gmp coefficients

[stla]

Hello,

I've just done a package which implements some polynomials. Their coefficients are rational in general, I calculate them with gmp. It would be nice if mvp could deal with gmp coefficients. Is it doable ?

> JackPol(3, lambda = c(3,1), alpha = gmp::as.bigq(2,3))
mvp object algebraically equal to
14 x_1 x_2 x_3^2  +  14 x_1 x_2^2 x_3  +  14 x_1^2 x_2 x_3  +  20/3 x_1^2 x_2^2  +  20/3 x_1^2 x_3^2  +  20/3 x_2^2 x_3^2  +  50/9 x_1 x_2^3  +  50/9 x_1 x_3^3  +  50/9 x_1^3 x_2  +  50/9 x_1^3 x_3  +  50/9 x_2 x_3^3  +  50/9 x_2^3 x_3

[RobinHankin]

hello, thanks for this. As you point out, mvp objects with rational coefficients are perfectly well-defined (and indeed the complex generalization might be interesting too), and this would certainly be possible in principle. The problem is that, in the mvp package coefficient addition (and potential cancellation) has to be done in C, not R; so implementing this idea would need a major restructuring of the package. On the other hand, there is no problem having coefficients which are themselves mvp objects, or indeed multiplying everything by the LCD of the denominators, in the example you post this would be 9. But I know that this is an awkward and poor thing. What is your application?

[stla]

What is your application?

Sorry I forgot to link my package: https://github.com/stla/jackR

[stla]

Hi Robin,

I improved my package. I'm using Ryacas to evaluate polynomials with rational variables and coefficients.

[stla]

Hi Robin,

I did a new package, gmpoly, for multivariate polynomials with gmp rational coefficients. Everything is programmed in R, no C/C++.

> library(gmpoly)
> 
> pol <- gmpoly("4 x^(2, 1, 1) + 1/2 x^(0,1,0)")
> +pol
[1] "1/2 x^(0,1,0) + 4 x^(2,1,1)"
> -pol
[1] "-1/2 x^(0,1,0) - 4 x^(2,1,1)"
> 2 * pol
[1] "1 x^(0,1,0) + 8 x^(2,1,1)"
> pol / 2
[1] "1/4 x^(0,1,0) + 2 x^(2,1,1)"
> pol + 5
[1] "5 x^(0,0,0) + 1/2 x^(0,1,0) + 4 x^(2,1,1)"
> pol - 5
[1] "-5 x^(0,0,0) + 1/2 x^(0,1,0) + 4 x^(2,1,1)"
> pol^2
[1] "1/4 x^(0,2,0) + 4 x^(2,2,1) + 16 x^(4,2,2)"
> pol1 <- gmpoly("2 x^(1,1) - 5/3 x^(0,1)")
> pol2 <- gmpoly("-2 x^(1,1) + 3 x^(2,1)")
> pol1 + pol2
[1] "-5/3 x^(0,1) + 3 x^(2,1)"
> pol1 * pol2
[1] "10/3 x^(1,2) - 9 x^(2,2) + 6 x^(3,2)"

[RobinHankin]

that is a great piece of work. It is cool to have everything in R. I've been playing with it, why do you not allow negative powers?

@.***>

On Fri, Feb 18, 2022 at 2:26 AM stla @.***> wrote:

Hi Robin,

I did a new package, gmpoly https://github.com/stla/gmpoly, for multivariate polynomials with gmp rational coefficients. Everything is programmed in R, no C/C++.

library(gmpoly)> > pol <- gmpoly("4 x^(2, 1, 1) + 1/2 x^(0,1,0)")> +pol [1] "1/2 x^(0,1,0) + 4 x^(2,1,1)"> -pol [1] "-1/2 x^(0,1,0) - 4 x^(2,1,1)"> 2 pol [1] "1 x^(0,1,0) + 8 x^(2,1,1)"> pol / 2 [1] "1/4 x^(0,1,0) + 2 x^(2,1,1)"> pol + 5 [1] "5 x^(0,0,0) + 1/2 x^(0,1,0) + 4 x^(2,1,1)"> pol - 5 [1] "-5 x^(0,0,0) + 1/2 x^(0,1,0) + 4 x^(2,1,1)"> pol^2 [1] "1/4 x^(0,2,0) + 4 x^(2,2,1) + 16 x^(4,2,2)"> pol1 <- gmpoly("2 x^(1,1) - 5/3 x^(0,1)")> pol2 <- gmpoly("-2 x^(1,1) + 3 x^(2,1)")> pol1 + pol2 [1] "-5/3 x^(0,1) + 3 x^(2,1)"> pol1 pol2 [1] "10/3 x^(1,2) - 9 x^(2,2) + 6 x^(3,2)"

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[stla]

Good suggestion. I will think about it. Thanks.