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• I have 3 real-valued functions $f(x,y,z,t)$, $g(x,y,z,t)$, $h(x,y,z,t)$ which contain some non-zero parameters/coefficients $a,b,c,d,e$ .

• At carefully selected values of those parameters, the functions are each forced to be approximately zero for all the points parametrized by $(x=r\cos\theta,y=r\sin\theta,m,t)$, where $0 \le t$ with $0 < r \le R$ and $0 < \theta \le 2\pi$. How do I brute-force or solve for the parameters which drive those functions to zero?

• I have 3 real-valued functions $f(x,y,z,t)$, $g(x,y,z,t)$, $h(x,y,z,t)$ which contain some non-zero parameters/coefficients $a,b,c,d,e$ .

• At carefully selected values of those parameters, the functions are each forced to be approximately zero for all the points parametrized by $(x=r\cos\theta,y=r\sin\theta,m,t)$, where $0 \le t$ with $0 < r \le R$ and $0 < \theta \le 2\pi$. How do I brute-force or solve for the parameters which drive those functions to zero?

• In this question, by zero I mean some number $\epsilon$ such that $abs(\epsilon) > 10^{−5}$

• Consider $p(x,y,z,t) = e^t(ax^2 + by^2 + cz^2)$ and I seek the values of $a,b,c$ which make $p\approx0$ at the point $(x=r\cos\theta,y=r\sin\theta,m,t)$ for all $t\ge0$ where $0 < \theta \le 2\pi$. A solution will be $(a,b,c)=\{(m/r)^2,(m/r)^2,-1\}$. How could I have found this in Mathematica?

• I have 3 real-valued functions $f(x,y,z,t)$, $g(x,y,z,t)$, $h(x,y,z,t)$ which contain some parameters/coefficients $a,b,c,d,e$ .

• At carefully selected values of those parameters, the functions are each forced to be approximately zero for all the points parametrized by $(x=r\cos\theta,y=r\sin\theta,m,t)$, where $0 \le t$ with $0 < r \le R$ and $0 < \theta \le 2\pi$. How do I brute-force or solve for the parameters which drive those functions to zero?

Find $a,b,d$ such that at all the parametrized points as defined above, then $f\approx0$ && $g\approx0$ && $\textrm{Norm}[h]\approx0$ where

• Consider $p(x,y,z,t) = e^t(ax^2 + by^2 + cz^2)$ and I seek the values of $a,b,c$ which make $p\approx0$ at the point $(x=r\cos\theta,y=r\sin\theta,m,t)$ for all $t\ge0$ where $0 < \theta \le 2\pi$. A non-trivial solution will be $(a,b,c)=\{(m/r)^2,(m/r)^2,-1\}$. How could I have found this in Mathematica?

• I have 3 real-valued functions $f(x,y,z,t)$, $g(x,y,z,t)$, $h(x,y,z,t)$ which contain some non-zero parameters/coefficients $a,b,c,d,e$ .

• At carefully selected values of those parameters, the functions are each forced to be approximately zero for all the points parametrized by $(x=r\cos\theta,y=r\sin\theta,m,t)$, where $0 \le t$ with $0 < r \le R$ and $0 < \theta \le 2\pi$. How do I brute-force or solve for the parameters which drive those functions to zero?

Find non-zero $a,b,d$ such that at all the parametrized points as defined above, then $f\approx0$ && $g\approx0$ && $\textrm{Norm}[h]\approx0$ where

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