Resume SynthData0523 main/c6 batch 2

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SynthData0523/main/c6/ctgan/ctgan-c6-20260422_025941/staged/ctgan/adapter_transforms_applied.json

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SynthData0523/main/c6/ctgan/ctgan-c6-20260422_025941/staged/ctgan/model_input_manifest.json

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+{
+  "dataset_id": "c6",
+  "model": "ctgan",
+  "target_column": "Type of Answer",
+  "task_type": "classification",
+  "column_schema": [
+    {
+      "name": "Student ID",
+      "role": "feature",
+      "semantic_type": "numeric",
+      "nullable": false,
+      "missing_tokens": [],
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+      "impute_strategy": "median",
+      "profile_stats": {
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+        "unique_count": 367,
+        "unique_ratio": 0.048062,
+        "example_values": [
+          "473",
+          "351",
+          "967",
+          "1557",
+          "394"
+        ]
+      }
+    },
+    {
+      "name": "Student Country",
+      "role": "feature",
+      "semantic_type": "categorical",
+      "nullable": false,
+      "missing_tokens": [],
+      "parse_format": null,
+      "impute_strategy": "mode",
+      "profile_stats": {
+        "missing_rate": 0.0,
+        "unique_count": 8,
+        "unique_ratio": 0.001048,
+        "example_values": [
+          "Portugal",
+          "Italy",
+          "Lithuania",
+          "Slovenia",
+          "Ireland"
+        ]
+      }
+    },
+    {
+      "name": "Question ID",
+      "role": "feature",
+      "semantic_type": "numeric",
+      "nullable": false,
+      "missing_tokens": [],
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+          "796",
+          "453",
+          "87",
+          "325"
+        ]
+      }
+    },
+    {
+      "name": "Type of Answer",
+      "role": "target",
+      "semantic_type": "boolean",
+      "nullable": false,
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+          "0",
+          "1"
+        ]
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+    },
+    {
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+      "role": "feature",
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+        "example_values": [
+          "Advanced",
+          "Basic"
+        ]
+      }
+    },
+    {
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+      "role": "feature",
+      "semantic_type": "text",
+      "nullable": false,
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+        "unique_count": 14,
+        "unique_ratio": 0.001833,
+        "example_values": [
+          "Complex Numbers",
+          "Fundamental Mathematics",
+          "Linear Algebra",
+          "Real Functions of a single variable",
+          "Analytic Geometry"
+        ]
+      }
+    },
+    {
+      "name": "Subtopic",
+      "role": "feature",
+      "semantic_type": "text",
+      "nullable": false,
+      "missing_tokens": [],
+      "parse_format": null,
+      "impute_strategy": "keep_raw",
+      "profile_stats": {
+        "missing_rate": 0.0,
+        "unique_count": 24,
+        "unique_ratio": 0.003143,
+        "example_values": [
+          "Complex Numbers",
+          "Algebraic expressions, Equations, and Inequalities",
+          "Vector Spaces",
+          "Limits and Continuity",
+          "Linear Transformations"
+        ]
+      }
+    },
+    {
+      "name": "Keywords",
+      "role": "feature",
+      "semantic_type": "text",
+      "nullable": false,
+      "missing_tokens": [],
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+      "impute_strategy": "keep_raw",
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+        "unique_count": 360,
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+        "example_values": [
+          "Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part",
+          "Logarithmic function,Exponential function,Simplify expressions",
+          "Linear independence,Span,Linear dependence",
+          "Indeterminate forms,Limits",
+          "Range,Kernel"
+        ]
+      }
+    }
+  ],
+  "public_manifest": "/data/jialinzhang/SynthesizePipeline-server/output-SpecializedModels/c6/ctgan/ctgan-c6-20260422_025941/public_gate/staged_input_manifest.json",
+  "train_csv": "/data/jialinzhang/SynthesizePipeline-server/output-SpecializedModels/c6/ctgan/ctgan-c6-20260422_025941/staged/public/train.csv",
+  "val_csv": "/data/jialinzhang/SynthesizePipeline-server/output-SpecializedModels/c6/ctgan/ctgan-c6-20260422_025941/staged/public/val.csv",
+  "test_csv": "/data/jialinzhang/SynthesizePipeline-server/output-SpecializedModels/c6/ctgan/ctgan-c6-20260422_025941/staged/public/test.csv",
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+}

