query: Why don't quaternions contradict the Fundamental Theorem of Algebra?
positive_passages.docid: 21743
positive_passages.text: Why are the solutions of polynomial equations so unconstrained over the quaternions?
negative_passages.docid: 49503
negative_passages.text: Why does the natural quotient metric works in this case?
negative_passages.docid: 152451
negative_passages.text: REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
negative_passages.docid: 57105
negative_passages.text: Probs. 12 & 13 , Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Existence of only right-sided identity and right-sided inverses suffice
negative_passages.docid: 105147
negative_passages.text: Converting a quaternion in a right to left handed coordinate system
negative_passages.docid: 26698
negative_passages.text: Math beyond Quaternions
negative_passages.docid: 81480
negative_passages.text: What is wrong with this deduction to show that within a multiplet different state has different square angular momentum?
negative_passages.docid: 41572
negative_passages.text: $G/Z$ cannot be isomorphic to quaternion group
negative_passages.docid: 46378
negative_passages.text: Trig substitution; why can we ignore the absolute value?
negative_passages.docid: 18465
negative_passages.text: Sum and product of two transcendental numbers can't be both algebraic
negative_passages.docid: 74244
negative_passages.text: Converting a rotation matrix to a quaternion
negative_passages.docid: 43178
negative_passages.text: Why can't prime numbers satisfy the Pythagoras Theorem? That is, why can't a set of 3 prime numbers be a Pythagorean triplet?
negative_passages.docid: 155120
negative_passages.text: Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?
negative_passages.docid: 118577
negative_passages.text: Fallacious proof involving trigonometry
negative_passages.docid: 35509
negative_passages.text: Noether's Theorem: Lie groups vs. Lie algebras; finite vs. infinitesimal symmetries
negative_passages.docid: 150320
negative_passages.text: Why does $a^{b}·a^{c}=a^{b+c}$?
negative_passages.docid: 41943
negative_passages.text: Why is it that when proving trig identities, one must work both sides independently?