【摘要】 证明了Gauss整数环Z[i]中非零元素在映射φ的作用下的最小值的原像α0~1,由此给出了求Z[i]中元素最大公因子的两种方法:辗转相除法和矩阵的广义初等变换法.更多还原

【Abstract】 We proved α0~1,where α0 is preimage of nonzero elements in Z[i],and image of this nonzero elements under φ is equal to minimum value.Two methods of calculating greatest common factor of elements in Z[i] were given,that is division algorithm and generalized elementary transformation of matrix.更多还原