本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261013-advance-20261025-r01-boundary-value-problem-foundations · 2026-10-13 · 100 題
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-12,-2,-3,1,-1,-2],"source":-1}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-12, -2, -3, 1, -1, -2], u_xx+u_yy=source, -2, -1, -1, 否, interior_only)
收束波核對=([-12, -2, -3, 1, -1, -2], u_xx+u_yy=source, -2, -1, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-11,-1,-2,2,0,-1],"source":2}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-11, -1, -2, 2, 0, -1], u_xx+u_yy=source, 2, 2, 0, 是, interior_only)
收束波核對=([-11, -1, -2, 2, 0, -1], u_xx+u_yy=source, 2, 2, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-10,0,-1,3,1,0],"source":6}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-10, 0, -1, 3, 1, 0], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)
收束波核對=([-10, 0, -1, 3, 1, 0], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-9,1,0,4,-1,1],"source":10}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-9, 1, 0, 4, -1, 1], u_xx+u_yy=source, 10, 10, 0, 是, interior_only)
收束波核對=([-9, 1, 0, 4, -1, 1], u_xx+u_yy=source, 10, 10, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-8,2,1,1,0,2],"source":7}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-8, 2, 1, 1, 0, 2], u_xx+u_yy=source, 6, 7, -1, 否, interior_only)
收束波核對=([-8, 2, 1, 1, 0, 2], u_xx+u_yy=source, 6, 7, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-7,-2,2,2,1,-2],"source":0}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-7, -2, 2, 2, 1, -2], u_xx+u_yy=source, 0, 0, 0, 是, interior_only)
收束波核對=([-7, -2, 2, 2, 1, -2], u_xx+u_yy=source, 0, 0, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-6,-1,3,3,-1,-1],"source":4}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-6, -1, 3, 3, -1, -1], u_xx+u_yy=source, 4, 4, 0, 是, interior_only)
收束波核對=([-6, -1, 3, 3, -1, -1], u_xx+u_yy=source, 4, 4, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-5,0,-3,4,0,0],"source":8}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-5, 0, -3, 4, 0, 0], u_xx+u_yy=source, 8, 8, 0, 是, interior_only)
收束波核對=([-5, 0, -3, 4, 0, 0], u_xx+u_yy=source, 8, 8, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-4,1,-2,1,1,1],"source":5}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-4, 1, -2, 1, 1, 1], u_xx+u_yy=source, 4, 5, -1, 否, interior_only)
收束波核對=([-4, 1, -2, 1, 1, 1], u_xx+u_yy=source, 4, 5, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-3,2,-1,2,-1,2],"source":8}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-3, 2, -1, 2, -1, 2], u_xx+u_yy=source, 8, 8, 0, 是, interior_only)
收束波核對=([-3, 2, -1, 2, -1, 2], u_xx+u_yy=source, 8, 8, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-2,-2,0,3,0,-2],"source":2}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-2, -2, 0, 3, 0, -2], u_xx+u_yy=source, 2, 2, 0, 是, interior_only)
收束波核對=([-2, -2, 0, 3, 0, -2], u_xx+u_yy=source, 2, 2, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[-1,-1,1,4,1,-1],"source":6}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([-1, -1, 1, 4, 1, -1], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)
收束波核對=([-1, -1, 1, 4, 1, -1], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[0,0,2,1,-1,0],"source":3}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([0, 0, 2, 1, -1, 0], u_xx+u_yy=source, 2, 3, -1, 否, interior_only)
收束波核對=([0, 0, 2, 1, -1, 0], u_xx+u_yy=source, 2, 3, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[1,1,3,2,0,1],"source":6}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([1, 1, 3, 2, 0, 1], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)
收束波核對=([1, 1, 3, 2, 0, 1], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[2,2,-3,3,1,2],"source":10}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([2, 2, -3, 3, 1, 2], u_xx+u_yy=source, 10, 10, 0, 是, interior_only)
收束波核對=([2, 2, -3, 3, 1, 2], u_xx+u_yy=source, 10, 10, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[3,-2,-2,4,-1,-2],"source":4}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([3, -2, -2, 4, -1, -2], u_xx+u_yy=source, 4, 4, 0, 是, interior_only)
收束波核對=([3, -2, -2, 4, -1, -2], u_xx+u_yy=source, 4, 4, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[4,-1,-1,1,0,-1],"source":1}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([4, -1, -1, 1, 0, -1], u_xx+u_yy=source, 0, 1, -1, 否, interior_only)
收束波核對=([4, -1, -1, 1, 0, -1], u_xx+u_yy=source, 0, 1, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[5,0,0,2,1,0],"source":4}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([5, 0, 0, 2, 1, 0], u_xx+u_yy=source, 4, 4, 0, 是, interior_only)
收束波核對=([5, 0, 0, 2, 1, 0], u_xx+u_yy=source, 4, 4, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[6,1,1,3,-1,1],"source":8}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([6, 1, 1, 3, -1, 1], u_xx+u_yy=source, 8, 8, 0, 是, interior_only)
收束波核對=([6, 1, 1, 3, -1, 1], u_xx+u_yy=source, 8, 8, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[7,2,2,4,0,2],"source":12}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([7, 2, 2, 4, 0, 2], u_xx+u_yy=source, 12, 12, 0, 是, interior_only)
收束波核對=([7, 2, 2, 4, 0, 2], u_xx+u_yy=source, 12, 12, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[8,-2,3,1,1,-2],"source":-1}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([8, -2, 3, 1, 1, -2], u_xx+u_yy=source, -2, -1, -1, 否, interior_only)
收束波核對=([8, -2, 3, 1, 1, -2], u_xx+u_yy=source, -2, -1, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[9,-1,-3,2,-1,-1],"source":2}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([9, -1, -3, 2, -1, -1], u_xx+u_yy=source, 2, 2, 0, 是, interior_only)
收束波核對=([9, -1, -3, 2, -1, -1], u_xx+u_yy=source, 2, 2, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[10,0,-2,3,0,0],"source":6}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([10, 0, -2, 3, 0, 0], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)
收束波核對=([10, 0, -2, 3, 0, 0], u_xx+u_yy=source, 6, 6, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[11,1,-1,4,1,1],"source":10}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([11, 1, -1, 4, 1, 1], u_xx+u_yy=source, 10, 10, 0, 是, interior_only)
