On Tuesday, July 12, 2016 at 3:27:38 AM UTC+1, saad khalid wrote:
>
> Hey everyone:
>
> So, it turns out that Macaulay2 has an inbuilt function to convert it's
> ascii output of exponents into a normal string. It can be seen at the end
> this example:
>
> reset()
> macaulay2.eval("""
> K = toField(QQ[zet]/(zet^6 + zet^3 + 1))
> A=matrix{{zet^1,0},{0,zet^8}}
> needsPackage "InvariantRing"
> G=generateGroup({A},K)
> P = molienSeries G
> X = toString P
> """)
>
>
> sage:
>
> PolynomialRing
>
> | zet 0 |
> | 0 -zet^5-zet^2 |
>
> 2 2
> Matrix K <--- K
>
> InvariantRing
>
> Package
>
> {| 1 0 |, | zet 0 |, | zet^5 0 |, | -zet^3-1 0 |, |
> -zet^4-zet 0 |, | zet^3 0 |, | zet^4 0 |, | -zet^5-zet^2 0
> |, | zet^2 0 |}
> | 0 1 | | 0 -zet^5-zet^2 | | 0 zet^4 | | 0 zet^3 | | 0
> zet^2 | | 0 -zet^3-1 | | 0 zet^5 | | 0 zet | | 0
> -zet^4-zet |
>
> List
>
> 2 3 4 5 6 7 8
> 1 - T + T - T + T - T + T - T + T
> ----------------------------------------
> 3 6 2 2
> (1 + T + T )(1 - T) (1 + T + T )
>
> Expression of class Divide
>
> (1-T+T^2-T^3+T^4-T^5+T^6-T^7+T^8)/((1+T^3+T^6)*(1-T)^2*(1+T+T^2))
>
>
> So, I want to be able to take that string output and define a Sage
> function from it, and then ideally be able to take its Taylor series. here
> is what I'm trying:
>
> var('T')
> str(T) = macaulay2('X')
>
this line does not look right to me.
>
> str(1)
>
>
> sage:T
> sage:(1-T+T^2-T^3+T^4-T^5+T^6-T^7+T^8)/((1+T^3+T^6)*(1-T)^2*(1+T+T^2))
>
> this seems to say that T is no longer a variable, but an expression.
What you seem to have done is to define an expression in SR (i.e. in
Symbolic Ring), but in a variable that is no longer an SR variable.
>
> For some reason, it won't recognize T as a variable and won't let me make
> a function out of it. Would anyone have any tricks on making this work?
>
>
I thought I already told you a trick - convert things into Sage polynomials
first, and then convert them into SR elements. E.g.
sage: R.<t,u>=QQ[]
sage: p=t^2+1+7*u # you can also get such a polynomial from M2
sage: type(p)
<type
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
sage: type(SR(p))
<type 'sage.symbolic.expression.Expression'>
sage: sin(SR(p)).diff(t)
2*t*cos(t^2 + 7*u + 1)
sage: sin(SR(p)).diff(u)
7*cos(t^2 + 7*u + 1)
Hope this helps,
Dima
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