algsys and "quotient by zero"
- Subject: algsys and "quotient by zero"
- From: andre maute
- Date: Sun, 07 Oct 2012 00:05:37 +0200
On 10/06/2012 02:53 PM, Barton Willis wrote:
> For a workaround, try some combination of
>
> (1) try solving for more variables
> (2) set algebraic to true
no square roots
> (3) try other values for gcd (the user documentation for gcd lists them)
gcd : ez; --> gives a lisp error
gcd : subres; --> quotient by zero
gcd : res; --> quotient by zero
gcd : spmod; --> quotient by zero
> (4) compute the grobner basis--the easiest way for me to to use the to poly solver:
>
> (%i14) load(to_poly_solve)$
>
> (%i16) %solve([x^2+y^2-a^2,x+y=b],[x,y], use_grobner=true);
> (%o16) %union([x=-(sqrt(2*a^2-b^2)-b)/2,y=(sqrt(2*a^2-b^2)+b)/2],[x=(sqrt(2*a^2-b^2)+b)/2,y=-(sqrt(2*a^2-b^2)-b)/2])
gives unable to solve
> These tricks have a low chance of helping, but I have seen equations where they do workaround the quotient by zero bug.
>
Thanks
Andre
P.S.: I have attached a test file.
P.S.S. : I am trying to somehow optimize 8 polynomial bases.
-------------- next part --------------
display2d : false;
eqs :
[(3*zz012[[1,1],[2,0]]-5*zz012[[0,2],[2,0]]+5*zz01[[0,2],[2,0]])/5 = 0,-((3*zz012[[1,1],[2,0]]-5*zz012[[0,2],[2,0]]+5*zz01[[0,2],[2,0]])*zz012[[2,0],[1,0]]-3*zz012[[1,1],[1,0]]+5*zz012[[0,2],[1,0]]-5*zz01[[0,2],[1,0]]-10*zz012[[0,1],[1,0]])/5 = 0,((3*zz012[[1,0],[0,0]]*zz012[[1,1],[2,0]]+(5*zz01[[0,2],[2,0]]-5*zz012[[0,2],[2,0]])*zz012[[1,0],[0,0]])*zz012[[2,0],[1,0]]+(-3*zz012[[1,1],[2,0]]+5*zz012[[0,2],[2,0]]-5*zz01[[0,2],[2,0]])*zz012[[2,0],[0,0]]-3*zz012[[1,0],[0,0]]*zz012[[1,1],[1,0]]+3*zz012[[1,1],[0,0]]+(5*zz012[[0,2],[1,0]]-5*zz01[[0,2],[1,0]]-10*zz012[[0,1],[1,0]])*zz012[[1,0],[0,0]]-5*zz012[[0,2],[0,0]]+5*zz01[[0,2],[0,0]]+10*zz012[[0,1],[0,0]])/5 = 0,
