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Discover Ludwig'have purchased' is correct and usable in written English.
You can use it when expressing the idea of having bought something in the past. Example: I have purchased the new house down the street.
Exact(60)
"They have purchased that.
Other holders have purchased them.
Also, 15 Argentines have purchased plots.
Sarah is dressed in ribbons that I have purchased new.
Many hedge funds have purchased securities backed by mortgages.
The libraries have purchased 1,000 paperback copies.
You have purchased a twelve month Shelf Improvement fiction package.
Normally that would have purchased name-above-the-title rights.
You have purchased a twelve month Shelf Improvement mixed package.
Recently they have purchased companies internationally to expand their reach.
He claimed to have purchased one, if I remember.
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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