12/30/2023 0 Comments Integer overflow mathematica![]() ![]() There are five solutions since there is $(k y -1)^2$, which doubles three integer solutions of elliptic curve and one is degenerate. $(6y-1)^2=12 x^3+12 x^2$ and it is straightforward to get the canonical elliptic cure equation by a simple linear transformation of $x$. With the original Reduce result one can find that is equivalent to To answer a question on how many solutions one might expect, we observe that the original equation is an example of an elliptic cure equation ( $q^2 = 4 p^3-g_2 p -g_3)$), we know that if there are two integer pairs of solutions there is also a third integer pair. ![]() I found later a question ( Solutions given by WolframAlpha, asked a few hours ago) regarding the same equation. Such a suplement is quite natural for those who are familiar with equation solving functionality. 100 <= y <= 100 this solves the problem Nonetheless one can make Reduce find all integer solutions adding some restriction on y since there are infinitely many integer y, however when you put e.g. To define the correlation coefficient, first consider the sum of squared values ss. Backsubstitution -> True which is sometimes helpful in similar problems, however not in our case. The correlation coefficient, sometimes also called the cross-correlation coefficient, Pearson correlation coefficient (PCC), Pearson's r, the Perason product-moment correlation coefficient (PPMCC), or the bivariate correlation, is a quantity that gives the quality of a least squares fitting to the original data. Given the equation there are some options in Reduce, e.g. A natural suggestion is to reformulate the input since there are two variables $x$ and $y$ while we have the only one equation and so in general there is a continuum (a submanifold) of solutions, even in integers one might expect infinitiely many solutions, although the latter is not the case here. Quite frequently we get similar expressions in the output. ![]() Regarding the title of the question, is the result of Reduce really odd? Reduce simply reduces systems of equations, inequalities, domain specifications, logical expressions etc. ![]()
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