Re: How can I solve these simultaneous quadratic equations in Mathemetica?

• To: mathgroup at smc.vnet.net
• Subject: [mg65902] Re: How can I solve these simultaneous quadratic equations in Mathemetica?
• From: "Chris Chiasson" <chris.chiasson at gmail.com>
• Date: Sat, 22 Apr 2006 04:54:22 -0400 (EDT)
• References: <200604160748.DAA11097@smc.vnet.net><e22hah\$e5h\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Here is a way to get a function/plot of the variables vs c by combining
Lichtblau's NSolve with Woll's homotopic continuation:

initc is the point where NSolve will be called to give an initial
condition
halfinterval is the range of c to the right and left of initc

eqns[4] is keyed to find a Real solution for the initial condition

eqns[1]={1+3c/2+x(1+c+y+z-x)+c*y+(y+z+x)/2-w(2y+2x-3w+3+2c)\[Equal]0,
c/2+w(y+z-w+3/2+c)-x(2w+2z-3x+2)\[Equal]0,
1+2c+w(1+c)+z(w+x-z+3/2+c)-y(2w+2z-3y+4+2c)\[Equal]0,
y(x+w-y+1+c)-c(1+w)+(y+w-x)/2-z(2y+2x-3z)\[Equal]0};
reps[1]=Cases[Variables[eqns[1]/.Equal\[Rule]List],
blah_Symbol\[RuleDelayed]Rule[blah,blah[c]]/;blah=!=c];
eqns[2]=eqns[1]/.reps[1];
eqns[3]=D[#,c]&/@eqns[2];
solvars[1]=Last/@reps[1];
initc=1/2;
halfinterval=3/8;
crangespec={c,initc-halfinterval,initc+halfinterval};
eqns[4]=Equal@@@
First[Cases[Apply[NSolve,{eqns[2],solvars[1]}/.c\[Rule]initc],
Map[Rule[#,_Real]&,solvars[1]/.c->initc]]]