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