Obravnavamo polinome v nekomutirajočih spremenljivkah, ki dovoljujejo vsoto hermitskih kvadratov in komutatorske dekompozicije. Spomnimo na algoritme za iskanje dekompozicij tega tipa, osnovanih na ...semidefinitnem programiranju. Glavni del članka preučuje, kako najti takšne dekompozicije z racionalnimi koeficienti, če ima tudi prvotni polinom racionalne koeficiente. Pokažemo, da lahko s pomočjo numeričnih kazalcev, dobljenih z uporabo Gramove matrike in semidefinitnim programiranjem, kar je ponavadi bolj ali manj izvedljivo, pogosto pridobimo eksakten certifikat z uporabo racionalnih števil. Pri Slaterjevih točkah se da uporabiti Peyrl-Parrilovo zaokrožanje in projektne metode. Po drugi strani, kadar nimamo stroge izvedljivosti, sibility, predlagamo varianto redukcije lic, s katero reduciramo velikost semidefinitnega programa in vsilimo eksistenco Slaterjevih točk. Vse te metode so implementirane na našem odprtokodnem paketu računske algebre NCSOStools. V samem članku predstavimo številne izdelane primere, ki ponazarjajo naše rezultate.
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