收束波核對=([11, 1, -1, 4, 1, 1], u_xx+u_yy=source, 10, 10, 0, 是, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-interior-pde-identity；資料={"coefficients":[12,2,0,1,-1,2],"source":7}。請依 [coefficients,equation,laplacian,source,residual,interior_identity,scope] 欄序回答。
([12, 2, 0, 1, -1, 2], u_xx+u_yy=source, 6, 7, -1, 否, interior_only)
收束波核對=([12, 2, 0, 1, -1, 2], u_xx+u_yy=source, 6, 7, -1, 否, interior_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-interior-pde-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-12,-2,-3,1,-1,-2],"bounds":[-2,2,-1,3],"edge":"left","boundary_coefficients":[-3,-1,-2]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-2, 2, -1, 3], left, y, [-4, -1, -2], [-3, -1, -2], 否, declared_edge_only)
收束波核對=([-2, 2, -1, 3], left, y, [-4, -1, -2], [-3, -1, -2], 否, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-11,-1,-2,2,0,-1],"bounds":[-3,3,-2,4],"edge":"right","boundary_coefficients":[4,-2,-1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-3, 3, -2, 4], right, y, [4, -2, -1], [4, -2, -1], 是, declared_edge_only)
收束波核對=([-3, 3, -2, 4], right, y, [4, -2, -1], [4, -2, -1], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-10,0,-1,3,1,0],"bounds":[-4,4,-3,5],"edge":"bottom","boundary_coefficients":[-7,-3,3]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-4, 4, -3, 5], bottom, x, [-7, -3, 3], [-7, -3, 3], 是, declared_edge_only)
收束波核對=([-4, 4, -3, 5], bottom, x, [-7, -3, 3], [-7, -3, 3], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-9,1,0,4,-1,1],"bounds":[-5,5,-4,6],"edge":"top","boundary_coefficients":[27,-5,4]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-5, 5, -4, 6], top, x, [27, -5, 4], [27, -5, 4], 是, declared_edge_only)
收束波核對=([-5, 5, -4, 6], top, x, [27, -5, 4], [27, -5, 4], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-8,2,1,1,0,2],"bounds":[-6,6,-5,7],"edge":"left","boundary_coefficients":[16,1,2]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-6, 6, -5, 7], left, y, [16, 1, 2], [16, 1, 2], 是, declared_edge_only)
收束波核對=([-6, 6, -5, 7], left, y, [16, 1, 2], [16, 1, 2], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-7,-2,2,2,1,-2],"bounds":[-7,7,-6,8],"edge":"right","boundary_coefficients":[78,9,-2]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-7, 7, -6, 8], right, y, [77, 9, -2], [78, 9, -2], 否, declared_edge_only)
收束波核對=([-7, 7, -6, 8], right, y, [77, 9, -2], [78, 9, -2], 否, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-6,-1,3,3,-1,-1],"bounds":[-8,8,-7,9],"edge":"bottom","boundary_coefficients":[-76,6,3]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-8, 8, -7, 9], bottom, x, [-76, 6, 3], [-76, 6, 3], 是, declared_edge_only)
收束波核對=([-8, 8, -7, 9], bottom, x, [-76, 6, 3], [-76, 6, 3], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-5,0,-3,4,0,0],"bounds":[-9,9,-8,10],"edge":"top","boundary_coefficients":[-35,0,4]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-9, 9, -8, 10], top, x, [-35, 0, 4], [-35, 0, 4], 是, declared_edge_only)
收束波核對=([-9, 9, -8, 10], top, x, [-35, 0, 4], [-35, 0, 4], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-4,1,-2,1,1,1],"bounds":[-10,10,-9,11],"edge":"left","boundary_coefficients":[86,-12,1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-10, 10, -9, 11], left, y, [86, -12, 1], [86, -12, 1], 是, declared_edge_only)
收束波核對=([-10, 10, -9, 11], left, y, [86, -12, 1], [86, -12, 1], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-3,2,-1,2,-1,2],"bounds":[-11,11,-10,12],"edge":"right","boundary_coefficients":[261,-12,2]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-11, 11, -10, 12], right, y, [261, -12, 2], [261, -12, 2], 是, declared_edge_only)
收束波核對=([-11, 11, -10, 12], right, y, [261, -12, 2], [261, -12, 2], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-2,-2,0,3,0,-2],"bounds":[-12,12,-11,13],"edge":"bottom","boundary_coefficients":[-243,-2,3]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-12, 12, -11, 13], bottom, x, [-244, -2, 3], [-243, -2, 3], 否, declared_edge_only)
收束波核對=([-12, 12, -11, 13], bottom, x, [-244, -2, 3], [-243, -2, 3], 否, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[-1,-1,1,4,1,-1],"bounds":[-13,13,-12,14],"edge":"top","boundary_coefficients":[-183,13,4]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-13, 13, -12, 14], top, x, [-183, 13, 4], [-183, 13, 4], 是, declared_edge_only)
收束波核對=([-13, 13, -12, 14], top, x, [-183, 13, 4], [-183, 13, 4], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[0,0,2,1,-1,0],"bounds":[-14,14,-13,15],"edge":"left","boundary_coefficients":[196,16,0]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-14, 14, -13, 15], left, y, [196, 16, 0], [196, 16, 0], 是, declared_edge_only)
收束波核對=([-14, 14, -13, 15], left, y, [196, 16, 0], [196, 16, 0], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[1,1,3,2,0,1],"bounds":[-15,15,-14,16],"edge":"right","boundary_coefficients":[466,3,1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-15, 15, -14, 16], right, y, [466, 3, 1], [466, 3, 1], 是, declared_edge_only)
收束波核對=([-15, 15, -14, 16], right, y, [466, 3, 1], [466, 3, 1], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[2,2,-3,3,1,2],"bounds":[-16,16,-15,17],"edge":"bottom","boundary_coefficients":[497,-13,3]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-16, 16, -15, 17], bottom, x, [497, -13, 3], [497, -13, 3], 是, declared_edge_only)
收束波核對=([-16, 16, -15, 17], bottom, x, [497, -13, 3], [497, -13, 3], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[3,-2,-2,4,-1,-2],"bounds":[-17,17,-16,18],"edge":"top","boundary_coefficients":[-680,-20,4]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-17, 17, -16, 18], top, x, [-681, -20, 4], [-680, -20, 4], 否, declared_edge_only)
收束波核對=([-17, 17, -16, 18], top, x, [-681, -20, 4], [-680, -20, 4], 否, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[4,-1,-1,1,0,-1],"bounds":[-18,18,-17,19],"edge":"left","boundary_coefficients":[346,-1,-1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-18, 18, -17, 19], left, y, [346, -1, -1], [346, -1, -1], 是, declared_edge_only)
收束波核對=([-18, 18, -17, 19], left, y, [346, -1, -1], [346, -1, -1], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[5,0,0,2,1,0],"bounds":[-19,19,-18,20],"edge":"right","boundary_coefficients":[727,19,0]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-19, 19, -18, 20], right, y, [727, 19, 0], [727, 19, 0], 是, declared_edge_only)