-((6*zz012[[1,0],[0,0]]*zz012[[1,1],[2,0]]-6*zz012[[1,0],[0,0]]*zz01[[1,1],[2,0]])*zz012[[2,0],[1,0]]+(6*zz01[[1,1],[2,0]]-6*zz012[[1,1],[2,0]])*zz012[[2,0],[0,0]]-6*zz012[[1,0],[0,0]]*zz012[[1,1],[1,0]]+6*zz012[[1,0],[0,0]]*zz01[[1,1],[1,0]]+6*zz012[[1,1],[0,0]]-6*zz01[[1,1],[0,0]]-5*zz012[[0,1],[1,0]]*zz012[[1,0],[0,0]]+5*zz012[[0,1],[0,0]])/6 = 0,zz012[[1,0],[0,0]]*zz012[[2,0],[1,0]]-zz012[[1,0],[0,0]]*zz01[[2,0],[1,0]]-zz012[[2,0],[0,0]]+zz01[[2,0],[0,0]] = 0,(6*zz12[[1,1],[2,0]]-5*zz12[[0,2],[2,0]]+5*zz1[[0,2],[2,0]])/5 = 0,-((6*zz12[[1,1],[2,0]]-5*zz12[[0,2],[2,0]]+5*zz1[[0,2],[2,0]])*zz12[[2,0],[1,0]]-6*zz12[[1,1],[1,0]]+5*zz12[[0,2],[1,0]]-5*zz1[[0,2],[1,0]]-15*zz12[[0,1],[1,0]])/5 = 0,
((6*zz12[[1,0],[0,0]]*zz12[[1,1],[2,0]]+(5*zz1[[0,2],[2,0]]-5*zz12[[0,2],[2,0]])*zz12[[1,0],[0,0]])*zz12[[2,0],[1,0]]+(-6*zz12[[1,1],[2,0]]+5*zz12[[0,2],[2,0]]-5*zz1[[0,2],[2,0]])*zz12[[2,0],[0,0]]-6*zz12[[1,0],[0,0]]*zz12[[1,1],[1,0]]+6*zz12[[1,1],[0,0]]+(5*zz12[[0,2],[1,0]]-5*zz1[[0,2],[1,0]]-15*zz12[[0,1],[1,0]])*zz12[[1,0],[0,0]]-5*zz12[[0,2],[0,0]]+5*zz1[[0,2],[0,0]]+15*zz12[[0,1],[0,0]])/5 = 0,-((2*zz12[[1,0],[0,0]]*zz12[[1,1],[2,0]]-2*zz12[[1,0],[0,0]]*zz1[[1,1],[2,0]])*zz12[[2,0],[1,0]]+(2*zz1[[1,1],[2,0]]-2*zz12[[1,1],[2,0]])*zz12[[2,0],[0,0]]-2*zz12[[1,0],[0,0]]*zz12[[1,1],[1,0]]+2*zz12[[1,0],[0,0]]*zz1[[1,1],[1,0]]+2*zz12[[1,1],[0,0]]-2*zz1[[1,1],[0,0]]-5*zz12[[0,1],[1,0]]*zz12[[1,0],[0,0]]+5*zz12[[0,1],[0,0]])/2 = 0,zz12[[1,0],[0,0]]*zz12[[2,0],[1,0]]-zz12[[1,0],[0,0]]*zz1[[2,0],[1,0]]-zz12[[2,0],[0,0]]+zz1[[2,0],[0,0]] = 0,(3*zz02[[1,1],[2,0]]-5*zz02[[0,2],[2,0]]+5*zz0[[0,2],[2,0]])/5 = 0,
-((3*zz02[[1,1],[2,0]]-5*zz02[[0,2],[2,0]]+5*zz0[[0,2],[2,0]])*zz02[[2,0],[1,0]]-3*zz02[[1,1],[1,0]]+5*zz02[[0,2],[1,0]]-5*zz0[[0,2],[1,0]]-15*zz02[[0,1],[1,0]])/5 = 0,((3*zz02[[1,0],[0,0]]*zz02[[1,1],[2,0]]+(5*zz0[[0,2],[2,0]]-5*zz02[[0,2],[2,0]])*zz02[[1,0],[0,0]])*zz02[[2,0],[1,0]]+(-3*zz02[[1,1],[2,0]]+5*zz02[[0,2],[2,0]]-5*zz0[[0,2],[2,0]])*zz02[[2,0],[0,0]]-3*zz02[[1,0],[0,0]]*zz02[[1,1],[1,0]]+3*zz02[[1,1],[0,0]]+(5*zz02[[0,2],[1,0]]-5*zz0[[0,2],[1,0]]-15*zz02[[0,1],[1,0]])*zz02[[1,0],[0,0]]-5*zz02[[0,2],[0,0]]+5*zz0[[0,2],[0,0]]+15*zz02[[0,1],[0,0]])/5 = 0,(zz02[[1,0],[0,0]]*zz0[[1,1],[2,0]]-zz02[[1,0],[0,0]]*zz02[[1,1],[2,0]])*zz02[[2,0],[1,0]]+(zz02[[1,1],[2,0]]-zz0[[1,1],[2,0]])*zz02[[2,0],[0,0]]+zz02[[1,0],[0,0]]*zz02[[1,1],[1,0]]-zz02[[1,0],[0,0]]*zz0[[1,1],[1,0]]-zz02[[1,1],[0,0]]+zz0[[1,1],[0,0]] = 0,zz02[[1,0],[0,0]]*zz02[[2,0],[1,0]]-zz02[[1,0],[0,0]]*zz0[[2,0],[1,0]]-zz02[[2,0],[0,0]]+zz0[[2,0],[0,0]] = 0,
(6*zz2[[1,1],[2,0]]+5*zze[[0,2],[2,0]]-5*zz2[[0,2],[2,0]])/5 = 0,-((6*zz2[[1,1],[2,0]]+5*zze[[0,2],[2,0]]-5*zz2[[0,2],[2,0]])*zz2[[2,0],[1,0]]-6*zz2[[1,1],[1,0]]-5*zze[[0,2],[1,0]]+5*zz2[[0,2],[1,0]]-30*zz2[[0,1],[1,0]])/5 = 0,((6*zz2[[1,0],[0,0]]*zz2[[1,1],[2,0]]+(5*zze[[0,2],[2,0]]-5*zz2[[0,2],[2,0]])*zz2[[1,0],[0,0]])*zz2[[2,0],[1,0]]+(-6*zz2[[1,1],[2,0]]-5*zze[[0,2],[2,0]]+5*zz2[[0,2],[2,0]])*zz2[[2,0],[0,0]]-6*zz2[[1,0],[0,0]]*zz2[[1,1],[1,0]]+6*zz2[[1,1],[0,0]]+(-5*zze[[0,2],[1,0]]+5*zz2[[0,2],[1,0]]-30*zz2[[0,1],[1,0]])*zz2[[1,0],[0,0]]+5*zze[[0,2],[0,0]]-5*zz2[[0,2],[0,0]]+30*zz2[[0,1],[0,0]])/5 = 0,(zz2[[1,0],[0,0]]*zze[[1,1],[2,0]]-zz2[[1,0],[0,0]]*zz2[[1,1],[2,0]])*zz2[[2,0],[1,0]]+(zz2[[1,1],[2,0]]-zze[[1,1],[2,0]])*zz2[[2,0],[0,0]]-zz2[[1,0],[0,0]]*zze[[1,1],[1,0]]+zz2[[1,0],[0,0]]*zz2[[1,1],[1,0]]+zze[[1,1],[0,0]]-zz2[[1,1],[0,0]] = 0,-zz2[[1,0],[0,0]]*zze[[2,0],[1,0]]+zz2[[1,0],[0,0]]*zz2[[2,0],[1,0]]+zze[[2,0],[0,0]]-zz2[[2,0],[0,0]] = 0,
zz02[[0,2],[2,0]]-zz012[[0,2],[2,0]] = 0,(zz012[[0,2],[2,0]]-zz02[[0,2],[2,0]])*zz012[[2,0],[1,0]]+zz02[[0,2],[1,0]]-zz012[[0,2],[1,0]] = 0,(zz02[[0,2],[2,0]]-zz012[[0,2],[2,0]])*zz012[[1,0],[0,0]]*zz012[[2,0],[1,0]]+(zz012[[0,2],[2,0]]-zz02[[0,2],[2,0]])*zz012[[2,0],[0,0]]+(zz012[[0,2],[1,0]]-zz02[[0,2],[1,0]])*zz012[[1,0],[0,0]]+zz02[[0,2],[0,0]]-zz012[[0,2],[0,0]] = 0,zz02[[1,1],[2,0]]-zz012[[1,1],[2,0]] = 0,-((3*zz02[[1,1],[2,0]]-3*zz012[[1,1],[2,0]])*zz012[[2,0],[1,0]]-3*zz02[[1,1],[1,0]]+3*zz012[[1,1],[1,0]]-5*zz012[[0,1],[1,0]])/3 = 0,((3*zz012[[1,0],[0,0]]*zz02[[1,1],[2,0]]-3*zz012[[1,0],[0,0]]*zz012[[1,1],[2,0]])*zz012[[2,0],[1,0]]+(3*zz012[[1,1],[2,0]]-3*zz02[[1,1],[2,0]])*zz012[[2,0],[0,0]]-3*zz012[[1,0],[0,0]]*zz02[[1,1],[1,0]]+3*zz012[[1,0],[0,0]]*zz012[[1,1],[1,0]]+3*zz02[[1,1],[0,0]]-3*zz012[[1,1],[0,0]]-5*zz012[[0,1],[1,0]]*zz012[[1,0],[0,0]]+5*zz012[[0,1],[0,0]])/3 = 0,
-zz012[[1,0],[0,0]]*zz02[[2,0],[1,0]]+zz012[[1,0],[0,0]]*zz012[[2,0],[1,0]]+zz02[[2,0],[0,0]]-zz012[[2,0],[0,0]] = 0,zz02[[0,1],[1,0]]-zz012[[0,1],[1,0]] = 0,(zz012[[0,1],[1,0]]-zz02[[0,1],[1,0]])*zz012[[1,0],[0,0]]+zz02[[0,1],[0,0]]-zz012[[0,1],[0,0]] = 0,zz2[[0,2],[2,0]]-zz12[[0,2],[2,0]] = 0,(zz12[[0,2],[2,0]]-zz2[[0,2],[2,0]])*zz12[[2,0],[1,0]]+zz2[[0,2],[1,0]]-zz12[[0,2],[1,0]] = 0,(zz2[[0,2],[2,0]]-zz12[[0,2],[2,0]])*zz12[[1,0],[0,0]]*zz12[[2,0],[1,0]]+(zz12[[0,2],[2,0]]-zz2[[0,2],[2,0]])*zz12[[2,0],[0,0]]+(zz12[[0,2],[1,0]]-zz2[[0,2],[1,0]])*zz12[[1,0],[0,0]]+zz2[[0,2],[0,0]]-zz12[[0,2],[0,0]] = 0,zz2[[1,1],[2,0]]-zz12[[1,1],[2,0]] = 0,-((2*zz2[[1,1],[2,0]]-2*zz12[[1,1],[2,0]])*zz12[[2,0],[1,0]]-2*zz2[[1,1],[1,0]]+2*zz12[[1,1],[1,0]]-5*zz12[[0,1],[1,0]])/2 = 0,
((2*zz12[[1,0],[0,0]]*zz2[[1,1],[2,0]]-2*zz12[[1,0],[0,0]]*zz12[[1,1],[2,0]])*zz12[[2,0],[1,0]]+(2*zz12[[1,1],[2,0]]-2*zz2[[1,1],[2,0]])*zz12[[2,0],[0,0]]-2*zz12[[1,0],[0,0]]*zz2[[1,1],[1,0]]+2*zz12[[1,0],[0,0]]*zz12[[1,1],[1,0]]+2*zz2[[1,1],[0,0]]-2*zz12[[1,1],[0,0]]-5*zz12[[0,1],[1,0]]*zz12[[1,0],[0,0]]+5*zz12[[0,1],[0,0]])/2 = 0,-zz12[[1,0],[0,0]]*zz2[[2,0],[1,0]]+zz12[[1,0],[0,0]]*zz12[[2,0],[1,0]]+zz2[[2,0],[0,0]]-zz12[[2,0],[0,0]] = 0,zz2[[0,1],[1,0]]-zz12[[0,1],[1,0]] = 0,(zz12[[0,1],[1,0]]-zz2[[0,1],[1,0]])*zz12[[1,0],[0,0]]+zz2[[0,1],[0,0]]-zz12[[0,1],[0,0]] = 0,zz0[[0,2],[2,0]]-zz01[[0,2],[2,0]] = 0,(zz01[[0,2],[2,0]]-zz0[[0,2],[2,0]])*zz01[[2,0],[1,0]]-zz01[[0,2],[1,0]]+zz0[[0,2],[1,0]] = 0,(zz0[[0,2],[2,0]]-zz01[[0,2],[2,0]])*zz01[[1,0],[0,0]]*zz01[[2,0],[1,0]]+(zz01[[0,2],[2,0]]-zz0[[0,2],[2,0]])*zz01[[2,0],[0,0]]+(zz01[[0,2],[1,0]]-zz0[[0,2],[1,0]])*zz01[[1,0],[0,0]]-zz01[[0,2],[0,0]]+zz0[[0,2],[0,0]] = 0,zz0[[1,1],[2,0]]-zz01[[1,1],[2,0]] = 0,
