Simplifying complex expresion (without ComplexExpand or User defined rules)

Many times, I’ve struggled with simplifying complex expressions, such as this extraordinarily simple expression, and Mathematica wont do it:

$Assumptions = {l>0,a>0,a (Element)Reals, l (Element)Reals}
Conjugate((Exp(I a))^(2 l)) //FullSimplify

Where Mathematica returns the same thing with no simplification.
I told it the assumptions which make it very obvious to just change the sign of the exponent, and I don’t understand why it doesn’t work.

I looked here, but it seems like they have to define their own rules to do this kind of thing. I’m also saw here that you can do //ComplexExpand //FullSimplify for this expression, but it doesn’t seem to work in all cases. Why should it be nessecary and why doesn’t FullSimplify do it already? Also, I think ComplexExpand assumes that all variables are real, which was the case in this expression, but isn’t always the case. So how would I do it then?

visas – Taiwan maximum stay rules with reentry

As a US passport holder, you’re “visa-exempt” and will generally be granted 90 days on arrival, no questions asked:

The nationals of the following countries are eligible for the visa
exemption program, which permits a duration of stay up to 90 days: …
U.S.A. …

Now, making a quick visit to another country for the sole purpose of renewing your visa is known as a “visa run”. Most countries will get suspicious if you do this too often, but fortunately, anecdotal evidence for Taiwan seems to indicate that they don’t care:

According to experiences on this forum, you can continue to do this as
long as you like. Of course, like anything, Immigration has the final
say, but as long as you keep your nose clean (ie. don’t overstay your
visa, don’t commit any felonies, etc.) you should be fine.

(courtesy “Steve4nLanguage” on Forumosa, the definitive Taiwan forum)

So the answers to your questions appear to be:

  1. No
  2. No

All that said, I wouldn’t rely on this for more than a few renewals. If you’re planning on staying in Taiwan for a longer time, you’d definitely best be off working out some sort of “real” visa that actually allows you to work legally.

CSF allow rules [split thread]

While installing csf, it will change default policy to DROP so all requests to server other than open ports in csf will be blocked.

In your case, you need to block all requests from internet and only allow US IP’s. So try remove the required ports ( 80 and 443 for http ) from the CSF TCP_IN and allow US UP using CC_ALLOW = “US” to accept request from US only.

Please make sure to whitelist your IP in allow list while doing these tests.

Schengen entry rules for a UK resident with EU-citizen spouse

Does the 90 day rule apply to me (when I travel alone), given the 2 documents I possess are a Brazilian passport and a UK residence card?

Yes. You are exempt from the 90-day rule when you travel with (or to join) your Italian spouse. Otherwise, you are supposed to comply with it.

How exactly is the rule applied? Based on my understanding of the rule, the calculator at is incorrect, since it only factors in the last 90 days. Edit: this is the calculation I think is incorrect (for planning)

The calculator is definitely correct, but it does not apply to you because you are Brazilian. If you read the user guide, you’ll find this:

Please note that the change (effective October 18, 2013) does not apply to the visa waiver agreements concluded between the EU and Antigua and Barbuda, The Bahamas, Barbados, Brazil, Saint Kitts and Nevis, Mauritius, and Seychelles where the old definition (“3 months during a 6 months period following the date of first entry”) continues to apply. For citizens of these 7 third countries the calculator is not recommended to be used.

For you, it works like this: The first time you enter the Schengen area, a 180-day period starts within which you may stay up to 90 days. If you are in the Schengen area 181 days later, a new 180-day period starts on that day. Otherwise, a new 180-day period starts when you next enter the Schengen area.

(The reason the calculator results can be confusing is that some days of presence that are less than 180 days before you enter will nonetheless be more than 180 days old before you get to the 90-day limit. For example, only the last one of those three days from 31 December to 2 January counts toward your total days of presence when you enter on 29 June, but on the next day it no longer does because it is 180 days old — in a leap year, the 180-day period that ends on 30 June begins on 3 January. But as noted above, you don’t need to worry about that.)

