Update queryExtension.ts

zenyanbo · Nov 5, 2024 · ae55b7d · ae55b7d
1 parent e91e49f
commit ae55b7d
Showing 1 changed file with 3 additions and 13 deletions.
diff --git a/packages/service/core/ai/functions/queryExtension.ts b/packages/service/core/ai/functions/queryExtension.ts
@@ -31,19 +31,9 @@ The output is only a standard list consist of alternative natural language descr
 <QUERY>如何从 $SO(3)$ 群推导得到CG系数？</QUERY>
 Reformulation list: ["Explain how to derive Clebsch-Gordan coefficients step by step using the representation theory of the $SO(3)$ group, focusing on the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations.", "Describe the procedure for calculating Clebsch-Gordan coefficients by considering the angular momentum addition of two quantum mechanical systems and exploiting the properties of the angular momentum operators and their eigenstates.", "Derive the Clebsch-Gordan coefficients for the coupling of two angular momenta $j_1$ and $j_2$ by constructing the coupled angular momentum states $|j, m\rangle$ as linear combinations of the uncoupled states $|j_1, m_1\rangle |j_2, m_2\rangle$ using the ladder operators and orthogonality relations.", "Illustrate the derivation of Clebsch-Gordan coefficients through the use of the Wigner-Eckart theorem and the properties of the Wigner 3j-symbols, emphasizing the connection between the $SO(3)$ group and the quantum theory of angular momentum."]
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-<HISTORY>Kerr geodesics describe the paths of free-falling particles around rotating black holes in Einstein's theory of general relativity. Unlike geodesics around non-rotating black holes, they are generally non-planar and non-periodic due to the black hole's spin.
-
-Key Properties:
-Constants of motion: Due to the symmetry of spacetime, Kerr geodesics possess energy, axial angular momentum, and a Carter constant, making them integrable (analytically solvable).
-Innermost Stable Circular Orbit (ISCO): Similar to non-rotating black holes, there's a minimum radius for stable circular orbits.
-Mathematical Description:  Can be expressed in various forms, including second-order and first-order seperable differential equations, and action-angle variables.
-
-Applications:
-Extreme Mass Ratio Inspirals (EMRIs): Modeling the inspiral of smaller objects into supermassive black holes for gravitational wave detection.
-Accretion Disks: Understanding the motion of matter around black holes.
-Tests of General Relativity: Precise observations of EMRIs can verify Einstein's theory in strong gravitational fields.</HISTORY>
+<HISTORY>The Kerr spacetime is a stationary, axisymmetric, and asymptotically flat solution to the Einstein field equations, describing the spacetime geometry around a rotating black hole. (... The remaining content is omitted ...)</HISTORY>
 <QUERY>Introduce Kerr geodesic in detail. Note that the more detailed the better, generating reports of more than 4K words.</QUERY>
-Reformulation list: ["Review Kerr geodesic from Kerr metric and its symmetry, geodesic constants of motion and seperable Kerr geodesic equation, as well as its analytical solutions.","Analyze the orbital dynamics and properties of 'bound Kerr geodesic' from Kerr geodesic equations.","Discuss the properties of bound Kerr geodesic oscillations and introduce 'action-angle formalism'."]
+Reformulation list: ["Comprehensive explain (bound) Kerr geodesics, derived from the separable Kerr geodesic equation and its constants of motion (including the Carter constant, energy, and angular momentum). The analysis should encompass analytical solutions in terms of elliptic integrals, orbital dynamics properties (radial and polar oscillations, geometry/shape, etc), an introduction to the action-angle formalism in the context of Hamiltonian mechanics, and its application.", "Comprehensive explain (bound) Kerr geodesics, derived from the separable Kerr geodesic equation and its constants of motion (including the Carter constant, energy, and angular momentum). The analysis should encompass analytical solutions in terms of elliptic integrals, orbital dynamics properties (radial and polar oscillations, geometry/shape, etc), an introduction to the action-angle formalism in the context of Hamiltonian mechanics, and its application.", "Based geodesic equations, discuss the properties of unbound Kerr geodesics, including their orbital dynamics, scattering, and gravitational lensing effects. Illustrate the role of unbound Kerr geodesics in astrophysical contexts.", "Describe the applications of Kerr geodesics. Such as EMRI waveform modeling, the analysis of accretion disks/relativistic jets/gravitational lensing."]
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 <HISTORY></HISTORY>
 <QUERY>Solve the following differential equation: $\\frac{dy}{dx} + 2y = e^{-x}$</QUERY>
@@ -71,7 +61,7 @@ Reformulation list: ["Comprehensively outline General Relativity, including its
 Reformulation list: ["Determine the eigenvalues of the matrix $A = \\begin{pmatrix} 2 & 1 \\\\ -1 & 2 \\end{pmatrix}$ by solving the characteristic equation $|A - \\lambda I| = 0$, where $\\lambda$ represents the eigenvalues and $I$ is the identity matrix. Then, for each eigenvalue $\\lambda$, find the corresponding eigenvectors by solving the equation $(A - \\lambda I)v = 0$, where $v$ is the eigenvector.", "Calculate the eigenvalues and eigenvectors of the matrix $A = \\begin{pmatrix} 2 & 1 \\\\ -1 & 2 \\end{pmatrix}$ by diagonalizing the matrix.  Find a matrix $P$ such that $P^{-1}AP$ is a diagonal matrix, where the diagonal entries are the eigenvalues and the columns of $P$ are the corresponding eigenvectors."]
 
 # NOTES
-- Ensure alternative reformulations capture the core meaning and critical details of the query without diverting from the original intent. Therefore, pay attention to the following two points. 1. Exercise caution when generating reformulations for narrow and well-defined queries to avoid introducing unnecessary specificity. 2. Filter out reformulations that are too vague, ambiguous, or unrelated to the original query.
+- Reformulations should merely be a further refinement and extension of original QUERY and HISTORY (from different hierachy, angles, and paths). Ensure alternative reformulations capture the core meaning and critical details of the query without diverting from the original intent. Therefore, pay attention to the following two points. 1. Exercise caution when generating reformulations for narrow and well-defined queries to avoid introducing unnecessary specificity. 2. Filter out reformulations that are too vague, ambiguous, or deviate from the original query.
 - Alternative reformulations MUST be CORRECT, REASONABLE, CONSISTENT, INSIGHTFUL and VALUABLE.
 - Generally, it is enough to generate about 3 iterms in the output list, or less, but the maximum number should not exceed 6 iterms.
 - Each reformulation should be context-independent, semantically complete and self-contained.