''v'' ''s'' ''s'' called ''algebraic set'' ''v'' stands ''variety'' specific type algebraic set defined given subset ''u'' '''a''' sup ''n'' sup one recover set polynomials generate ''u'' ''any'' subset '''a''' sup ''n'' sup define ''i'' ''u'' set polynomials whose vanishing set contains ''u'' ''i'' stands ideal two polynomials ''f'' ''g'' vanish ''u'' ''f'' ''g'' vanishes ''u'' ''h'' polynomial ''hf'' vanishes ''u'' ''i'' ''u'' always ideal
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