Scouts 1e – Encounter rules while traveling in a caravan in the Jade Regent Campain

In the Jade Campain book, the caravan encounter rates are defined according to chapters with the following statements:

As the caravan heads north, There is a 10% chance of meeting each day. Encounters marked with an asterisk have a 50% chance of performing at night while the caravan camps. All other encounters take place while the caravan is underway. Encounters do not occur when the caravan is in a settlement. If an encounter occurs, see the table below for what the PCs encountered. Note that all of the following encounters are caravan encounters and use the rules for caravan fighting available online in the free Jade Regent Player & # 39; s Guide

What is not in bold is fairly simple, but I am struggling with the bold parts. If I read that correctly, these rules would mean that I roll for a 10% chance of an encounter every day (then of course I choose the encounter from the encounter table). Then, provided the party does not camp near a city, there would be an independent 50% chance that an encounter with an * would take place, which would mean that if multiple encounters had a * symbol, they would all be in one single night!

Of course, I searched the Internet, but couldn't find this question. However, I am more confused about a forum (did not save the source …) that the 10% chance every day was cumulative (day 1: 10%, day 2: 20% etc.) and reset to 10% was every time there was an encounter.

In the first chapter of the adventure, I used my understanding of the rules and the results were pretty slow. Only one event occurred during a ~ 14 day trip, which only resulted in bad weather. The night rule also seemed pretty tough regarding the fact that there weren't that many settlements on the street.

How should I interpret these rules?
Please note that my mother tongue is French and I may have overlooked important things
Nuances in the text (even French rules don't help to solve my question …).

the one ring – what is considered "wounded" in the sense of the rules for restoring a point of hope?

Page 81 of the core set of rules first mentions using a fellowship focus to restore hope without using fellowship points:

Each player can choose a companion of their choice as their focus. (…) With a Fellowship focus, a character can restore hope without spending Fellowship (at the risk of getting shadows if the focus is violated or killed). see page 133.

As mentioned earlier, pages 133-134 describe the mechanisms for a fellowship focus, including the rules for restoring hope or getting shadow points, depending on what happens to them. Under the heading "As a source of hope" it says:

The presence of a fellowship focus influences the way a character regains hope:

A player hero gets 1 point of hope back at the end of a session if his focus on companions has not been wounded, poisoned, miserable, or otherwise harmed by the Loremaster during play (e.g. locked up by orcs). and is in the same place as her.

A character will receive 1 shadow point at the end of the session if their fellowship focus was wounded, or 3 points if the focus was killed.

The capitalization here indicates that the game relates to the wounded, poisoned, and miserable conditions, as described on pages 128-130. However, note that the requirement is not limited to these three conditions. The rule gives the Loremaster the ability to determine that "serious damage" to a character prevents a hope point from being restored.

As long as the fellowship focus chosen by the player is in the same place at the end of the session and none of these three conditions or other serious damage has been suffered during the game, the player's character can regain 1 point of hope. If the selected Fellowship focus has suffered the wounded condition, the player hero does not get back a point of hope and also receives 1 point of shadow. If the selected Fellowship focus is killed, you will receive 3 Shadow Points instead.

Rules – grandfather to post


I'm trying to post in the graphic design competition forum, but it says I didn't meet the requirements. I have been a member since 2005 and do not want to post artificially to meet the requirements.

Can I be a grandfather for posting there? I prefer people here to make some money on my project instead of posting to another place that I'm not familiar with just because I don't post regularly. I understand there is a premium feature, but 15 years … really. Besides, it wasn't a thing when I got there.

Thanks a lot

Assessment – hypothetical application of rules / restriction of rules to a certain context?

I have the code TensorDimensions[TensorContract[c, {{1, 2}}]]. It is in normal form. But if I add the rules:

TensorDimensions[c] = {4, 4, 5}

then the code is evaluated too {5}.

I was wondering if there is a specific language construct that gives me the result of the assessment TensorDimensions[TensorContract[c, {{1, 2}}]] I would be add these rules without actually adding these rules in a global context?

I would like to see what would happen to the expression rating if The rules have been added, but not the rules. Is that possible? Like a "stronger" version of what ReplaceAll does.