Gemara

Moed Katan 25a (Beraisa): When a Chacham dies, everyone is like a relative. One must tear, bare his shoulder and eat the first meal after the burial from others' food in the street.

When Rav Safra died, Rabanan did not tear for him, because they had not learned from him.

Abaye: The Beraisa does not say that we tear (only) for a Rebbi that died. We tear for a Chacham that died! Also, every day we recite Rav Safra's teachings!

Rabanan thought that it was too late to correct their mistake.

Abaye: A Beraisa teaches that we tear as long as we are engaged in eulogizing.

Rabanan thought that they should tear immediately.

Abaye: A Beraisa teaches we honor a Chacham by tearing during the eulogy.

27a (Mishnah): During the Mo'ed we not leave the bier in the street, lest it lead people to eulogize.

27b (Rav Papa): Mo'ed does not affect (what we do to honor) a deceased Chacham, all the more so Chanukah and Purim do not.

This is only when the Chacham is there, but not in his absence.

Question: But Rav Kahana eulogized Rav Zevid of Neharda'a in Fum Nahara (during the Mo'ed, in his absence)!

Answer: That was on the day of the Shemu'ah. It is considered like in front of him.

Rishonim

Rif and Rosh (3:85): Mo'ed does not affect a deceased Chacham, all the more so Chanukah and Purim. This is only when the Chacham is there, but not in his absence. On the day of the Shemu'ah it is considered like in front of him.

Nimukei Yosef (DH Ein): We eulogize a Chacham normally on Chol ha'Mo'ed. Some say that 'the day of the Shemu'ah' must be the day of death and burial. Fum Nahara is close to Neharda'a, and Rav Kahana heard of the death of Rav Zevid and eulogized him that very day. Some say that we discuss a Chacham who can answer questions about any Halachos, even Maseches Kalah.

Nimukei Yosef (15a DH Gemara): We tear and cry over the death of any Chacham, but Aveilus is only for one's Rebbi.

Rambam (Hilchos Evel 9:11): Everyone must tear a Tefach for a Kosher person, even if he is not a Chacham. Everyone is like a relative when a Chacham dies. One tears until he bares his heart, and bares the right shoulder. The Chacham's Beis Medrash is idle for seven days. The custom is for Chachamim everywhere to tear for each other even if they are equal and one did not learn from the other.

Question: What is the source to bare the heart for a Chacham, even if he did not learn from him?

Answer #1 (Kesef Mishneh 3). A Beraisa obligates baring the shoulder for a Chacham. We must say that he tears enough to bare his heart.

Answer #2 (Lechem Mishneh 3): Rabanan did not tear for Rav Safra. One must tear for any Kosher person! The Rambam explains that they did not bare the heart, for they held that this is only for one's Rebbi. Abaye taught them that it is for any Chacham.

Rambam (12): If one tore for a Chacham, he may be Sholel once he turns away from the bier. It seems that he may sew it back normally the next day.

Radvaz: The Rambam omits the law of a Rebbi who was not his primary Rebbi. It seems that he holds that this is like a Chacham who died. However, a Chacham does not tear over the death of a smaller Chacham unless he learned from him.

Rambam (13): If there is a Shemu'ah that a Chacham died, we tear only during the eulogy. This honors the Chacham. One may Sholel the same day and be Me'acheh the next day.

Rambam (11:3,4): We do not leave the bier in the street during the Mo'ed, lest it lead people to eulogize. Likewise, we do not eulogize on Chanukah, Purim or Rosh Chodesh.

Rambam (5 and Hilchos Yom Tov 6:22): However, we eulogize a Chacham during the Mo'ed, all the more so on Chanukah, Purim or Rosh Chodesh. However, we do not eulogize on Yom Tov Sheni. On these days (Chol ha'Mo'ed, Chanukah,...) we eulogize only in front of him, but not after burial.

Kesef Mishneh: We do not allow on Yom Tov Sheni because it is in place of Yom Tov (Rishon, which is) mid'Oraisa.

Ra'avad (Yom Tov 6:22): The day of Shemu'ah is like in front of him.

Rambam (Hilchos Evel 5): A Shemu'ah, even Rechokah, is like in front of him.

Rebuttal (Migdal Oz and Ramach Yom Tov 6:22): Presumably, only a Shemu'ah Kerovah is like in front of him.

