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# switch(RingElement)

## Description

A binary form $F(t_0,t_1) = a_0\,t_0^n+n\,a_1\,t_0^{n-1}\,t_1+1/2\,n\,(n-1)\,a_2\,t_0^{n-2}\,t_1^2+\,\cdots\,+n\,a_{n-1}\,t_0\,t_1^{n-1}+a_n\,t_1^n$ can be identified with the list $\{a_0,a_1,\ldots,a_n\}$ of its coefficients, and also with the ideal of the corresponding point of $\mathbb{P}^n$. The method switch when applied to a binary form returns the list of its coefficients; when applied to a list of coefficients returns the ideal of the corresponding point; when applied to the ideal of a point returns the corresponding binary form.

 i1 : F = randomBinaryForm 9 9 8 7 2 6 3 5 4 4 5 3 6 2 7 o1 = 162t + 18t t + 81t t + 18t t + 36t t + 27t t + 54t t + 27t t + 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ------------------------------------------------------------------------ 8 9 63t t + 28t 0 1 1 o1 : QQ[t ..t ] 0 1 i2 : L = switch F 9 3 2 3 9 3 o2 = {162, 2, -, --, -, --, --, -, 7, 28} 4 14 7 14 14 4 o2 : List i3 : I = switch L o3 = ideal (4t - t , 112t - 3t , 392t - 9t , 392t - 3t , 98t - t , 392t 8 9 7 9 6 9 5 9 4 9 3 ------------------------------------------------------------------------ - 3t , 112t - 9t , 14t - t , 14t - 81t ) 9 2 9 1 9 0 9 o3 : Ideal of QQ[t ..t ] 0 9 i4 : switch I 9 8 7 2 6 3 5 4 4 5 3 6 2 7 o4 = 162t + 18t t + 81t t + 18t t + 36t t + 27t t + 54t t + 27t t + 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ------------------------------------------------------------------------ 8 9 63t t + 28t 0 1 1 o4 : QQ[t ..t ] 0 1 i5 : oo == F o5 = true