The difference between Algebraic integer and Phi
When used as nouns, algebraic integer means a real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers, whereas phi means φ, the 21st letter of the euclidean and modern greek alphabet, usually romanized as "ph".
check bellow for the other definitions of Algebraic integer and Phi
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Algebraic integer as a noun (algebra, number theory):
A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
Examples:
"A Gaussian integer <math> z = a + i b </math> is an [[algebraic integer]] since it is a solution of either the equation <math> z^2 + (-2 a) z + (a^2 + b^2) = 0 </math> or the equation <math> z - a = 0 </math>."
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Phi as a noun:
Φ, the 21st letter of the Euclidean and modern Greek alphabet, usually romanized as "ph".
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Phi as a noun (mathematics):
The golden ratio.
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Phi as a noun:
A visual illusion whereby a sequential pattern of lights produces a false sense of motion.