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The phrase "after composition of" is correct and usable in written English.
It can be used in contexts where you are referring to the completion of a written work or document, such as a report, essay, or piece of music.
Example: "After composition of the final report, the team submitted it for review."
Alternatives: "following the creation of" or "subsequent to the drafting of".
Exact(2)
After composition of transforms, the functional data were resampled in one step to 3 mm isotropic voxels.
Recently, preliminary results of a study have been presented in which the Bruker system correctly recognized C. difficile PCR ribotypes 027 and 078 after composition of a new database encompassing at least ten spectra of each type [ 6].
Similar(56)
Today, novelists writing a hundred years after the composition of Ulysses still write in the shadow of this extraordinary achievement.
The greatest thing about Pepys, after the composition of the diary, was his decision to preserve it.
He said longer-term leadership would probably be selected next year, after the composition of a larger government, now under negotiation, was decided.
Sibelius began to write works for male-voice chorus in the mid-1890s, afthe the composition of his programme symphony with chorus, Kullervo, and before the completion of his purely orchestral First Symphony.
After the composition of Shakespeare's last tragedies — the opulent, spacious "Antony and Cleopatra" (1606-1607), the cold, rhetorically contorted "Coriolanus" (1607-08), and the rough-hewn, one-note "Timon of Athens" (1607-08) — there is a slackening, as if something had snapped.
Since The Pilgrim's Progress was published soon after this, in February 1678, it is probable that he had begun to write it not in the second imprisonment but in the first, soon after the composition of Grace Abounding, and when the examination of his inner life contained in that book was still strong.
The Doctrines of the Philosophers may have been a text that was initially unconnected to the Incoherence or that was generated after the composition of the latter.
This attribution is clearly a hoax; in fact the only thing we know about the circumstances under which the work was composed is that it must have been before 1366, when the earliest manuscript is dated, and after the composition of Eustratios' commentary, on which it draws.
The iconic (though fictional) scene of Martin Luther nailing his Ninety-Five Theses to the church door until October 31, 1517, over a millennium after the composition of the Vulgate.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com