Jeroen Demeyer on Sat, 16 Apr 2005 13:04:42 +0200

 Weierstrass equation help

For those like me ;-) who always forget how to call ellinit(): a patch for the ellinit() help.
```Index: doc/usersch3.tex
===================================================================
RCS file: /home/cvs/pari/doc/usersch3.tex,v
retrieving revision 1.400
diff -u -r1.400 usersch3.tex
--- doc/usersch3.tex	12 Apr 2005 14:53:01 -0000	1.400
+++ doc/usersch3.tex	15 Apr 2005 18:57:48 -0000
@@ -2669,8 +2669,12 @@
\syn{mathell}{E,x,\var{prec}}.

\subsecidx{ellinit}\$(E,\{\fl=0\})\$: computes some fixed data concerning the
-elliptic curve given by the five-component vector \$E\$, which will be
-essential for most further computations on the curve. The result is a
+given elliptic curve which will be essential
+for most further computations on the curve.
+\$E\$ is a \$5\$-component vector \$a_1,a_2,a_3,a_4,a_6\$
+defining the elliptic curve with Weierstrass equation
+\$\$ Y^2 + a_1 XY + a_3 Y = X^3 + a_2 X^2 + a_4 X + a_6 \$\$
+The result of \tet{ellinit} is a
19-component vector E (called a long vector in this section), shortened
to 13 components (medium vector) if \$\fl=1\$. Both contain the
following information in the first 13 components:
Index: src/functions/elliptic_curves/ellinit
===================================================================
RCS file: /home/cvs/pari/src/functions/elliptic_curves/ellinit,v
retrieving revision 1.1
diff -u -r1.1 ellinit
--- src/functions/elliptic_curves/ellinit	26 Jun 2003 18:49:32 -0000	1.1
+++ src/functions/elliptic_curves/ellinit	15 Apr 2005 18:57:48 -0000
@@ -2,8 +2,8 @@
Section: elliptic_curves
C-Name: ellinit0
Prototype: GD0,L,p
-Help: ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the
- vector:
+Help: ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the
+ curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector:
[a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area].
If the curve is defined over a p-adic field, the last six components are
replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether
```