I know this might be touchy, and certain people have strong and/or well founded opinions, so let me start with where my question comes from. I'm a graduate mathematics student, and we have a shared vocabulary with many fields of science, and the layman for that matter, but we use them in more specifically defined ways. For example, homogenized. In mathematics, it's where all terms are of the same power, ex. a^2 + b^2 = c^2. If I were to divide by c^2, it would be called dehomoginizing, leading to x^2 + y^2 = 1, where x = a/c and y = b/c.

That being said, if I'm unable to find mathematical terms already in use in Esperanto, what would be the best way to generate or create new words? Mash together roots that expresses the meaning, mash together roots that come up with a word that closely matches an English equivalent, or create a new root?

Note, in mathematics, it is common for the author to create a new word, or use a word in a new context, if they provide a definition for it. You can look at Euclid's Elements to see how the concept of a point, line, intersect... were defined before being utilized in the subsequent proofs.

Perhaps you would be interested in this or that.

When in doubt, you can probably use the esperanto system of joining morphemes to get your word. You may wish to make things a little clearer the first time in a text by adding something like, 'matematika..' i.e. 'matematika homogena...'

AmericanBull:I know this might be touchy, and certain people have strong and/or well founded opinions, so let me start with where my question comes from. I'm a graduate mathematics student, and we have a shared vocabulary with many fields of science, and the layman for that matter, but we use them in more specifically defined ways. For example, homogenized. In mathematics, it's where all terms are of the same power, ex. a^2 + b^2 = c^2. If I were to divide by c^2, it would be called dehomoginizing, leading to x^2 + y^2 = 1, where x = a/c and y = b/c.

That being said, if I'm unable to find mathematical terms already in use in Esperanto, what would be the best way to generate or create new words? Mash together roots that expresses the meaning, mash together roots that come up with a word that closely matches an English equivalent, or create a new root?

Note, in mathematics, it is common for the author to create a new word, or use a word in a new context, if they provide a definition for it. You can look at Euclid's Elements to see how the concept of a point, line, intersect... were defined before being utilized in the subsequent proofs.

It is very easy in Esperanto. You don't need to create a new word. You just use the prefixes and suffixes to convey the desired meaning as usual in Esperanto.

For instance:

homogeneous = homogena
homogenize = make homogeneus = homogenigi
dehomoginizing = make not homogeneus = malhomogenigi (or malhomogenigo/malhomogenigado as a gerund)

When you create a brand new word, you must make others to understand it. It is much better if they could use words they already knew.

Amike: Grzesiek

Technical vocabulary in Esperanto is less problematic than it might at first sight seem.

Firstly, many such terms are common to the European languages, and with the appropriate changes may be immediately adopted into Esperanto under rule 15 (international words).

Secondly, it may well be that there is an obvious solution by combining well-known roots eg retumilo for an internet browser.

Thirdly Esperanto has been around long enough for specialist terminaroj to have been developed - many of which are multi-lingual, so that your can quickly judge whether the proposed solution is an arbitrary elpensitajxo of the author or likely to be readily accepted.

(I would be surprised to find that there is only one matematika terminaro in existence. I would expect several to have been produced over Esperanto's long history.)

In short, although there maybe a dearth of technical and scientific literature in Esperanto, you may find yourself remarkably well-equipped to author your own contribution in your specialist field.

homogeneous = homogena
homogenize = make homogeneus = homogenigi
dehomoginizing = make not homogeneus = malhomogenigi (or malhomogenigo/malhomogenigado as a gerund); malhomeniganta
(de)homogenized = (mal)homogenigita
being (de)homogenized = (mal)homogenigata
and so on

As you can see from one root you can easily create the whole word family.

The word "homogena" was introduced by Zamenhof and it is used also in mathematical sense:

homogen/a Z
1 Tia, ke ĉiuj ĝiaj partoj havas la saman konsiston, la samajn ecojn: homogena miksaĵo, pasto, loĝantaro, taĉmento; la homogeneco de fandaĵo. ☞ heterogena.
2 (pp polinomo) Tia, ke ĉiuj ĝiaj termoj estas samgradaj.
3 (pp ekvacio) Tia, ke ĝia konstanta termo nulas: al la nehomogena ekvacio 2x + 3y = 5 respondas la homogena ekvacio 2x + 3y = 0.
homogenigi. Fari ion homogena: homogenigi bakterian likvon.

There are a lot of Esperanto math people, I would try to get in touch with such a person and look at a math glossary before considering taking one of the options mentioned above for inventing your own term.