Given $y=x^2$ how can I use a computer algebra system to output all the integer values that this graph intersects? for example (1,1),(2,4),(3,9),etc.
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You can also include $(0,0)$ and $(-1, 1), (-2, 4), (-3, 9)$. There will be a countably infinite number of such points, so I doubt any CAS can output them all. Realize, unless you've left out restrictions on the domain of $x$ other than that $x$ is an integer, we have $f: \mathbb Z \to \mathbb Z_{\geq 0}$, where $f(x) = y=x^2$. – jordan_glen Jan 19 '19 at 19:57
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Also, the graph $y=x^2$ when graphed, shows us $g:\mathbb R \to \mathbb R_{\geq 0}$, where $g(x) = y = x^2$. It is a parabola, and it intersects a countably infinite number of points consisting of an ordered pair integer $x$, $(x, x^2),$ when $x \in \mathbb Z$. – jordan_glen Jan 19 '19 at 20:01
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@jordan_glen I want to generalize this proceedure to any curve. I am not familiar with R-->R0 functions on CAS, how do they work? – User3910 Jan 19 '19 at 20:05