query: Algebraic Manipulations
positive_passages.docid: 26287
positive_passages.text: Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
negative_passages.docid: 9118
negative_passages.text: Polynomial division: an obvious trick? [reducing mod $\textit{simpler}$ multiples]
negative_passages.docid: 83363
negative_passages.text: Finding the real root of a cubic algebraically
negative_passages.docid: 77424
negative_passages.text: Reference for Algebraic Geometry
negative_passages.docid: 28109
negative_passages.text: Conjectural closed-form representations of sums, products or integrals
negative_passages.docid: 158511
negative_passages.text: "Non-linear" algebra
negative_passages.docid: 74058
negative_passages.text: Sums and products of algebraic numbers
negative_passages.docid: 17584
negative_passages.text: Integer matrices with integer inverses
negative_passages.docid: 80295
negative_passages.text: Field extensions and algebraic/transcendental elements
negative_passages.docid: 148310
negative_passages.text: Showing rational numbers are algebraic
negative_passages.docid: 76892
negative_passages.text: Factoring inequalities on Double Summation (Donald Knuth's Concrete Mathematics)
negative_passages.docid: 107281
negative_passages.text: Proof of Existence of Algebraic Closure: Too simple to be true?
negative_passages.docid: 127664
negative_passages.text: Inverse elements in the absence of identities/associativity.
negative_passages.docid: 30045
negative_passages.text: Solving linear congruences by hand: modular fractions and inverses
negative_passages.docid: 103654
negative_passages.text: A finite field extension that is not simple
negative_passages.docid: 133295
negative_passages.text: How to solve this set of symmetric polynomial expressions
negative_passages.docid: 59898
negative_passages.text: Elementary manipulation with elements of group