SynthData0523/main/c6/ctgan/ctgan-c6-20260422_025941/staged/public/staged_features.json

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+[
+  {
+    "feature_name": "Student ID",
+    "data_type": "continuous",
+    "is_target": false
+  },
+  {
+    "feature_name": "Student Country",
+    "data_type": "categorical",
+    "is_target": false
+  },
+  {
+    "feature_name": "Question ID",
+    "data_type": "continuous",
+    "is_target": false
+  },
+  {
+    "feature_name": "Type of Answer",
+    "data_type": "binary",
+    "is_target": true
+  },
+  {
+    "feature_name": "Question Level",
+    "data_type": "categorical",
+    "is_target": false
+  },
+  {
+    "feature_name": "Topic",
+    "data_type": "categorical",
+    "is_target": false
+  },
+  {
+    "feature_name": "Subtopic",
+    "data_type": "categorical",
+    "is_target": false
+  },
+  {
+    "feature_name": "Keywords",
+    "data_type": "categorical",
+    "is_target": false
+  }
+]

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SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_gen.py

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+
+import joblib, pandas as pd
+m, meta = joblib.load(r'/work/output-Benchmark-trainonly-v1/c6/forestdiffusion/forest-c6-20260510_205308/forestdiffusion_model.joblib')
+# generate：batch_size 为样本数
+arr = m.generate(batch_size=int(7636))
+df = pd.DataFrame(arr, columns=meta["column_names"])
+df.to_csv(r'/work/output-Benchmark-trainonly-v1/c6/forestdiffusion/forest-c6-20260510_205308/forest-c6-7636-20260510_205311.csv', index=False)
+print("saved", len(df))

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SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_train.py

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+
+import os, shutil, json
+with open('/tmp/pgrep', 'w') as _f:
+    _f.write("#!/usr/bin/env python3\n")
+    _f.write("import subprocess, sys\n")
+    _f.write("ppid = sys.argv[-1]\n")
+    _f.write("out = subprocess.check_output(['ps', '-o', 'pid=', '--ppid', str(ppid)], text=True)\n")
+    _f.write("print(out, end='')\n")
+os.chmod('/tmp/pgrep', 0o755)
+os.environ['PATH'] = '/tmp:' + os.environ.get('PATH', '')
+shutil.copy(r'/work/output-Benchmark-trainonly-v1/c6/forestdiffusion/forest-c6-20260510_205308/_fd_X_host.npy', '/tmp/fd_X.npy')
+with open(r'/work/output-Benchmark-trainonly-v1/c6/forestdiffusion/forest-c6-20260510_205308/_fd_meta_host.json') as f:
+    open('/tmp/fd_meta.json','w').write(f.read())
+
+import numpy as np, joblib, json, os
+from ForestDiffusion import ForestDiffusionModel
+X = np.load("/tmp/fd_X.npy")
+with open("/tmp/fd_meta.json") as f:
+    meta = json.load(f)
+cat_indexes = meta["cat_indexes"]
+print(
+    "[ForestDiffusion] train config: "
+    f"rows={X.shape[0]} cols={X.shape[1]} n_t=2 "
+    f"n_estimators=1 duplicate_K=1 n_jobs=1 "
+    f"max_depth=2 xgb_verbosity=0 xgb_nthread=1",
+    flush=True,
+)
+m = ForestDiffusionModel(
+    X, n_t=2, n_estimators=1, duplicate_K=1, n_jobs=1,
+    model="xgboost", max_depth=2, tree_method="hist", cat_indexes=cat_indexes,
+    verbosity=0, nthread=1,
+)
+joblib.dump((m, meta), "/tmp/fd_model.joblib")
+print("ForestDiffusion train OK")
+
+shutil.copy('/tmp/fd_model.joblib', r'/work/output-Benchmark-trainonly-v1/c6/forestdiffusion/forest-c6-20260510_205308/forestdiffusion_model.joblib')