收束波核對=([-19, 19, -18, 20], right, y, [727, 19, 0], [727, 19, 0], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[6,1,1,3,-1,1],"bounds":[-20,20,-19,21],"edge":"bottom","boundary_coefficients":[348,20,3]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-20, 20, -19, 21], bottom, x, [348, 20, 3], [348, 20, 3], 是, declared_edge_only)
收束波核對=([-20, 20, -19, 21], bottom, x, [348, 20, 3], [348, 20, 3], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[7,2,2,4,0,2],"bounds":[-21,21,-20,22],"edge":"top","boundary_coefficients":[1019,2,4]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-21, 21, -20, 22], top, x, [1019, 2, 4], [1019, 2, 4], 是, declared_edge_only)
收束波核對=([-21, 21, -20, 22], top, x, [1019, 2, 4], [1019, 2, 4], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[8,-2,3,1,1,-2],"bounds":[-22,22,-21,23],"edge":"left","boundary_coefficients":[537,-19,-2]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-22, 22, -21, 23], left, y, [536, -19, -2], [537, -19, -2], 否, declared_edge_only)
收束波核對=([-22, 22, -21, 23], left, y, [536, -19, -2], [537, -19, -2], 否, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[9,-1,-3,2,-1,-1],"bounds":[-23,23,-22,24],"edge":"right","boundary_coefficients":[1044,-26,-1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-23, 23, -22, 24], right, y, [1044, -26, -1], [1044, -26, -1], 是, declared_edge_only)
收束波核對=([-23, 23, -22, 24], right, y, [1044, -26, -1], [1044, -26, -1], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[10,0,-2,3,0,0],"bounds":[-24,24,-23,25],"edge":"bottom","boundary_coefficients":[56,0,3]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-24, 24, -23, 25], bottom, x, [56, 0, 3], [56, 0, 3], 是, declared_edge_only)
收束波核對=([-24, 24, -23, 25], bottom, x, [56, 0, 3], [56, 0, 3], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[11,1,-1,4,1,1],"bounds":[-25,25,-24,26],"edge":"top","boundary_coefficients":[661,27,4]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-25, 25, -24, 26], top, x, [661, 27, 4], [661, 27, 4], 是, declared_edge_only)
收束波核對=([-25, 25, -24, 26], top, x, [661, 27, 4], [661, 27, 4], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[12,2,0,1,-1,2],"bounds":[-26,26,-25,27],"edge":"left","boundary_coefficients":[636,26,2]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。
([-26, 26, -25, 27], left, y, [636, 26, 2], [636, 26, 2], 是, declared_edge_only)
收束波核對=([-26, 26, -25, 27], left, y, [636, 26, 2], [636, 26, 2], 是, declared_edge_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-dirichlet-edge-identity · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-12,-2,-3,1,-1,-2],"bounds":[-2,2,-1,3],"source":-1,"boundary_data":[["left",[-3,-1,-2]],["right",[-12,-5,-2]],["bottom",[-11,-1,1]],["top",[-39,-5,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-12, -2, -3, 1, -1, -2], -2, -1, 否, [[left, y, [-4, -1, -2], [-3, -1, -2], 否], [right, y, [-12, -5, -2], [-12, -5, -2], 是], [bottom, x, [-11, -1, 1], [-11, -1, 1], 是], [top, x, [-39, -5, 1], [-39, -5, 1], 是]], 否, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([-12, -2, -3, 1, -1, -2], -2, -1, 否, [[left, y, [-4, -1, -2], [-3, -1, -2], 否], [right, y, [-12, -5, -2], [-12, -5, -2], 是], [bottom, x, [-11, -1, 1], [-11, -1, 1], 是], [top, x, [-39, -5, 1], [-39, -5, 1], 是]], 否, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-11,-1,-2,2,0,-1],"bounds":[-3,3,-2,4],"source":2,"boundary_data":[["left",[10,-2,-1]],["right",[4,-2,-1]],["bottom",[-11,-1,2]],["top",[-35,-1,2]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-11, -1, -2, 2, 0, -1], 2, 2, 是, [[left, y, [10, -2, -1], [10, -2, -1], 是], [right, y, [4, -2, -1], [4, -2, -1], 是], [bottom, x, [-11, -1, 2], [-11, -1, 2], 是], [top, x, [-35, -1, 2], [-35, -1, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-11, -1, -2, 2, 0, -1], 2, 2, 是, [[left, y, [10, -2, -1], [10, -2, -1], 是], [right, y, [4, -2, -1], [4, -2, -1], 是], [bottom, x, [-11, -1, 2], [-11, -1, 2], 是], [top, x, [-35, -1, 2], [-35, -1, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-10,0,-1,3,1,0],"bounds":[-4,4,-3,5],"source":6,"boundary_data":[["left",[38,-5,0]],["right",[38,3,0]],["bottom",[-7,-3,3]],["top",[-15,5,3]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-10, 0, -1, 3, 1, 0], 6, 6, 是, [[left, y, [38, -5, 0], [38, -5, 0], 是], [right, y, [38, 3, 0], [38, 3, 0], 是], [bottom, x, [-7, -3, 3], [-7, -3, 3], 是], [top, x, [-15, 5, 3], [-15, 5, 3], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-10, 0, -1, 3, 1, 0], 6, 6, 是, [[left, y, [38, -5, 0], [38, -5, 0], 是], [right, y, [38, 3, 0], [38, 3, 0], 是], [bottom, x, [-7, -3, 3], [-7, -3, 3], 是], [top, x, [-15, 5, 3], [-15, 5, 3], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-9,1,0,4,-1,1],"bounds":[-5,5,-4,6],"source":10,"boundary_data":[["left",[86,5,1]],["right",[96,-5,1]],["bottom",[7,5,4]],["top",[27,-5,4]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-9, 1, 0, 4, -1, 1], 10, 10, 是, [[left, y, [86, 5, 1], [86, 5, 1], 是], [right, y, [96, -5, 1], [96, -5, 1], 是], [bottom, x, [7, 5, 4], [7, 5, 4], 是], [top, x, [27, -5, 4], [27, -5, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-9, 1, 0, 4, -1, 1], 10, 10, 是, [[left, y, [86, 5, 1], [86, 5, 1], 是], [right, y, [96, -5, 1], [96, -5, 1], 是], [bottom, x, [7, 5, 4], [7, 5, 4], 是], [top, x, [27, -5, 4], [27, -5, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-8,2,1,1,0,2],"bounds":[-6,6,-5,7],"source":6,"boundary_data":[["left",[16,1,2]],["right",[40,1,2]],["bottom",[37,2,1]],["top",[97,2,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-8, 2, 1, 1, 0, 2], 6, 6, 是, [[left, y, [16, 1, 2], [16, 1, 2], 是], [right, y, [40, 1, 2], [40, 1, 2], 是], [bottom, x, [37, 2, 1], [37, 2, 1], 是], [top, x, [97, 2, 1], [97, 2, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-8, 2, 1, 1, 0, 2], 6, 6, 是, [[left, y, [16, 1, 2], [16, 1, 2], 是], [right, y, [40, 1, 2], [40, 1, 2], 是], [bottom, x, [37, 2, 1], [37, 2, 1], 是], [top, x, [97, 2, 1], [97, 2, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-7,-2,2,2,1,-2],"bounds":[-7,7,-6,8],"source":0,"boundary_data":[["left",[105,-5,-2]],["right",[77,9,-2]],["bottom",[-91,-8,2]],["top",[-119,6,2]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-7, -2, 