((2*zz01[[1,1],[2,0]]-2*zz0[[1,1],[2,0]])*zz01[[2,0],[1,0]]-2*zz01[[1,1],[1,0]]+2*zz0[[1,1],[1,0]]+5*zz01[[0,1],[1,0]])/2 = 0,-((2*zz01[[1,0],[0,0]]*zz01[[1,1],[2,0]]-2*zz01[[1,0],[0,0]]*zz0[[1,1],[2,0]])*zz01[[2,0],[1,0]]+(2*zz0[[1,1],[2,0]]-2*zz01[[1,1],[2,0]])*zz01[[2,0],[0,0]]-2*zz01[[1,0],[0,0]]*zz01[[1,1],[1,0]]+2*zz01[[1,0],[0,0]]*zz0[[1,1],[1,0]]+2*zz01[[1,1],[0,0]]-2*zz0[[1,1],[0,0]]+5*zz01[[0,1],[1,0]]*zz01[[1,0],[0,0]]-5*zz01[[0,1],[0,0]])/2 = 0,zz01[[1,0],[0,0]]*zz01[[2,0],[1,0]]-zz01[[1,0],[0,0]]*zz0[[2,0],[1,0]]-zz01[[2,0],[0,0]]+zz0[[2,0],[0,0]] = 0,zz0[[0,1],[1,0]]-zz01[[0,1],[1,0]] = 0,(zz01[[0,1],[1,0]]-zz0[[0,1],[1,0]])*zz01[[1,0],[0,0]]-zz01[[0,1],[0,0]]+zz0[[0,1],[0,0]] = 0,zze[[0,2],[2,0]]-zz1[[0,2],[2,0]] = 0,(zz1[[0,2],[2,0]]-zze[[0,2],[2,0]])*zz1[[2,0],[1,0]]+zze[[0,2],[1,0]]-zz1[[0,2],[1,0]] = 0,
(zze[[0,2],[2,0]]-zz1[[0,2],[2,0]])*zz1[[1,0],[0,0]]*zz1[[2,0],[1,0]]+(zz1[[0,2],[2,0]]-zze[[0,2],[2,0]])*zz1[[2,0],[0,0]]+(zz1[[0,2],[1,0]]-zze[[0,2],[1,0]])*zz1[[1,0],[0,0]]+zze[[0,2],[0,0]]-zz1[[0,2],[0,0]] = 0,zze[[1,1],[2,0]]-zz1[[1,1],[2,0]] = 0,(zz1[[1,1],[2,0]]-zze[[1,1],[2,0]])*zz1[[2,0],[1,0]]+zze[[1,1],[1,0]]-zz1[[1,1],[1,0]]+5*zz1[[0,1],[1,0]] = 0,(zz1[[1,0],[0,0]]*zze[[1,1],[2,0]]-zz1[[1,0],[0,0]]*zz1[[1,1],[2,0]])*zz1[[2,0],[1,0]]+(zz1[[1,1],[2,0]]-zze[[1,1],[2,0]])*zz1[[2,0],[0,0]]-zz1[[1,0],[0,0]]*zze[[1,1],[1,0]]+zz1[[1,0],[0,0]]*zz1[[1,1],[1,0]]+zze[[1,1],[0,0]]-zz1[[1,1],[0,0]]-5*zz1[[0,1],[1,0]]*zz1[[1,0],[0,0]]+5*zz1[[0,1],[0,0]] = 0,-zz1[[1,0],[0,0]]*zze[[2,0],[1,0]]+zz1[[1,0],[0,0]]*zz1[[2,0],[1,0]]+zze[[2,0],[0,0]]-zz1[[2,0],[0,0]] = 0,zze[[0,1],[1,0]]-zz1[[0,1],[1,0]] = 0,(zz1[[0,1],[1,0]]-zze[[0,1],[1,0]])*zz1[[1,0],[0,0]]+zze[[0,1],[0,0]]-zz1[[0,1],[0,0]] = 0,-(3*zz012[[1,1],[2,0]]-5*zz12[[0,2],[2,0]]+5*zz012[[0,2],[2,0]])/5 = 0,