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"210": "7___CATEGORICAL___Keywords___Euclidean spaces,Orthogonal basis", "211": "7___CATEGORICAL___Keywords___Euclidean spaces,Orthogonal basis,Basis", "212": "7___CATEGORICAL___Keywords___Event,Addition, multiplication, and total probability rules,Independence", "213": "7___CATEGORICAL___Keywords___Event,Addition, multiplication, and total probability rules,Sample space", "214": "7___CATEGORICAL___Keywords___Event,Axioms of probability", "215": "7___CATEGORICAL___Keywords___Event,Axioms of probability,Addition, multiplication, and total probability rules,Sample space", "216": "7___CATEGORICAL___Keywords___Event,Axioms of probability,Sample space", "217": "7___CATEGORICAL___Keywords___Event,Independence,Addition, multiplication, and total probability rules", "218": "7___CATEGORICAL___Keywords___Event,Sample space", "219": "7___CATEGORICAL___Keywords___Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability", "220": "7___CATEGORICAL___Keywords___Exact differential form,Cauchy problem", "221": "7___CATEGORICAL___Keywords___Excel solver add-in,Simplex method,Linear programming", "222": "7___CATEGORICAL___Keywords___Excel solver add-in,Simplex method,Linear programming,Transportation problem", "223": "7___CATEGORICAL___Keywords___Exponential function,Simplify expressions", "224": "7___CATEGORICAL___Keywords___Exponential rule", "225": "7___CATEGORICAL___Keywords___First order", "226": "7___CATEGORICAL___Keywords___First order,Directional derivative", "227": "7___CATEGORICAL___Keywords___First order,Directional derivative,Gradient", "228": "7___CATEGORICAL___Keywords___First order,Gradient", "229": "7___CATEGORICAL___Keywords___First order,Second order", "230": "7___CATEGORICAL___Keywords___Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median", "231": "7___CATEGORICAL___Keywords___Frequency,Quantile,Mean,Variance,Median,Mode", "232": "7___CATEGORICAL___Keywords___Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency", "233": "7___CATEGORICAL___Keywords___Fundamental theorem of Calculus,Volume of revolution", "234": "7___CATEGORICAL___Keywords___Geometric solids", "235": "7___CATEGORICAL___Keywords___Geometric solids,Geometrical figures,Classification of geometric solids", "236": "7___CATEGORICAL___Keywords___Geometrical figures", "237": "7___CATEGORICAL___Keywords___Geometrical figures,Polygons", "238": "7___CATEGORICAL___Keywords___Geometrical figures,Quadrilaterals,Rhombus", "239": "7___CATEGORICAL___Keywords___Geometrical figures,Triangles,Classification of geometrical figures", "240": "7___CATEGORICAL___Keywords___Gradient,Directional derivative", "241": "7___CATEGORICAL___Keywords___Gradient,First order", "242": "7___CATEGORICAL___Keywords___Gradient,First order,Directional derivative", "243": "7___CATEGORICAL___Keywords___Graphical method,Linear programming", "244": "7___CATEGORICAL___Keywords___Homogeneous equation", "245": "7___CATEGORICAL___Keywords___Homogeneous equation,Cauchy problem", "246": "7___CATEGORICAL___Keywords___Imaginary part,Complex plane ,Real part", "247": "7___CATEGORICAL___Keywords___Imaginary part,Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers", "248": "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers", "249": "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Operations with complex numbers,Real part,Equations involving complex numbers", "250": "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part", "251": "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part", "252": "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system", "253": "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system", "254": "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Homogeneous system,Consistent system", "255": "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system", "256": "7___CATEGORICAL___Keywords___Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system", "257": "7___CATEGORICAL___Keywords___Indeterminate forms,Limits", "258": "7___CATEGORICAL___Keywords___Injective linear application,Invertible linear operator,Isomorphism", "259": "7___CATEGORICAL___Keywords___Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism", "260": "7___CATEGORICAL___Keywords___Injective linear application,Isomorphism", "261": "7___CATEGORICAL___Keywords___Injective linear