我想指出的是，这个问题通常无法完全解决.对于二次案例(y ^ 2)引用的解决方案可以扩展到三次案例和四分之一的情况(有一个通用的复杂解决方案).但是，有一个数学定理(来自 Galois理论)指出，对于五次方程式(依此类​​推).在您的情况下，最大度为3，因此您可以使用***的三次方程式.对于心脏图形，写:x ^ 2 * y ^ 3-y ^ 2-(x ^ 2-1)= 0并将x视为常数.对于sqrt情况，请摆脱它.将等式的两边平方，将y隔离，最后得到y的四次方程，您可以使用***的四次方程知识来解决.

I'd like to point out that this problem cannot be solved exactly in general. The cited solution for the quadratic case (y^2) can be extended to the cubic case and quartic case (there are a general complicated solutions). But there is a math theorem (from Galois theory) that states that there is no general solution for the quintic equation (and so on). In your case, maximum degree is 3, so you can use the cubic equation from wikipedia. For the heart graphic write: x^2*y^3 - y^2 -(x^2-1) = 0 and treat x as constant. For the sqrt case, get rid of it. Square both sides of equation, isolate y and you end up with a quartic equation on y, that you can solve using wikipedia's quartic equation knowledge.

无论如何，如果您没有充分的理由执行此操作，请不要执行此操作，因为计算机可以为您数字地解决此问题.标准方法是像您绘制的图一样隐式计算此值.

Anyway, if you don't have a very strong reason to do this, don't do it, as the computer can solve this numerically for you. Standard approach is to calculate this implicitly, as in the plots you made.

我希望这会有所帮助.