((3*zz012[[1,1],[2,0]]-5*zz12[[0,2],[2,0]]+5*zz012[[0,2],[2,0]])*zz012[[2,0],[1,0]]-3*zz012[[1,1],[1,0]]+5*zz12[[0,2],[1,0]]-5*zz012[[0,2],[1,0]]-10*zz012[[0,1],[1,0]])/5 = 0,-((3*zz012[[1,0],[0,0]]*zz012[[1,1],[2,0]]+(5*zz012[[0,2],[2,0]]-5*zz12[[0,2],[2,0]])*zz012[[1,0],[0,0]])*zz012[[2,0],[1,0]]+(-3*zz012[[1,1],[2,0]]+5*zz12[[0,2],[2,0]]-5*zz012[[0,2],[2,0]])*zz012[[2,0],[0,0]]-3*zz012[[1,0],[0,0]]*zz012[[1,1],[1,0]]+3*zz012[[1,1],[0,0]]+(5*zz12[[0,2],[1,0]]-5*zz012[[0,2],[1,0]]-10*zz012[[0,1],[1,0]])*zz012[[1,0],[0,0]]-5*zz12[[0,2],[0,0]]+5*zz012[[0,2],[0,0]]+10*zz012[[0,1],[0,0]])/5 = 0,((6*zz012[[1,0],[0,0]]*zz12[[1,1],[2,0]]-6*zz012[[1,0],[0,0]]*zz012[[1,1],[2,0]])*zz012[[2,0],[1,0]]+(6*zz012[[1,1],[2,0]]-6*zz12[[1,1],[2,0]])*zz012[[2,0],[0,0]]-6*zz012[[1,0],[0,0]]*zz12[[1,1],[1,0]]+6*zz012[[1,0],[0,0]]*zz012[[1,1],[1,0]]+6*zz12[[1,1],[0,0]]-6*zz012[[1,1],[0,0]]+5*zz012[[0,1],[1,0]]*zz012[[1,0],[0,0]]-5*zz012[[0,1],[0,0]])/6 = 0,
-zz012[[1,0],[0,0]]*zz12[[2,0],[1,0]]+zz012[[1,0],[0,0]]*zz012[[2,0],[1,0]]+zz12[[2,0],[0,0]]-zz012[[2,0],[0,0]] = 0,-(3*zz02[[1,1],[2,0]]-5*zz2[[0,2],[2,0]]+5*zz02[[0,2],[2,0]])/5 = 0,((3*zz02[[1,1],[2,0]]-5*zz2[[0,2],[2,0]]+5*zz02[[0,2],[2,0]])*zz02[[2,0],[1,0]]-3*zz02[[1,1],[1,0]]+5*zz2[[0,2],[1,0]]-5*zz02[[0,2],[1,0]]-15*zz02[[0,1],[1,0]])/5 = 0,-((3*zz02[[1,0],[0,0]]*zz02[[1,1],[2,0]]+(5*zz02[[0,2],[2,0]]-5*zz2[[0,2],[2,0]])*zz02[[1,0],[0,0]])*zz02[[2,0],[1,0]]+(-3*zz02[[1,1],[2,0]]+5*zz2[[0,2],[2,0]]-5*zz02[[0,2],[2,0]])*zz02[[2,0],[0,0]]-3*zz02[[1,0],[0,0]]*zz02[[1,1],[1,0]]+3*zz02[[1,1],[0,0]]+(5*zz2[[0,2],[1,0]]-5*zz02[[0,2],[1,0]]-15*zz02[[0,1],[1,0]])*zz02[[1,0],[0,0]]-5*zz2[[0,2],[0,0]]+5*zz02[[0,2],[0,0]]+15*zz02[[0,1],[0,0]])/5 = 0,
