Gemara

(Beraisa): A case occurred in which Reuven planted (his own) seeds (of other species) in Shimon's vineyard. Chachamim forbade what grew from the seeds, and permitted the vines.

Inference: We do not make a Kal va'Chomer to say that since vines forbid but do not become forbidden, so all the more so seeds, which do not forbid, do not become forbidden!

Rejection: Normally, we make such a Kal va'Chomer. Here is different. The Torah forbids Kilai ha'Kerem (crossbreeds in a vineyard) only with Kanvus (hemp) and Luf (a kind of onion);

(Mishnah): If hemp or Luf was planted in a field, other seeds may not be planted there for three years, for these plants produce after three years.

Chachamim fined to punish (only) Reuven, for he transgressed.

Rishonim

Rambam (Hilchos Kilayim 1:1): One who plants two kinds of grain or two kinds of Yerek (vegetables) with seeds of a vineyard is lashed twice, for "Sadcha Lo Sizra Kilayim" and "Lo Sizra Karmecha Kilayim."

Rambam (5:3): One is lashed mid'Oraisa only for hemp and Luf and similar Zera'im (seeds) that finish with the yield of the vineyard. Other Zera'im are forbidden only mid'Rabanan. Similarly, it is forbidden mid'Rabanan to plant Kil'ai ha'Kerem (diverse species in a vineyard) in Chutz la'Aretz.

Ri Korkus: The Rambam says that other Zera'im are forbidden only mid'Rabanan. They are forbidden mid'Oraisa due to Kil'ai Zera'im! Regarding Kil'ai Zera'im we do not distinguish hemp and Luf from other Zera'im. 'Finishing with the yield of the vineyard' does not apply. In Halachah 6, the Rambam forbids only grain in a Kerem, but permits other Zera'im, i.e. even mid'Rabanan. Rashi explains that hemp and Luf make clusters, and their seed does not degenerate; they have a root that endures. This is close to the Rambam's reason. Perhaps the Rambam discusses when one distanced the proper distance so that there is no Isur of Kil'ai Zera'im (but not enough to permit Kil'ai ha'Kerem). Alternatively, he teaches about what forbids eating and Hana'ah due to Kil'ai ha'Kerem; in any case one may not plant due to Kil'ai Zera'im. Alternatively, he forbids even one (other) Min (species) in a Kerem. The first answer is best.

Ri Korkus: Perhaps here the Rambam discusses Eretz Yisrael, and forbids mid'Rabanan. Below (Halachah 6) he totally permits in Chutz la'Aretz. Some say that below the Rambam permits mid'Oraisa, but it is forbidden mid'Rabanan, like he said above. This is difficult, for he says there 'other Zera'im may be planted in a vineyard, and all the more so other trees', i.e. l'Chatchilah. The Bartenura and R. Shimshon say that all trees are forbidden only mid'Rabanan, like it says in Menachos. I say that the Rambam forbids Zera'im mid'Rabanan, i.e. grain or Yerek that do not finish with the Kerem, like hemp and cotton. Grain and Yerek are called Zera'im. Because the verse says "Tevu'as ha'Kerem", Chachamim forbade only grain, and Yerek, which is like grain. Luf is a kind of onion, i.e. Yerek (Rambam Hilchos Pe'ah 6:10). Even though hemp is not Yerek, the Torah forbids it, just like it forbids cotton, Kindas and similar species. Below (Halachos 19), the Rambam repeated that the Torah forbids hemp. He did not need to mention Luf, for it is surely a Yerek.

Kesef Mishneh: The Rambam explains that one is liable for hemp and Luf among Zera'im that are not eaten. They are finished with the produce of the vineyard. "Karmecha Kil'ayim" connotes that the Zera'im are like the vineyard, but other kinds of Zera'im are forbidden in a vineyard only mid'Rabanan. This refers to what is eaten. What is not eaten is permitted even mid'Rabanan. 'Finished with the produce of the vineyard' means that they produce only after three years, like hemp and Luf. Produce of the vineyard is permitted only after three years of Orlah. The Rambam obligates lashes for Zera'im that are eaten, like grain, legumes and Yerek; this connotes that it is mid'Oraisa. Surely, the Torah forbids the five grains, like Tosfos and the Ran (below) say. It seems that they argue with the Rambam about Yerek.

Tosfos Yom Tov (Kil'ayim 5:9): According to the Rambam, the Gemara brought the Mishnah to teach that Hemp and Luf produce after three years, therefore, they are forbidden. According to Rashi (below), why was it brought?!

Note: In some texts, the Gemara does not bring the Mishnah.

Rambam (6): Only grain and Yerek are forbidden due to Kil'ai ha'Kerem. Other Zera'im may be planted in a vineyard, and all the more so other trees.