2, 2, 1, -2], 0, 0, 是, [[left, y, [105, -5, -2], [105, -5, -2], 是], [right, y, [77, 9, -2], [77, 9, -2], 是], [bottom, x, [-91, -8, 2], [-91, -8, 2], 是], [top, x, [-119, 6, 2], [-119, 6, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-7, -2, 2, 2, 1, -2], 0, 0, 是, [[left, y, [105, -5, -2], [105, -5, -2], 是], [right, y, [77, 9, -2], [77, 9, -2], 是], [bottom, x, [-91, -8, 2], [-91, -8, 2], 是], [top, x, [-119, 6, 2], [-119, 6, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-6,-1,3,3,-1,-1],"bounds":[-8,8,-7,9],"source":4,"boundary_data":[["left",[195,11,-1]],["right",[178,-5,-1]],["bottom",[-76,6,3]],["top",[-60,-10,3]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-6, -1, 3, 3, -1, -1], 4, 4, 是, [[left, y, [194, 11, -1], [195, 11, -1], 否], [right, y, [178, -5, -1], [178, -5, -1], 是], [bottom, x, [-76, 6, 3], [-76, 6, 3], 是], [top, x, [-60, -10, 3], [-60, -10, 3], 是]], 否, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([-6, -1, 3, 3, -1, -1], 4, 4, 是, [[left, y, [194, 11, -1], [195, 11, -1], 否], [right, y, [178, -5, -1], [178, -5, -1], 是], [bottom, x, [-76, 6, 3], [-76, 6, 3], 是], [top, x, [-60, -10, 3], [-60, -10, 3], 是]], 否, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-5,0,-3,4,0,0],"bounds":[-9,9,-8,10],"source":9,"boundary_data":[["left",[319,-3,0]],["right",[319,-3,0]],["bottom",[19,0,4]],["top",[-35,0,4]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-5, 0, -3, 4, 0, 0], 8, 9, 否, [[left, y, [319, -3, 0], [319, -3, 0], 是], [right, y, [319, -3, 0], [319, -3, 0], 是], [bottom, x, [19, 0, 4], [19, 0, 4], 是], [top, x, [-35, 0, 4], [-35, 0, 4], 是]], 是, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([-5, 0, -3, 4, 0, 0], 8, 9, 否, [[left, y, [319, -3, 0], [319, -3, 0], 是], [right, y, [319, -3, 0], [319, -3, 0], 是], [bottom, x, [19, 0, 4], [19, 0, 4], 是], [top, x, [-35, 0, 4], [-35, 0, 4], 是]], 是, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-4,1,-2,1,1,1],"bounds":[-10,10,-9,11],"source":4,"boundary_data":[["left",[86,-12,1]],["right",[106,8,1]],["bottom",[95,-8,1]],["top",[95,12,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-4, 1, -2, 1, 1, 1], 4, 4, 是, [[left, y, [86, -12, 1], [86, -12, 1], 是], [right, y, [106, 8, 1], [106, 8, 1], 是], [bottom, x, [95, -8, 1], [95, -8, 1], 是], [top, x, [95, 12, 1], [95, 12, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-4, 1, -2, 1, 1, 1], 4, 4, 是, [[left, y, [86, -12, 1], [86, -12, 1], 是], [right, y, [106, 8, 1], [106, 8, 1], 是], [bottom, x, [95, -8, 1], [95, -8, 1], 是], [top, x, [95, 12, 1], [95, 12, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-3,2,-1,2,-1,2],"bounds":[-11,11,-10,12],"source":8,"boundary_data":[["left",[217,10,2]],["right",[261,-12,2]],["bottom",[207,12,2]],["top",[273,-10,2]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-3, 2, -1, 2, -1, 2], 8, 8, 是, [[left, y, [217, 10, 2], [217, 10, 2], 是], [right, y, [261, -12, 2], [261, -12, 2], 是], [bottom, x, [207, 12, 2], [207, 12, 2], 是], [top, x, [273, -10, 2], [273, -10, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-3, 2, -1, 2, -1, 2], 8, 8, 是, [[left, y, [217, 10, 2], [217, 10, 2], 是], [right, y, [261, -12, 2], [261, -12, 2], 是], [bottom, x, [207, 12, 2], [207, 12, 2], 是], [top, x, [273, -10, 2], [273, -10, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-2,-2,0,3,0,-2],"bounds":[-12,12,-11,13],"source":2,"boundary_data":[["left",[454,0,-2]],["right",[406,0,-2]],["bottom",[-244,-2,3]],["top",[-340,-2,3]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-2, -2, 0, 3, 0, -2], 2, 2, 是, [[left, y, [454, 0, -2], [454, 0, -2], 是], [right, y, [406, 0, -2], [406, 0, -2], 是], [bottom, x, [-244, -2, 3], [-244, -2, 3], 是], [top, x, [-340, -2, 3], [-340, -2, 3], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-2, -2, 0, 3, 0, -2], 2, 2, 是, [[left, y, [454, 0, -2], [454, 0, -2], 是], [right, y, [406, 0, -2], [406, 0, -2], 是], [bottom, x, [-244, -2, 3], [-244, -2, 3], 是], [top, x, [-340, -2, 3], [-340, -2, 3], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[-1,-1,1,4,1,-1],"bounds":[-13,13,-12,14],"source":6,"boundary_data":[["left",[688,-12,-1]],["right",[662,14,-1]],["bottom",[-157,-13,4]],["top",[-183,13,4]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([-1, -1, 1, 4, 1, -1], 6, 6, 是, [[left, y, [688, -12, -1], [688, -12, -1], 是], [right, y, [662, 14, -1], [662, 14, -1], 是], [bottom, x, [-157, -13, 4], [-157, -13, 4], 是], [top, x, [-183, 13, 4], [-183, 13, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([-1, -1, 1, 4, 1, -1], 6, 6, 是, [[left, y, [688, -12, -1], [688, -12, -1], 是], [right, y, [662, 14, -1], [662, 14, -1], 是], [bottom, x, [-157, -13, 4], [-157, -13, 4], 是], [top, x, [-183, 13, 4], [-183, 13, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[0,0,2,1,-1,0],"bounds":[-14,14,-13,15],"source":2,"boundary_data":[["left",[197,16,0]],["right",[196,-12,0]],["bottom",[-26,13,1]],["top",[30,-15,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([0, 0, 2, 1, -1, 0], 2, 2, 是, [[left, y, [196, 16, 0], [197, 16, 0], 否], [right, y, [196, -12, 0], [196, -12, 0], 是], [bottom, x, [-26, 13, 1], [-26, 13, 1], 是], [top, x, [30, -15, 1], [30, -15, 1], 是]], 否, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([0, 0, 2, 1, -1, 0], 2, 2, 是, [[left, y, [196, 16, 0], [197, 16, 0], 否], [right, y, [196, -12, 0], [196, -12, 0], 是], [bottom, x, [-26, 13, 1], [-26, 13, 1], 是], [top, x, [30, -15, 1], [30, -15, 1], 是]], 否, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[1,1,3,2,0,1],"bounds":[-15,15,-14,16],"source":6,"boundary_data":[["left",[436,3,1]],["right",[466,3,1]],["bottom",[155,1,2]],["top",[305,1,2]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([1, 1, 3, 2, 0, 1], 6, 6, 是, [[left, y, [436, 3, 1], [436, 3, 1], 是], [right, y, [466, 3, 1], [466, 3, 1], 是], [bottom, x, [155, 1, 2], [155, 1, 2], 是], [top, x, [305, 1, 2], [305, 1, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([1, 1, 3, 2, 0, 1], 6, 6, 是, [[left, y, [436, 3, 1], [436, 3, 1], 是], [right, y, [466, 3, 1], [466, 3, 1], 是], [bottom, x, [155, 1, 2], [155, 1, 2], 是], [top, x, [305, 1, 2], [305, 1, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[2,2,-3,3,1,2],"bounds":[-16,16,-15,17],"source":11,"boundary_data":[["left",[738,-19,2]],["right",[802,13,2]],["bottom",[497,-13,3]],["top",[529,19,3]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([2, 2, -3, 3, 1, 2], 10, 11, 否, [[left, y, [738, -19, 2], [738, -19, 2], 是], [right, y, [802, 13, 2], [802, 13, 2], 是], [bottom, x, [497, -13, 3], [497, -13, 3], 是], [top, x, [529, 19, 3], [529, 19, 3], 是]], 是, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([2, 2, -3, 3, 1, 2], 10, 11, 否, [[left, y, [738, -19, 2], [738, -19, 2], 是], [right, y, [802, 13, 2], [802, 13, 2], 是], [bottom, x, [497, -13, 3], [497, -13, 3], 是], [top, x, [529, 19, 3], [529, 19, 3], 是]], 是, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[3,-2,-2,4,-1,-2],"bounds":[-17,17,-16,18],"source":4,"boundary_data":[["left",[1193,15,-2]],["right",[1125,-19,-2]],["bottom",[-477,14,4]],["top",[-681,-20,4]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([3, -2, -2, 4, -1, -2], 4, 4, 是, [[left, y, [1193, 15, -2], [1193, 15, -2], 是], [right, y, [1125, -19, -2], [1125, -19, -2], 是], [bottom, x, [-477, 14, 4], [-477, 14, 4], 是], [top, x, [-681, -20, 4], [-681, -20, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([3, -2, -2, 4, -1, -2], 4, 4, 是, [[left, y, [1193, 15, -2], [1193, 15, -2], 是], [right, y, [1125, -19, -2], [1125, -19, -2], 是], [bottom, x, [-477, 14, 4], [-477, 14, 4], 是], [top, x, [-681, -20, 4], [-681, -20, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[4,-1,-1,1,0,-1],"bounds":[-18,18,-17,19],"source":0,"boundary_data":[["left",[346,-1,-1]],["right",[310,-1,-1]],["bottom",[-268,-1,1]],["top",[-376,-1,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([4, -1, -1, 1, 0, -1], 0, 0, 是, [[left, y, [346, -1, -1], [346, -1, -1], 是], [right, y, [310, -1, -1], [310, -1, -1], 是], [bottom, x, [-268, -1, 1], [-268, -1, 1], 是], [top, x, [-376, -1, 1], [-376, -1, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([4, -1, -1, 1, 0, -1], 0, 0, 是, [[left, y, [346, -1, -1], [346, -1, -1], 是], [right, y, [310, -1, -1], [310, -1, -1], 是], [bottom, x, [-268, -1, 1], [-268, -1, 1], 是], [top, x, [-376, -1, 1], [-376, -1, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[5,0,0,2,1,0],"bounds":[-19,19,-18,20],"source":4,"boundary_data":[["left",[727,-19,0]],["right",[727,19,0]],["bottom",[5,-18,2]],["top",[5,20,2]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([5, 0, 0, 2, 1, 0], 4, 4, 是, [[left, y, [727, -19, 0], [727, -19, 0], 是], [right, y, [727, 19, 0], [727, 19, 0], 是], [bottom, x, [5, -18, 2], [5, -18, 2], 是], [top, x, [5, 20, 2], [5, 20, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([5, 0, 0, 2, 1, 0], 4, 4, 是, [[left, y, [727, -19, 0], [727, -19, 0], 是], [right, y, [727, 19, 0], [727, 19, 0], 是], [bottom, x, [5, -18, 2], [5, -18, 2], 是], [top, x, [5, 20, 2], [5, 20, 2], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[6,1,1,3,-1,1],"bounds":[-20,20,-19,21],"source":8,"boundary_data":[["left",[1187,21,1]],["right",[1226,-19,1]],["bottom",[348,20,3]],["top",[468,-20,3]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([6, 1, 1, 3, -1, 1], 8, 8, 是, [[left, y, [1186, 21, 1], [1187, 21, 1], 否], [right, y, [1226, -19, 1], [1226, -19, 1], 是], [bottom, x, [348, 20, 3], [348, 20, 3], 是], [top, x, [468, -20, 3], [468, -20, 3], 是]], 否, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([6, 1, 1, 3, -1, 1], 8, 8, 是, [[left, y, [1186, 21, 1], [1187, 21, 1], 否], [right, y, [1226, -19, 1], [1226, -19, 1], 是], [bottom, x, [348, 20, 3], [348, 20, 3], 是], [top, x, [468, -20, 3], [468, -20, 3], 是]], 否, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[7,2,2,4,0,2],"bounds":[-21,21,-20,22],"source":12,"boundary_data":[["left",[1729,2,2]],["right",[1813,2,2]],["bottom",[767,2,4]],["top",[1019,2,4]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([7, 2, 2, 4, 0, 2], 12, 12, 是, [[left, y, [1729, 2, 2], [1729, 2, 2], 是], [right, y, [1813, 2, 2], [1813, 2, 2], 是], [bottom, x, [767, 2, 4], [767, 2, 4], 是], [top, x, [1019, 2, 4], [1019, 2, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([7, 2, 2, 4, 0, 2], 12, 12, 是, [[left, y, [1729, 2, 2], [1729, 2, 2], 是], [right, y, [1813, 2, 2], [1813, 2, 2], 是], [bottom, x, [767, 2, 4], [767, 2, 4], 是], [top, x, [1019, 2, 4], [1019, 2, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[8,-2,3,1,1,-2],"bounds":[-22,22,-21,23],"source":-2,"boundary_data":[["left",[536,-19,-2]],["right",[448,25,-2]],["bottom",[-937,-23,1]],["top",[-981,21,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([8, -2, 3, 1, 1, -2], -2, -2, 是, [[left, y, [536, -19, -2], [536, -19, -2], 是], [right, y, [448, 25, -2], [448, 25, -2], 是], [bottom, x, [-937, -23, 1], [-937, -23, 1], 是], [top, x, [-981, 21, 1], [-981, 21, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([8, -2, 3, 1, 1, -2], -2, -2, 是, [[left, y, [536, -19, -2], [536, -19, -2], 是], [right, y, [448, 25, -2], [448, 25, -2], 是], [bottom, x, [-937, -23, 1], [-937, -23, 1], 是], [top, x, [-981, 21, 1], [-981, 21, 1], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[9,-1,-3,2,-1,-1],"bounds":[-23,23,-22,24],"source":3,"boundary_data":[["left",[1090,20,-1]],["right",[1044,-26,-1]],["bottom",[-409,21,2]],["top",[-639,-25,2]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([9, -1, -3, 2, -1, -1], 2, 3, 否, [[left, y, [1090, 20, -1], [1090, 20, -1], 是], [right, y, [1044, -26, -1], [1044, -26, -1], 是], [bottom, x, [-409, 21, 2], [-409, 21, 2], 是], [top, x, [-639, -25, 2], [-639, -25, 2], 是]], 是, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([9, -1, -3, 2, -1, -1], 2, 3, 否, [[left, y, [1090, 20, -1], [1090, 20, -1], 是], [right, y, [1044, -26, -1], [1044, -26, -1], 是], [bottom, x, [-409, 21, 2], [-409, 21, 2], 是], [top, x, [-639, -25, 2], [-639, -25, 2], 是]], 是, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[10,0,-2,3,0,0],"bounds":[-24,24,-23,25],"source":6,"boundary_data":[["left",[1738,-2,0]],["right",[1738,-2,0]],["bottom",[56,0,3]],["top",[-40,0,3]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([10, 0, -2, 3, 0, 0], 6, 6, 是, [[left, y, [1738, -2, 0], [1738, -2, 0], 是], [right, y, [1738, -2, 0], [1738, -2, 0], 是], [bottom, x, [56, 0, 3], [56, 0, 3], 是], [top, x, [-40, 0, 3], [-40, 0, 3], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([10, 0, -2, 3, 0, 0], 6, 6, 是, [[left, y, [1738, -2, 0], [1738, -2, 0], 是], [right, y, [1738, -2, 0], [1738, -2, 0], 是], [bottom, x, [56, 0, 3], [56, 0, 3], 是], [top, x, [-40, 0, 3], [-40, 0, 3], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[11,1,-1,4,1,1],"bounds":[-25,25,-24,26],"source":10,"boundary_data":[["left",[2486,-26,1]],["right",[2536,24,1]],["bottom",[611,-23,4]],["top",[661,27,4]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([11, 1, -1, 4, 1, 1], 10, 10, 是, [[left, y, [2486, -26, 1], [2486, -26, 1], 是], [right, y, [2536, 24, 1], [2536, 24, 1], 是], [bottom, x, [611, -23, 4], [611, -23, 4], 是], [top, x, [661, 27, 4], [661, 27, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)