(zz02[[1,0],[0,0]]*zz2[[1,1],[2,0]]-zz02[[1,0],[0,0]]*zz02[[1,1],[2,0]])*zz02[[2,0],[1,0]]+(zz02[[1,1],[2,0]]-zz2[[1,1],[2,0]])*zz02[[2,0],[0,0]]-zz02[[1,0],[0,0]]*zz2[[1,1],[1,0]]+zz02[[1,0],[0,0]]*zz02[[1,1],[1,0]]+zz2[[1,1],[0,0]]-zz02[[1,1],[0,0]] = 0,-zz02[[1,0],[0,0]]*zz2[[2,0],[1,0]]+zz02[[1,0],[0,0]]*zz02[[2,0],[1,0]]+zz2[[2,0],[0,0]]-zz02[[2,0],[0,0]] = 0,zz1[[0,2],[2,0]]-zz01[[0,2],[2,0]] = 0,(zz01[[0,2],[2,0]]-zz1[[0,2],[2,0]])*zz01[[2,0],[1,0]]+zz1[[0,2],[1,0]]-zz01[[0,2],[1,0]] = 0,(zz1[[0,2],[2,0]]-zz01[[0,2],[2,0]])*zz01[[1,0],[0,0]]*zz01[[2,0],[1,0]]+(zz01[[0,2],[2,0]]-zz1[[0,2],[2,0]])*zz01[[2,0],[0,0]]+(zz01[[0,2],[1,0]]-zz1[[0,2],[1,0]])*zz01[[1,0],[0,0]]+zz1[[0,2],[0,0]]-zz01[[0,2],[0,0]] = 0,
((2*zz01[[1,0],[0,0]]*zz1[[1,1],[2,0]]-2*zz01[[1,0],[0,0]]*zz01[[1,1],[2,0]])*zz01[[2,0],[1,0]]+(2*zz01[[1,1],[2,0]]-2*zz1[[1,1],[2,0]])*zz01[[2,0],[0,0]]-2*zz01[[1,0],[0,0]]*zz1[[1,1],[1,0]]+2*zz01[[1,0],[0,0]]*zz01[[1,1],[1,0]]+2*zz1[[1,1],[0,0]]-2*zz01[[1,1],[0,0]]+5*zz01[[0,1],[1,0]]*zz01[[1,0],[0,0]]-5*zz01[[0,1],[0,0]])/2 = 0,-zz01[[1,0],[0,0]]*zz1[[2,0],[1,0]]+zz01[[1,0],[0,0]]*zz01[[2,0],[1,0]]+zz1[[2,0],[0,0]]-zz01[[2,0],[0,0]] = 0,zze[[0,2],[2,0]]-zz0[[0,2],[2,0]] = 0,(zz0[[0,2],[2,0]]-zze[[0,2],[2,0]])*zz0[[2,0],[1,0]]+zze[[0,2],[1,0]]-zz0[[0,2],[1,0]] = 0,(zze[[0,2],[2,0]]-zz0[[0,2],[2,0]])*zz0[[1,0],[0,0]]*zz0[[2,0],[1,0]]+(zz0[[0,2],[2,0]]-zze[[0,2],[2,0]])*zz0[[2,0],[0,0]]+(zz0[[0,2],[1,0]]-zze[[0,2],[1,0]])*zz0[[1,0],[0,0]]+zze[[0,2],[0,0]]-zz0[[0,2],[0,0]] = 0,
(zz0[[1,0],[0,0]]*zze[[1,1],[2,0]]-zz0[[1,0],[0,0]]*zz0[[1,1],[2,0]])*zz0[[2,0],[1,0]]+(zz0[[1,1],[2,0]]-zze[[1,1],[2,0]])*zz0[[2,0],[0,0]]-zz0[[1,0],[0,0]]*zze[[1,1],[1,0]]+zz0[[1,0],[0,0]]*zz0[[1,1],[1,0]]+zze[[1,1],[0,0]]-zz0[[1,1],[0,0]] = 0,-zz0[[1,0],[0,0]]*zze[[2,0],[1,0]]+zz0[[1,0],[0,0]]*zz0[[2,0],[1,0]]+zze[[2,0],[0,0]]-zz0[[2,0],[0,0]] = 0];
length(eqs);
length(listofvars(eqs));
/* gcd : ez; */
gcd : subres;
/* gcd : red; */
/* gcd : spmod; */
algsys(eqs,listofvars(eqs));
/* load(to_poly_solve)$ */
/* */
/* %solve(eqs,listofvars(eqs),use_grobner=true); */