Variables get lost in Substitution

[manuelbb-upb]

Hi, I noticed something strange: When there are variables with a zero coefficient and one performs substitution, these variables get lost.

MWE:

using DynamicPolynomials
@polyvar x[1:2]
p = 1 * x[1] + 0 * x[2]
variables(p) == x

P = subs(p, x => x)
variables(P) == x[1]    # x[2] gets lost

My current dumb workaround is to add sum(0*x) after substitution to "restore" the variable information.

[manuelbb-upb]

I now have had a bit of time to look into it. This seems to be similar to https://github.com/JuliaAlgebra/DynamicPolynomials.jl/issues/80.

To fix it, I propose to change q = zero(Polynomial{C, Tout}) in this line to

q = zero_with_variables(Polynomial{C,Tout}, variables(p))

This makes the MWE work as expected.

@blegat Does that seem ok to you? If so, I can gladly make a PR :)

[blegat]

Yes, that's a good suggestion, PR welcome :)

[votroto]

Ouch, I guess it's in the spirit of "dynamicity", but I didn't expect this:

@polyvar x y
p = x + y
subs(p, x => 1) |> variables # returns [x, y]

I expected [y]. Is there a workaround?

[blegat]

You can use effective_variables

[votroto]

Good point, sorry for being cryptic. My current issue is that e.g. SumOfSquares.jl uses MultivariatePolynomials.jl and this commit breaks it slightly, as it uses all variables. Let's say I want to optimize a polynomial after making substitutions; How can I force the "expected" variables for the polynomial?

[blegat]

Good point, SumOfSquares should probably use effective_variables. Could you open an issue in SumOfSquares ? You would have the same issue with variables(x^2 + y^2 - y^2) being [x, y] so I think this change with substitution is consistent. I should have probably made a breaking release though, you're right.

[manuelbb-upb]

Ouch, I guess it's in the spirit of "dynamicity", but I didn't expect this

Just as a sidenote, I might on elaborate why I expected of variables to contain zero-coefficient variables and those substituted with constants:

Indeed, I have "dynamic" use case: polynomial interpolation / regression of data. Zero-coefficients might naturally occur. If the variables were not kept when there is a zero-coefficient then I would get an error when (lazily) evaluating the eventual interpolation polynomial because the length of the input feature vector and the number of variables mismatched.

The substitution issue showed up when I had a min-max-scaling polynomial for the features that accidentally also set some variables to zero when substituted into some of the interpolation polynomials and led to the same evaluation issues when plugging in the feature vectors.

Of course, the evaluation error can be avoided without the suggested fixes by always having the original variables around and doing a more verbose evaluation (in fact the way it is recommended, I believe):

using DynamicPolynomials
@polyvar x[1:2]
p1 = x[1]
subs( p1, x[1] => 1.0, x[2] => 1.0 )  # works as expected
p1( [1.0; 1.0] )  # does not work

I have mostly used the second notation because of its convenience (which is what I mean by "lazily" above) and because I guessed that the variable ordering is not an issue if I only use a single @polyvar call and a vector of variables. I am not familiar with the inner workings of the @polyvar macro but this comment seemed to confirm my thoughts.

[blegat]

Yes, the order is guaranteed;