收束波核對=([11, 1, -1, 4, 1, 1], 10, 10, 是, [[left, y, [2486, -26, 1], [2486, -26, 1], 是], [right, y, [2536, 24, 1], [2536, 24, 1], 是], [bottom, x, [611, -23, 4], [611, -23, 4], 是], [top, x, [661, 27, 4], [661, 27, 4], 是]], 是, 是, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-joint-candidate-audit；資料={"coefficients":[12,2,0,1,-1,2],"bounds":[-26,26,-25,27],"source":6,"boundary_data":[["left",[637,26,2]],["right",[740,-26,2]],["bottom",[1262,27,1]],["top",[1470,-25,1]]]}。請依 [coefficients,laplacian,source,interior_identity,boundary_rows,boundary_identity,candidate_satisfies_declared_BVP,scope] 欄序回答。
([12, 2, 0, 1, -1, 2], 6, 6, 是, [[left, y, [636, 26, 2], [637, 26, 2], 否], [right, y, [740, -26, 2], [740, -26, 2], 是], [bottom, x, [1262, 27, 1], [1262, 27, 1], 是], [top, x, [1470, -25, 1], [1470, -25, 1], 是]], 否, 否, candidate_satisfies_declared_BVP_only)
收束波核對=([12, 2, 0, 1, -1, 2], 6, 6, 是, [[left, y, [636, 26, 2], [637, 26, 2], 否], [right, y, [740, -26, 2], [740, -26, 2], 是], [bottom, x, [1262, 27, 1], [1262, 27, 1], 是], [top, x, [1470, -25, 1], [1470, -25, 1], 是]], 否, 否, candidate_satisfies_declared_BVP_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-joint-candidate-audit · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-12,-2,-3,1,-1,-2],"bounds":[-2,2,-1,3],"source":-1,"boundary_data":[["left",[-4,-1,-2]],["right",[-12,-5,-2]],["bottom",[-11,-1,1]],["top",[-39,-5,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(-2, -1, 否, [[left, y, [-4, -1, -2], [-4, -1, -2], 是], [right, y, [-12, -5, -2], [-12, -5, -2], 是], [bottom, x, [-11, -1, 1], [-11, -1, 1], 是], [top, x, [-39, -5, 1], [-39, -5, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(-2, -1, 否, [[left, y, [-4, -1, -2], [-4, -1, -2], 是], [right, y, [-12, -5, -2], [-12, -5, -2], 是], [bottom, x, [-11, -1, 1], [-11, -1, 1], 是], [top, x, [-39, -5, 1], [-39, -5, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-11,-1,-2,2,0,-1],"bounds":[-3,3,-2,4],"source":2,"boundary_data":[["left",[11,-2,-1]],["right",[4,-2,-1]],["bottom",[-11,-1,2]],["top",[-35,-1,2]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(2, 2, 是, [[left, y, [10, -2, -1], [11, -2, -1], 否], [right, y, [4, -2, -1], [4, -2, -1], 是], [bottom, x, [-11, -1, 2], [-11, -1, 2], 是], [top, x, [-35, -1, 2], [-35, -1, 2], 是]], 否, interior_pass_boundary_fail)
收束波核對=(2, 2, 是, [[left, y, [10, -2, -1], [11, -2, -1], 否], [right, y, [4, -2, -1], [4, -2, -1], 是], [bottom, x, [-11, -1, 2], [-11, -1, 2], 是], [top, x, [-35, -1, 2], [-35, -1, 2], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-10,0,-1,3,1,0],"bounds":[-4,4,-3,5],"source":7,"boundary_data":[["left",[38,-5,0]],["right",[38,3,0]],["bottom",[-7,-3,3]],["top",[-15,5,3]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(6, 7, 否, [[left, y, [38, -5, 0], [38, -5, 0], 是], [right, y, [38, 3, 0], [38, 3, 0], 是], [bottom, x, [-7, -3, 3], [-7, -3, 3], 是], [top, x, [-15, 5, 3], [-15, 5, 3], 是]], 是, boundary_pass_interior_fail)
收束波核對=(6, 7, 否, [[left, y, [38, -5, 0], [38, -5, 0], 是], [right, y, [38, 3, 0], [38, 3, 0], 是], [bottom, x, [-7, -3, 3], [-7, -3, 3], 是], [top, x, [-15, 5, 3], [-15, 5, 3], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-9,1,0,4,-1,1],"bounds":[-5,5,-4,6],"source":10,"boundary_data":[["left",[87,5,1]],["right",[96,-5,1]],["bottom",[7,5,4]],["top",[27,-5,4]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(10, 10, 是, [[left, y, [86, 5, 1], [87, 5, 1], 否], [right, y, [96, -5, 1], [96, -5, 1], 是], [bottom, x, [7, 5, 4], [7, 5, 4], 是], [top, x, [27, -5, 4], [27, -5, 4], 是]], 否, interior_pass_boundary_fail)
收束波核對=(10, 10, 是, [[left, y, [86, 5, 1], [87, 5, 1], 否], [right, y, [96, -5, 1], [96, -5, 1], 是], [bottom, x, [7, 5, 4], [7, 5, 4], 是], [top, x, [27, -5, 4], [27, -5, 4], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-8,2,1,1,0,2],"bounds":[-6,6,-5,7],"source":7,"boundary_data":[["left",[16,1,2]],["right",[40,1,2]],["bottom",[37,2,1]],["top",[97,2,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(6, 7, 否, [[left, y, [16, 1, 2], [16, 1, 2], 是], [right, y, [40, 1, 2], [40, 1, 2], 是], [bottom, x, [37, 2, 1], [37, 2, 1], 是], [top, x, [97, 2, 1], [97, 2, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(6, 7, 否, [[left, y, [16, 1, 2], [16, 1, 2], 是], [right, y, [40, 1, 2], [40, 1, 2], 是], [bottom, x, [37, 2, 1], [37, 2, 1], 是], [top, x, [97, 2, 1], [97, 2, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-7,-2,2,2,1,-2],"bounds":[-7,7,-6,8],"source":0,"boundary_data":[["left",[106,-5,-2]],["right",[77,9,-2]],["bottom",[-91,-8,2]],["top",[-119,6,2]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(0, 0, 是, [[left, y, [105, -5, -2], [106, -5, -2], 否], [right, y, [77, 9, -2], [77, 9, -2], 是], [bottom, x, [-91, -8, 2], [-91, -8, 2], 是], [top, x, [-119, 6, 2], [-119, 6, 2], 是]], 否, interior_pass_boundary_fail)
收束波核對=(0, 0, 是, [[left, y, [105, -5, -2], [106, -5, -2], 否], [right, y, [77, 9, -2], [77, 9, -2], 是], [bottom, x, [-91, -8, 2], [-91, -8, 2], 是], [top, x, [-119, 6, 2], [-119, 6, 2], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-6,-1,3,3,-1,-1],"bounds":[-8,8,-7,9],"source":5,"boundary_data":[["left",[194,11,-1]],["right",[178,-5,-1]],["bottom",[-76,6,3]],["top",[-60,-10,3]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(4, 5, 否, [[left, y, [194, 11, -1], [194, 11, -1], 是], [right, y, [178, -5, -1], [178, -5, -1], 是], [bottom, x, [-76, 6, 3], [-76, 6, 3], 是], [top, x, [-60, -10, 3], [-60, -10, 3], 是]], 是, boundary_pass_interior_fail)
