Michael's profile - activity

Thanks, this is the kind of solution I was hoping for.

Shashank told you how to do it in matplotlib (which comes with Sage) - matplotlib allows you a lot of control over your plots (I often use it for this reason), but as you can see, it involves a fair bit of boilerplate compared to Sage's plotting.

If you want to add a formula to a Sage plot, then you can just use latex inside dollar signs, like you would in a .tex document:

text(r"Here's a formula $\frac{\sqrt{3}}{2}$ and some text",(1,2))

Here the r" is necessary due to all the slashes in the string–if you don't include the r then you'll have to escape each of the slashes (check out the python String documentation for more info on that).

Thanks for this example, i'll need some time though to learn what all the commands do.

I know that using

text("Sage is really neat!!",(1,2))

one can easily add text to a plot in Sage. But searching the documentation I couldn't find a way to add a formula, say $\frac{1}{\sqrt{x^2-1}}$.

So is there a way to add a formula to a plot?

Ideally using LaTeX to enter the formula.

First of all, when you define a_ij=var('a_ij') then you define symbolic variables. But when you later do (with inject_on()) PolynomialRing(QQ,a_ij), then a_ij becomes a generator of a polynomial ring.

It is a very common mistake to confuse these two very different objects, and I recommend that you carefully decide whether you want to work with polynomials (i.e., you have a polynomial ring, ideals, want to compute Gröbner bases and those things) or with symbolic expressions (they may happen to look like a polynomial, but provide largely different features).

In particular, since a_ij has completely changed its meaning, it is no surprise that the latex name has gone.

You could do:

sage: R.<a_12,a_23> = QQ[]  # you don't need inject_on()
sage: type(a_12)  # It is not a symbolic variable!
<type 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
sage: latex(a_12)  # This is not how you like it
a_{12}
sage: R._latex_names  # This is where the names are stored
['a_{12}', 'a_{23}']
sage: R._latex_names = ['a_{1,2}','a_{2,3}'] # Override it...
sage: latex(a_12)  # ... and enjoy
a_{1,2}

I think it is a hack, and there should be a method, say, R.set_latex_names(), but unfortunately there isn't, yet.

Thanks! That seems to work. Indeed there are several things I don't quite understand about variables and how they are handled and accessed. I knew that there was a difference between symbolic variables and generators of a polynomial ring. So in my example the symbolic variable was redefined to be a generator of a polynomial ring and got lost? Anyway I do indeed need Groebner bases so symbolic variables should not be of interest in my situation.

Apologies if I don't use the right terminology in my question. I'm fairly new to Sage and programming.

The question is basically in the title but here are more details:

Ideally I would like to create a multivariate polynomial ring with generators indexed by multiindices. As far as I understand this is not directly supported at the moment, although I've found a useful workaround here.

What I'm missing though is the ability to display these generators correctly in LaTex (say as a_{i,j}). I know that one can assign latex names to symbolic variables with the command

sage: a_ij=var('a_ij', latex_name="a_{i,j}");

sage: latex(a_ij);

a_{i,j}

And I've tried putting this before the definition of my polynomial ring. But as soon as I declare the polynomial ring the latex name I assigned seems to be forgotten:

sage: inject_on();

sage: PolynomialRing(QQ,a_ij)

sage: latex(a_ij);

a_{\mbox{ij}}

So:

Question: How can I define a multivariate polynomial ring in Sage and assign my preferred latex names to its generators?