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The motivation is solving the following equations: $$ f(x,y)=0, x=L-kL, y=ks $$ $k$ is the variable, $L$ and $s$ are constants. The plan is: First, to factorize the polynomial as $(a_1x+b_1y+c_1) (a_2x+b_2y+c_2)…=0$;

Second, to solve $a_1(L-kL)+b_1ks+c1=0,\;a_2(L-kL)+b_2ks+c2=0$, and so forth.

The polynomial f(x,y) is massy ($c$, and $d$ is rational constant): $$ f(x,y)= \{[( x^2-y^2+c)^2-(2xy+d)^2+c]^2 - [2(x^2-y^2+c)(2xy+d)+d]^2+c\}^2+\{2[( x^2-y^2+c)^2-(2xy+d)^2+c][2(x^2-y^2+c)(2xy+d)+d]+d\}^2-1/2 $$ I have expanded it as: $$ x^8+y^8+4x^6y^2+6x^4y^4+4x^2y^6+\\ 4c(x^6-y^6)+8d(x^5y+xy^5)+4c(x^4y^2-x^2y^4)+16dx^3y^3+\\ (6c^2+2d^2+2c)(x^4+y^4)+(16cd+8d)(x^3y-xy^3)+(-4c^2+20d^2-12c)x^2y^2+\\ (4c^3+4cd^2+4c^2+4d^2)(x^2-y^2)+(8c^2d+8d^3)xy+\\ c^4+d^4+2c^2d^2+2c^3+2cd^2+c^2+d^2-1/2 $$ How to factorize such polynomial with $2$ variable $(x,y)$ ? Any references?

whitegreen
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  • If you're trying to solve for $k$, plug in what $x$ and $y$ are in terms of $k$. If you have particular values of the constants, plug them in too. Then, throw it at Mathematica's Factor function or Roots function and see if it factors or theres a nice form for the roots. If not, either show you have a suitable solution for $k$, or solve it numerically if thats possible. – Batman Dec 17 '15 at 06:48

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