## Stream: general

### Topic: Lean's proof of FTA is "obviously wrong"

#### Kevin Buzzard (May 10 2020 at 13:28):

This has come up before, but this time it's pretty horrible, at least I think it is.

Take a look at the docs for complex.exists_root, the Lean proof of the fundamental theorem of algebra. Read the statement of the theorem. You see what it says about all polynomials having a root? What about the polynomial $f(z)=37$? It has degree 0 and no root.

Exercise: what is going on?

#### Shing Tak Lam (May 10 2020 at 13:30):

The theorem requires 0 < degree f? So f(z) = 37 has degree 0 and isn't accepted?

#### Reid Barton (May 10 2020 at 13:31):

Good point. The theorem ought to say 1 ≦ f.degree.

#### Shing Tak Lam (May 10 2020 at 13:32):

This is a less than sign which is underlined, not a less than or equal sign...

#### Chris Hughes (May 10 2020 at 13:33):

I think it would be good to get rid of that underlining.

#### Reid Barton (May 10 2020 at 13:33):

Interesting, it looks less bad here:
image.png

#### Shing Tak Lam (May 10 2020 at 13:37):

I just tried a few different browsers, Firefox (posted above) has a thick underline, (old) Edge and Internet explorer has a thin underline. So this isn't consistent across browsers...

#### Kevin Buzzard (May 10 2020 at 13:37):

Yes. The underlying issue apparently turning \lt into \le has been discussed before here, but it still made me look twice. IIRC the conclusion was that people didn't really know what to do instead, and some people weren't bothered by it.

#### Chris Hughes (May 10 2020 at 13:38):

use a different colour for the links?

#### Chris Hughes (May 10 2020 at 13:38):

Or just not highlight them at all?

(duplicate)

#### Kevin Buzzard (May 10 2020 at 13:39):

Ideally one would use a colour which, when clicked, does not turn into a dark purple which looks like a black. But light blue generally works for stuff like this, doesn't it? As long as it stayed light blue?

#### Patrick Massot (May 10 2020 at 13:43):

My answer is always the same: remove all link decoration here. Every word is a link, what's the point?

#### Shing Tak Lam (May 10 2020 at 13:55):

Here's a few images of what it'd look like without the underlines

1. black links
2. darkblue links
3. lightblue links (obviously not using this)

Also with the setup right now, the links in the centre section should stay the same colour even after it has been clicked. The ones to the sides will change to purple, but that's separate.

#### Kevin Buzzard (May 10 2020 at 13:56):

Are there any <s in your examples?

#### Patrick Massot (May 10 2020 at 13:57):

Maybe darkblue is a good compromise

#### Patrick Massot (May 10 2020 at 13:57):

And all of them are better than underlines, including the awful light blue version

#### Shing Tak Lam (May 10 2020 at 13:58):

This one has <

#### Rob Lewis (May 10 2020 at 14:18):

Yes, this has come up before. It never looked very confusing on my browsers so I didn't really think about it. My preferred solution would be to remove underlining, keep the same colors as now, and make sure that the link colors change (subtly, not to blue or anything) on mouseover. I think they already do this.

#### Rob Lewis (May 10 2020 at 14:19):

I'm happy to accept a PR to the CSS changing this. Actually, I had a vague memory of there being a PR already, but I don't see it.

#### Ryan Lahfa (May 10 2020 at 14:20):

Rob Lewis said:

I'm happy to accept a PR to the CSS changing this. Actually, I had a vague memory of there being a PR already, but I don't see it.

Well, I wanted to do one in some topic, so I have a custom CSS userscript to remove those underlines personally and show them only on hover. It works pretty fine, I can bundle it into a PR.

#### Ryan Lahfa (May 10 2020 at 14:21):

Basically I just apply

.decl_type a:link, .structure_field a:link {
text-decoration: none !important;
}

.decl_type a:hover, .structure_field a:hover {
text-decoration: underline !important;
}


on mathlib (I can remove the !important in the PR of course.)

#### Rob Lewis (May 10 2020 at 14:22):

Sounds good to me.

#### Shing Tak Lam (May 10 2020 at 14:26):

I think this is where the new line should go? At least that's how I made those examples above

#### Ryan Lahfa (May 10 2020 at 14:27):

Shing Tak Lam said:

I think this is where the new line should go? At least that's how I made those examples above

I could put it there, @Rob Lewis what do you think?

#### Ryan Lahfa (May 10 2020 at 14:27):

@Shing Tak Lam Well if you've done the work, I can let you send the PR if you want :)

#### Shing Tak Lam (May 10 2020 at 14:28):

I haven't. I just used Firefox dev tools, which changes the page as I edit the CSS.

#### Ryan Lahfa (May 10 2020 at 14:28):

Shing Tak Lam said:

I haven't. I just used Firefox dev tools, which changes the page as I edit the CSS.

Oh okay

#### Rob Lewis (May 10 2020 at 14:29):

Yep! That looks right. It should be a very easy PR, you can even do it with the Github web editor.

#### Ryan Lahfa (May 10 2020 at 14:30):

I want to test before to send it, just to ensure I don't break anything, so I've forked and will send the PR soon :)

#### Shing Tak Lam (May 10 2020 at 14:30):

(and if you want to have an underline when hovering, I think it's Line 233 just below where I linked)

Thanks!

#### Ryan Lahfa (May 15 2020 at 21:35):

Last updated: May 14 2021 at 22:15 UTC