATA[
 ##  gap> Z(11,40);
@@ -270,7 +277,7 @@ DeclareCategoryCollections( "IsFFECollColl" );
 ##  true
 ##  gap> Z(256) > Z(101);
 ##  false
-##  gap> Z(2,20) < Z(2,20)^2; # this illustrates the lexicographic ordering
+##  gap> Z(2,30) < Z(2,30)^2; # this illustrates the lexicographic ordering
 ##  false
 ##  ]]></Example>
 ##  </Description>