Rebuttal (Ra'avad): The Rambam had an errant text, therefore, he erred.

Kesef Mishneh: A Mishnah (Kil'ayim 5:8) says 'Irus, Kisum, Shoshanas ha'Melech and all Minei Zera'im are not Kil'ai ha'Kerem.' The Rambam understood that even mid'Rabanan they are permitted. This refers to Zevachim that are not eaten. The Rambam taught above that other Zera'im that are eaten are forbidden mid'Rabanan.

Rambam (19): Irus, Kisum, Shoshanas ha'Melech and all Minei Zera'im are not Kil'ai ha'Kerem. Kanvas, Kirnas, and cotton are like other Yerakos, and they forbid in a Kerem. Similar, all kinds of grass that grow by themselves in a field, forbid in a Kerem. Mitzri bean is a kind of Zera'im; it is not Mekadesh. Reeds and roses are types of trees; they are not Kil'ai ha'Kerem.

Ri Korkus: The Ra'avad says that the correct text is 'Irus, Kisum, Shoshanas ha'Melech are kinds of Zera'im, and they are not Kil'ai ha'Kerem.' This is because people do not (intend to) grow them. Similarly, there are kinds of grass that are not Kil'ai ha'Kerem because people do not grow them. A Tosefta says so. The Rambam's text says 'and all Minei Zera'im are not Kil'ayim b'Kerem.' Chachamim decreed only about grain, and Yerek, which is like grain, but they are not finished with the Kerem, therefore, the Torah permits them. The Torah forbids Yerakos that finish with the Kerem; the Rambam did not need to mention them here. The Ra'avad holds that the Torah forbids only hemp and Luf, but all Zera'im are forbidden mid'Rabanan, i.e. grain, Yerek and other kinds of Zera'im. Perhaps one can resolve the Rambam even according to the Ra'avad's text. Since the Tosefta exempts because they are a species of Zera'im, this includes any Zera'im that are not grain or Yerek.

Kesef Mishneh: The Ra'avad (above) held that we must correct the Mishnah based on the Tosefta. The Rambam holds that the text of the Mishnah is primary. One can explain the Tosefta like the text of the Mishnah. The text of the Rambam should not say 'Kanvus (hemp)', for he already taught this. Also, if so, why did he omit Luf? Rather, it should say 'Kindas'.

Ran (Chulin 47a): In Menachos, we say that the Torah forbids only hemp and Luf. This does not exclude the five grains. Surely, they are Kil'ayim mid'Oraisa! Rather, it excludes garden seeds that are not eaten, like hemp and Luf. Hemp and Luf are forbidden because they grow greatly, and there is much mixing, and they make clusters like vines.

Rashi (15b DH Asrah): Hemp and Luf are kinds of legumes whose seeds do not degenerate; they have a root (that endures) Alternatively, they grow on clusters, like grapes.

Shitah Mekubetzes (15b:2): R. Chayim says that the Gemara asked incredulously, does Kilai ha'Kerem apply (mid'Oraisa) only with hemp and Luf, but all other species are mid'Rabanan?! Surely, they are mid'Oraisa when one person owns the vineyard and the Zera'im! Here the vines are permitted because one cannot forbid another's property. Chachamim fined, i.e. against the one who transgressed.

Tosfos (Shabbos 27b DH Kol): One may light Ner Shabbos with hemp, for it does not come from a tree. Menachos 15b shows that it is a kind of Zera'im.

Poskim

Shulchan Aruch (YD 296:1): One who plants two kinds of grain or two kinds of Yerek with seeds of a vineyard is lashed twice, for "Sadcha Lo Sizra Kilayim" and "Lo Sizra Karmecha Kilayim." One is liable mid'Oraisa only for hemp and Luf and similar Zera'im that finish with the yield of the vineyard. Other Zera'im are forbidden only mid'Rabanan.

Shulchan Aruch (2): We forbid due to Kil'ai ha'Kerem only kinds of grain or Yerek. Other Zera'im may be planted in a vineyard, and all the more so other trees.

Gra (7): If it is not b'Mapoles Yad (seeded near each other), even R. Yonason, who argues with R. Yoshiyah (who forbids only two diverse species mixed with a grape seed, b'Mapoles Yad), permits other Zera'im. A Tosefta says 'all of them are Kil'ai ha'Kerem, except for trees.' This is surely wrong. The Ra'avad holds that we exclude only species that people do not grow. The Rambam's text (3:15) lists many species that are not Kil'ayim, and concludes 'whatever produces leaves from its root, it is Yerek. Whatever does not produce leaves from its root, it is a tree.' We need not say that it is not Kil'ayim. Many Mishnayos teach that Kil'ayim applies to Yerek and grain.