application,Range,Kernel,Isomorphism", "262": "7___CATEGORICAL___Keywords___Integration by parts", "263": "7___CATEGORICAL___Keywords___Integration by parts,Fundamental theorem of Calculus", "264": "7___CATEGORICAL___Keywords___Integration by parts,Substitution,Simple integration,Direct inspection", "265": "7___CATEGORICAL___Keywords___Intersection,Cartesian equations of a plane", "266": "7___CATEGORICAL___Keywords___Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix", "267": "7___CATEGORICAL___Keywords___Inverse matrix ,Determinant computation,Determinant properties,Matrix operations", "268": "7___CATEGORICAL___Keywords___Invertible linear operator,Isomorphism,Injective linear application", "269": "7___CATEGORICAL___Keywords___Iterate integrals", "270": "7___CATEGORICAL___Keywords___Iterate integrals,Area ,y-simple region (type I),Cartesian coordinates", "271": "7___CATEGORICAL___Keywords___Iterate integrals,Cartesian coordinates,y-simple region (type I)", "272": "7___CATEGORICAL___Keywords___Kernel,Isomorphism,Injective linear application,Range", "273": "7___CATEGORICAL___Keywords___Lagrange multipliers,Maximum,Minimum", "274": "7___CATEGORICAL___Keywords___Lagrange multipliers,Minimum,Maximum,Stationary point", "275": "7___CATEGORICAL___Keywords___Lagrange multipliers,Optimal solution,Minimum,Maximum", "276": "7___CATEGORICAL___Keywords___Lagrange's interpolation,Polynomial interpolation", "277": "7___CATEGORICAL___Keywords___Limits", "278": "7___CATEGORICAL___Keywords___Limits,Indeterminate forms", "279": "7___CATEGORICAL___Keywords___Linear application,Composition of linear applications", "280": "7___CATEGORICAL___Keywords___Linear application,Linearity", "281": "7___CATEGORICAL___Keywords___Linear combination,Span", "282": "7___CATEGORICAL___Keywords___Linear combination,Subspace,Span", "283": "7___CATEGORICAL___Keywords___Linear differential equation", "284": "7___CATEGORICAL___Keywords___Linear differential equation,Homogeneous equation", "285": "7___CATEGORICAL___Keywords___Linear differential equation,Integral curve,Cauchy problem", "286": "7___CATEGORICAL___Keywords___Linear equations,Quadratic equations,Simplify expressions", "287": "7___CATEGORICAL___Keywords___Linear independence,Span,Linear dependence", "288": "7___CATEGORICAL___Keywords___Linear independence,Subspace,Linear combination,Linear dependence,Span", "289": "7___CATEGORICAL___Keywords___Linear programming", "290": "7___CATEGORICAL___Keywords___Linear programming,Assignment problem,Excel solver add-in,Simplex method", "291": "7___CATEGORICAL___Keywords___Linear programming,Excel solver add-in,Simplex method", "292": "7___CATEGORICAL___Keywords___Linear regression", "293": "7___CATEGORICAL___Keywords___Linearity,Invertible linear operator,Composition of linear applications,Linear application", "294": "7___CATEGORICAL___Keywords___Linearity,Linear application", "295": "7___CATEGORICAL___Keywords___Linearity,Matrix of a linear transformation,Linear application", "296": "7___CATEGORICAL___Keywords___Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties", "297": "7___CATEGORICAL___Keywords___Linearly independent rows,Matrix rank", "298": "7___CATEGORICAL___Keywords___Locus,Distance", "299": "7___CATEGORICAL___Keywords___Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity", "300": "7___CATEGORICAL___Keywords___Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality", "301": "7___CATEGORICAL___Keywords___Logarithmic function,Exponential function,Simplify expressions", "302": "7___CATEGORICAL___Keywords___Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule", "303": "7___CATEGORICAL___Keywords___Logarithmic rule,Power rule,Trigonometric rules", "304": "7___CATEGORICAL___Keywords___Logarithmic rule,Product rule,Trigonometric rules", "305": "7___CATEGORICAL___Keywords___Logarithmic rule,Trigonometric rules", "306": "7___CATEGORICAL___Keywords___Matrix equivalent - echelon,Matrix rank,Matrix operations,Hermitian matrix,Matrix multiplication,Symmetric matrix,Linearly independent rows,Commuting matrices,Determinant computation,Determinant properties,Inverse matrix ,Solve matrix equation", "307": "7___CATEGORICAL___Keywords___Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation", "308": "7___CATEGORICAL___Keywords___Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Hermitian matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Matrix