收束波核對=(4, 5, 否, [[left, y, [194, 11, -1], [194, 11, -1], 是], [right, y, [178, -5, -1], [178, -5, -1], 是], [bottom, x, [-76, 6, 3], [-76, 6, 3], 是], [top, x, [-60, -10, 3], [-60, -10, 3], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-5,0,-3,4,0,0],"bounds":[-9,9,-8,10],"source":8,"boundary_data":[["left",[320,-3,0]],["right",[319,-3,0]],["bottom",[19,0,4]],["top",[-35,0,4]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(8, 8, 是, [[left, y, [319, -3, 0], [320, -3, 0], 否], [right, y, [319, -3, 0], [319, -3, 0], 是], [bottom, x, [19, 0, 4], [19, 0, 4], 是], [top, x, [-35, 0, 4], [-35, 0, 4], 是]], 否, interior_pass_boundary_fail)
收束波核對=(8, 8, 是, [[left, y, [319, -3, 0], [320, -3, 0], 否], [right, y, [319, -3, 0], [319, -3, 0], 是], [bottom, x, [19, 0, 4], [19, 0, 4], 是], [top, x, [-35, 0, 4], [-35, 0, 4], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-4,1,-2,1,1,1],"bounds":[-10,10,-9,11],"source":5,"boundary_data":[["left",[86,-12,1]],["right",[106,8,1]],["bottom",[95,-8,1]],["top",[95,12,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(4, 5, 否, [[left, y, [86, -12, 1], [86, -12, 1], 是], [right, y, [106, 8, 1], [106, 8, 1], 是], [bottom, x, [95, -8, 1], [95, -8, 1], 是], [top, x, [95, 12, 1], [95, 12, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(4, 5, 否, [[left, y, [86, -12, 1], [86, -12, 1], 是], [right, y, [106, 8, 1], [106, 8, 1], 是], [bottom, x, [95, -8, 1], [95, -8, 1], 是], [top, x, [95, 12, 1], [95, 12, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-3,2,-1,2,-1,2],"bounds":[-11,11,-10,12],"source":8,"boundary_data":[["left",[218,10,2]],["right",[261,-12,2]],["bottom",[207,12,2]],["top",[273,-10,2]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(8, 8, 是, [[left, y, [217, 10, 2], [218, 10, 2], 否], [right, y, [261, -12, 2], [261, -12, 2], 是], [bottom, x, [207, 12, 2], [207, 12, 2], 是], [top, x, [273, -10, 2], [273, -10, 2], 是]], 否, interior_pass_boundary_fail)
收束波核對=(8, 8, 是, [[left, y, [217, 10, 2], [218, 10, 2], 否], [right, y, [261, -12, 2], [261, -12, 2], 是], [bottom, x, [207, 12, 2], [207, 12, 2], 是], [top, x, [273, -10, 2], [273, -10, 2], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-2,-2,0,3,0,-2],"bounds":[-12,12,-11,13],"source":3,"boundary_data":[["left",[454,0,-2]],["right",[406,0,-2]],["bottom",[-244,-2,3]],["top",[-340,-2,3]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(2, 3, 否, [[left, y, [454, 0, -2], [454, 0, -2], 是], [right, y, [406, 0, -2], [406, 0, -2], 是], [bottom, x, [-244, -2, 3], [-244, -2, 3], 是], [top, x, [-340, -2, 3], [-340, -2, 3], 是]], 是, boundary_pass_interior_fail)
收束波核對=(2, 3, 否, [[left, y, [454, 0, -2], [454, 0, -2], 是], [right, y, [406, 0, -2], [406, 0, -2], 是], [bottom, x, [-244, -2, 3], [-244, -2, 3], 是], [top, x, [-340, -2, 3], [-340, -2, 3], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[-1,-1,1,4,1,-1],"bounds":[-13,13,-12,14],"source":6,"boundary_data":[["left",[689,-12,-1]],["right",[662,14,-1]],["bottom",[-157,-13,4]],["top",[-183,13,4]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(6, 6, 是, [[left, y, [688, -12, -1], [689, -12, -1], 否], [right, y, [662, 14, -1], [662, 14, -1], 是], [bottom, x, [-157, -13, 4], [-157, -13, 4], 是], [top, x, [-183, 13, 4], [-183, 13, 4], 是]], 否, interior_pass_boundary_fail)
收束波核對=(6, 6, 是, [[left, y, [688, -12, -1], [689, -12, -1], 否], [right, y, [662, 14, -1], [662, 14, -1], 是], [bottom, x, [-157, -13, 4], [-157, -13, 4], 是], [top, x, [-183, 13, 4], [-183, 13, 4], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[0,0,2,1,-1,0],"bounds":[-14,14,-13,15],"source":3,"boundary_data":[["left",[196,16,0]],["right",[196,-12,0]],["bottom",[-26,13,1]],["top",[30,-15,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(2, 3, 否, [[left, y, [196, 16, 0], [196, 16, 0], 是], [right, y, [196, -12, 0], [196, -12, 0], 是], [bottom, x, [-26, 13, 1], [-26, 13, 1], 是], [top, x, [30, -15, 1], [30, -15, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(2, 3, 否, [[left, y, [196, 16, 0], [196, 16, 0], 是], [right, y, [196, -12, 0], [196, -12, 0], 是], [bottom, x, [-26, 13, 1], [-26, 13, 1], 是], [top, x, [30, -15, 1], [30, -15, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[1,1,3,2,0,1],"bounds":[-15,15,-14,16],"source":6,"boundary_data":[["left",[437,3,1]],["right",[466,3,1]],["bottom",[155,1,2]],["top",[305,1,2]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(6, 6, 是, [[left, y, [436, 3, 1], [437, 3, 1], 否], [right, y, [466, 3, 1], [466, 3, 1], 是], [bottom, x, [155, 1, 2], [155, 1, 2], 是], [top, x, [305, 1, 2], [305, 1, 2], 是]], 否, interior_pass_boundary_fail)
收束波核對=(6, 6, 是, [[left, y, [436, 3, 1], [437, 3, 1], 否], [right, y, [466, 3, 1], [466, 3, 1], 是], [bottom, x, [155, 1, 2], [155, 1, 2], 是], [top, x, [305, 1, 2], [305, 1, 2], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[2,2,-3,3,1,2],"bounds":[-16,16,-15,17],"source":11,"boundary_data":[["left",[738,-19,2]],["right",[802,13,2]],["bottom",[497,-13,3]],["top",[529,19,3]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(10, 11, 否, [[left, y, [738, -19, 2], [738, -19, 2], 是], [right, y, [802, 13, 2], [802, 13, 2], 是], [bottom, x, [497, -13, 3], [497, -13, 3], 是], [top, x, [529, 19, 3], [529, 19, 3], 是]], 是, boundary_pass_interior_fail)
收束波核對=(10, 11, 否, [[left, y, [738, -19, 2], [738, -19, 2], 是], [right, y, [802, 13, 2], [802, 13, 2], 是], [bottom, x, [497, -13, 3], [497, -13, 3], 是], [top, x, [529, 19, 3], [529, 19, 3], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[3,-2,-2,4,-1,-2],"bounds":[-17,17,-16,18],"source":4,"boundary_data":[["left",[1194,15,-2]],["right",[1125,-19,-2]],["bottom",[-477,14,4]],["top",[-681,-20,4]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(4, 4, 是, [[left, y, [1193, 15, -2], [1194, 15, -2], 否], [right, y, [1125, -19, -2], [1125, -19, -2], 是], [bottom, x, [-477, 14, 4], [-477, 14, 4], 是], [top, x, [-681, -20, 4], [-681, -20, 4], 是]], 否, interior_pass_boundary_fail)
