query: $F = \langle yz-2xy^2, axz-2x^2y+z, xy+y \rangle$
positive_passages.docid: 156952
positive_passages.text: Vector Field Conceptual Question
negative_passages.docid: 122213
negative_passages.text: Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 139436
negative_passages.text: Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
negative_passages.docid: 147671
negative_passages.text: Find all ideals of $\mathbb R[x] / \langle x^2-3x+2\rangle$
negative_passages.docid: 25633
negative_passages.text: Is the function $f(z)=xy+iy$ analytic?
negative_passages.docid: 66772
negative_passages.text: $f(f(x)f(y))+f(x+y)=f(xy)$
negative_passages.docid: 146690
negative_passages.text: Basis for adjoint representation of $sl(2,F)$
negative_passages.docid: 41226
negative_passages.text: Find $f:f(xf(x)+f(y))=f(x)^2+y$
negative_passages.docid: 145279
negative_passages.text: Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$?
negative_passages.docid: 61539
negative_passages.text: proof for a basis in $L^2$
negative_passages.docid: 48498
negative_passages.text: Fourier coefficients $\langle x,e_k\rangle$ are at countable
negative_passages.docid: 102871
negative_passages.text: $\langle r\rangle$ maximal $\iff r$ irreducible
negative_passages.docid: 9223
negative_passages.text: Finding $\iiint_K (x^2 -z^2)\, dx\, dy \,dz$
negative_passages.docid: 12698
negative_passages.text: Orthonormal basis for $\mathcal{L}^2([0,1])$
negative_passages.docid: 111248
negative_passages.text: The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
negative_passages.docid: 60946
negative_passages.text: Find the matrix of $\langle f, g \rangle = \displaystyle\int_0^1 f(t) g(t) \, \mathrm dt$ with respect to the basis $\{1,t,\dots,t^n\}$