Rambam (Hilchos Talmud Torah 5:9): When one's Rebbi dies, he tears all his garments until he bares his heart. He may never Me'acheh. This refers to his primary Rebbi who taught him most of his Chachmah. If not, he is a Talmid Chaver, and tears for him like for other Mesim for which one is Mis'avel. This is even if he learned from him only one thing.

Lechem Mishneh: Here the Rambam discusses a Chacham tearing. He tears for another Chacham who was not his Rebbi like for other Mesim. In Hilchos Evel (9:11) the Rambam teaches that one who is not a Chacham must behe for any Chacham that dies.

Rabeinu Meir (brought in Rosh 59): One tears for a Chacham only if he knows Chidushei Torah of the Chacham. This is why Abaye needed to say 'every day we recite Rav Safra's teachings.'

Rebuttal (Rosh): Abaye said that the Beraisa does not say that we tear for a Rebbi, rather, for any Chacham! And even if the text would say 'for a Rebbi', every day we recite his teachings, so he is our Rebbi! Rashi says that Chachamim in Bavel tear for each other like for a Rebbi, i.e. they are never Me'acheh, but one must tear for any Chacham! The Ra'avad says that Rabanan thought that a Chacham is like a Kosher person, and during the Mo'ed one tears only in front of the Mes before burial. Abaye taught that for a Chacham one tears during the Mo'ed even for a Shemu'ah.

Defense (Shach YD 340:16): The Rosh's Perush is difficult. If Abaye meant 'even if we tear only for a Rebbi, he is our Rebbi', why does the Gemara omit this? And why did he need to say it? Rabanan knew that they say Rav Safra's teachings. If Rabanan held that this does not make him their Rebbi, how did Abaye make them retract? Rather, we must explain like Rabeinu Meir. 'Chacham' is one whose Chidusheui Torah we know. Abaye said 'And further, not only we know his Chidushim, we learn them all day!

Nimukei Yosef (Bava Metzi'a 18a DH Omar): Chachamim in Bavel were stringent. Each considered each other like his primary Rebbi. They stood for each other even outside four Amos, and would tear and never Me'acheh. The Ramban disagrees. He says that they were stringent to stand (within four Amos) and to tear (but do Ichuy) even for smaller Chachamim.

Poskim

Shulchan Aruch (340:7): For a Chacham who can answer a question about Halachah anywhere, we tear even for a Shemu'ah within 30 days.

Source (Ramban, brought in Beis Yosef DH v'Chosav ha'Ramban): When a Chacham dies, everyone is like a relative. A relative tears for a Shemu'ah only within 30 days.

Beis Yosef (DH v'Al): According to the Ra'avad (brought in the Rosh), it is best to tear upon hearing the Shemu'ah. If not, he tears during the eulogy. The Rambam holds that one should delay tearing until the eulogy.

Shach (14): He tears during the eulogy only if it is within 30 days of death.

Rema: If he did not tear within the period of eulogies, he does not tear afterwards.

Shulchan Aruch (ibid.): He tears until he bares his heart. It is the custom of Chachamim everywhere to tear a Tefach for each other, even if they are equal and one did not teach the other.

Question: Why do the Rambam, Ramban and Ran say that this is a custom? The Rosh proved that one must tear for a Chacham, even if he did not learn from him!

Answer (Beis Yosef DH Kosav ha'Rosh): They hold that it is obligatory only for a greater Chacham. Alternatively, it is obligatory even for an equal Chacham, but it is not obligatory for an equal Talmid Chacham.

Shach (15): An opinion (in Sa'if 8) says that one tears only a Tefach even for one's Rebbi. All the more so that opinion requires only a Tefach for a Chacham who is not his Rebbi!

Rema: Some say that we tear only if the Chacham was his Rebbi, or if we know his Chidushei Torah. We are lenient like this in these lands.

Shach (17): The Bach says that our custom is not to tear even for a greater Chacham. This is wrong. No one is so lenient! Perhaps people rely on the Agudah, who says that nowadays we do not have a Chacham who knows even Maseches Kalah.

Shulchan Aruch (401:1): We do not leave the bier in the street on Chol ha'Mo'ed lest it lead people to eulogize. It is permitted only for the honor of a Chacham.