收束波核對=(4, 4, 是, [[left, y, [1193, 15, -2], [1194, 15, -2], 否], [right, y, [1125, -19, -2], [1125, -19, -2], 是], [bottom, x, [-477, 14, 4], [-477, 14, 4], 是], [top, x, [-681, -20, 4], [-681, -20, 4], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[4,-1,-1,1,0,-1],"bounds":[-18,18,-17,19],"source":1,"boundary_data":[["left",[346,-1,-1]],["right",[310,-1,-1]],["bottom",[-268,-1,1]],["top",[-376,-1,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(0, 1, 否, [[left, y, [346, -1, -1], [346, -1, -1], 是], [right, y, [310, -1, -1], [310, -1, -1], 是], [bottom, x, [-268, -1, 1], [-268, -1, 1], 是], [top, x, [-376, -1, 1], [-376, -1, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(0, 1, 否, [[left, y, [346, -1, -1], [346, -1, -1], 是], [right, y, [310, -1, -1], [310, -1, -1], 是], [bottom, x, [-268, -1, 1], [-268, -1, 1], 是], [top, x, [-376, -1, 1], [-376, -1, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[5,0,0,2,1,0],"bounds":[-19,19,-18,20],"source":4,"boundary_data":[["left",[728,-19,0]],["right",[727,19,0]],["bottom",[5,-18,2]],["top",[5,20,2]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(4, 4, 是, [[left, y, [727, -19, 0], [728, -19, 0], 否], [right, y, [727, 19, 0], [727, 19, 0], 是], [bottom, x, [5, -18, 2], [5, -18, 2], 是], [top, x, [5, 20, 2], [5, 20, 2], 是]], 否, interior_pass_boundary_fail)
收束波核對=(4, 4, 是, [[left, y, [727, -19, 0], [728, -19, 0], 否], [right, y, [727, 19, 0], [727, 19, 0], 是], [bottom, x, [5, -18, 2], [5, -18, 2], 是], [top, x, [5, 20, 2], [5, 20, 2], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[6,1,1,3,-1,1],"bounds":[-20,20,-19,21],"source":9,"boundary_data":[["left",[1186,21,1]],["right",[1226,-19,1]],["bottom",[348,20,3]],["top",[468,-20,3]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(8, 9, 否, [[left, y, [1186, 21, 1], [1186, 21, 1], 是], [right, y, [1226, -19, 1], [1226, -19, 1], 是], [bottom, x, [348, 20, 3], [348, 20, 3], 是], [top, x, [468, -20, 3], [468, -20, 3], 是]], 是, boundary_pass_interior_fail)
收束波核對=(8, 9, 否, [[left, y, [1186, 21, 1], [1186, 21, 1], 是], [right, y, [1226, -19, 1], [1226, -19, 1], 是], [bottom, x, [348, 20, 3], [348, 20, 3], 是], [top, x, [468, -20, 3], [468, -20, 3], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[7,2,2,4,0,2],"bounds":[-21,21,-20,22],"source":12,"boundary_data":[["left",[1730,2,2]],["right",[1813,2,2]],["bottom",[767,2,4]],["top",[1019,2,4]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(12, 12, 是, [[left, y, [1729, 2, 2], [1730, 2, 2], 否], [right, y, [1813, 2, 2], [1813, 2, 2], 是], [bottom, x, [767, 2, 4], [767, 2, 4], 是], [top, x, [1019, 2, 4], [1019, 2, 4], 是]], 否, interior_pass_boundary_fail)
收束波核對=(12, 12, 是, [[left, y, [1729, 2, 2], [1730, 2, 2], 否], [right, y, [1813, 2, 2], [1813, 2, 2], 是], [bottom, x, [767, 2, 4], [767, 2, 4], 是], [top, x, [1019, 2, 4], [1019, 2, 4], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[8,-2,3,1,1,-2],"bounds":[-22,22,-21,23],"source":-1,"boundary_data":[["left",[536,-19,-2]],["right",[448,25,-2]],["bottom",[-937,-23,1]],["top",[-981,21,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(-2, -1, 否, [[left, y, [536, -19, -2], [536, -19, -2], 是], [right, y, [448, 25, -2], [448, 25, -2], 是], [bottom, x, [-937, -23, 1], [-937, -23, 1], 是], [top, x, [-981, 21, 1], [-981, 21, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(-2, -1, 否, [[left, y, [536, -19, -2], [536, -19, -2], 是], [right, y, [448, 25, -2], [448, 25, -2], 是], [bottom, x, [-937, -23, 1], [-937, -23, 1], 是], [top, x, [-981, 21, 1], [-981, 21, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[9,-1,-3,2,-1,-1],"bounds":[-23,23,-22,24],"source":2,"boundary_data":[["left",[1091,20,-1]],["right",[1044,-26,-1]],["bottom",[-409,21,2]],["top",[-639,-25,2]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(2, 2, 是, [[left, y, [1090, 20, -1], [1091, 20, -1], 否], [right, y, [1044, -26, -1], [1044, -26, -1], 是], [bottom, x, [-409, 21, 2], [-409, 21, 2], 是], [top, x, [-639, -25, 2], [-639, -25, 2], 是]], 否, interior_pass_boundary_fail)
收束波核對=(2, 2, 是, [[left, y, [1090, 20, -1], [1091, 20, -1], 否], [right, y, [1044, -26, -1], [1044, -26, -1], 是], [bottom, x, [-409, 21, 2], [-409, 21, 2], 是], [top, x, [-639, -25, 2], [-639, -25, 2], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[10,0,-2,3,0,0],"bounds":[-24,24,-23,25],"source":7,"boundary_data":[["left",[1738,-2,0]],["right",[1738,-2,0]],["bottom",[56,0,3]],["top",[-40,0,3]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(6, 7, 否, [[left, y, [1738, -2, 0], [1738, -2, 0], 是], [right, y, [1738, -2, 0], [1738, -2, 0], 是], [bottom, x, [56, 0, 3], [56, 0, 3], 是], [top, x, [-40, 0, 3], [-40, 0, 3], 是]], 是, boundary_pass_interior_fail)
收束波核對=(6, 7, 否, [[left, y, [1738, -2, 0], [1738, -2, 0], 是], [right, y, [1738, -2, 0], [1738, -2, 0], 是], [bottom, x, [56, 0, 3], [56, 0, 3], 是], [top, x, [-40, 0, 3], [-40, 0, 3], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[11,1,-1,4,1,1],"bounds":[-25,25,-24,26],"source":10,"boundary_data":[["left",[2487,-26,1]],["right",[2536,24,1]],["bottom",[611,-23,4]],["top",[661,27,4]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(10, 10, 是, [[left, y, [2486, -26, 1], [2487, -26, 1], 否], [right, y, [2536, 24, 1], [2536, 24, 1], 是], [bottom, x, [611, -23, 4], [611, -23, 4], 是], [top, x, [661, 27, 4], [661, 27, 4], 是]], 否, interior_pass_boundary_fail)
收束波核對=(10, 10, 是, [[left, y, [2486, -26, 1], [2487, -26, 1], 否], [right, y, [2536, 24, 1], [2536, 24, 1], 是], [bottom, x, [611, -23, 4], [611, -23, 4], 是], [top, x, [661, 27, 4], [661, 27, 4], 是]], 否, interior_pass_boundary_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate
內部PDE責任與矩形邊界資料分開。操作=bvp-obligation-separation；資料={"coefficients":[12,2,0,1,-1,2],"bounds":[-26,26,-25,27],"source":7,"boundary_data":[["left",[636,26,2]],["right",[740,-26,2]],["bottom",[1262,27,1]],["top",[1470,-25,1]]]}。請依 [laplacian,source,interior_identity,boundary_rows,boundary_identity,state] 欄序回答。
(6, 7, 否, [[left, y, [636, 26, 2], [636, 26, 2], 是], [right, y, [740, -26, 2], [740, -26, 2], 是], [bottom, x, [1262, 27, 1], [1262, 27, 1], 是], [top, x, [1470, -25, 1], [1470, -25, 1], 是]], 是, boundary_pass_interior_fail)
收束波核對=(6, 7, 否, [[left, y, [636, 26, 2], [636, 26, 2], 是], [right, y, [740, -26, 2], [740, -26, 2], 是], [bottom, x, [1262, 27, 1], [1262, 27, 1], 是], [top, x, [1470, -25, 1], [1470, -25, 1], 是]], 是, boundary_pass_interior_fail)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；符號恆等只證宣告的候選BVP；不宣稱存在唯一穩定正則或適定性。
邊界值問題 · qf-mod25-bvp-obligation-separation · candidate