equivalent - echelon", "309": "7___CATEGORICAL___Keywords___Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank", "310": "7___CATEGORICAL___Keywords___Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank", "311": "7___CATEGORICAL___Keywords___Matrix multiplication,Symmetric matrix,Matrix operations", "312": "7___CATEGORICAL___Keywords___Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties", "313": "7___CATEGORICAL___Keywords___Matrix of a linear transformation", "314": "7___CATEGORICAL___Keywords___Matrix of a linear transformation,Linear application,Linearity", "315": "7___CATEGORICAL___Keywords___Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix", "316": "7___CATEGORICAL___Keywords___Matrix operations,Determinant computation,Determinant properties,Inverse matrix", "317": "7___CATEGORICAL___Keywords___Matrix operations,Inverse matrix", "318": "7___CATEGORICAL___Keywords___Matrix operations,Matrix multiplication", "319": "7___CATEGORICAL___Keywords___Matrix operations,Matrix multiplication,Determinant computation,Determinant properties", "320": "7___CATEGORICAL___Keywords___Matrix rank,Linearly independent rows", "321": "7___CATEGORICAL___Keywords___Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation", "322": "7___CATEGORICAL___Keywords___Mean,Median,Mode", "323": "7___CATEGORICAL___Keywords___Mean,Median,Outliers,Interquartile range", "324": "7___CATEGORICAL___Keywords___Mean,Variance,Standard deviation,Median,Mode", "325": "7___CATEGORICAL___Keywords___Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance", "326": "7___CATEGORICAL___Keywords___Minimum,Maximum,Lagrange multipliers,Saddle point,Unconstrained optimization,Second derivative test", "327": "7___CATEGORICAL___Keywords___Minimum,Maximum,Stationary point,Second derivative test,Unconstrained optimization,Saddle point,Optimal solution", "328": "7___CATEGORICAL___Keywords___Minimum,Stationary point,Maximum,Saddle point,Optimal solution", "329": "7___CATEGORICAL___Keywords___Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median", "330": "7___CATEGORICAL___Keywords___Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number", "331": "7___CATEGORICAL___Keywords___Newton\u2019s interpolation,Polynomial interpolation", "332": "7___CATEGORICAL___Keywords___Newton\u2019s method,Nonlinear equation", "333": "7___CATEGORICAL___Keywords___Nonlinear equation,Newton\u2019s method", "334": "7___CATEGORICAL___Keywords___Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas", "335": "7___CATEGORICAL___Keywords___Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas", "336": "7___CATEGORICAL___Keywords___Operations with complex numbers", "337": "7___CATEGORICAL___Keywords___Operations with complex numbers,Conjugate number", "338": "7___CATEGORICAL___Keywords___Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part", "339": "7___CATEGORICAL___Keywords___Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form", "340": "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Maximum", "341": "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point", "342": "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Maximum,Stationary point,Saddle point", "343": "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Stationary point,Maximum,Saddle point", "344": "7___CATEGORICAL___Keywords___Optimal solution,Second derivative test,Minimum,Maximum,Stationary point,Saddle point", "345": "7___CATEGORICAL___Keywords___Optimal solution,Stationary point,Minimum,Maximum,Saddle point", "346": "7___CATEGORICAL___Keywords___Orthogonal projection,Distance,Cross product,Orthogonality", "347": "7___CATEGORICAL___Keywords___Orthogonality", "348": "7___CATEGORICAL___Keywords___Orthogonality,Cross product", "349": "7___CATEGORICAL___Keywords___Orthogonality,Cross product,Distance", "350": "7___CATEGORICAL___Keywords___Orthogonality,Distance,Cross product", "351": "7___CATEGORICAL___Keywords___Orthogonality,Distance,Scalar product", "352": "7___CATEGORICAL___Keywords___Orthogonality,Locus,Scalar product,Cross product,Collinearity", "353": "7___CATEGORICAL___Keywords___Orthogonality,Orthogonal projection,Cross product,Scalar product", "354": "7___CATEGORICAL___Keywords___Orthogonality,Orthogonal projection,Distance", "355": "7___CATEGORICAL___Keywords___Orthogonality,Scalar product", "356": "7___CATEGORICAL___Keywords___Path,Cycle and circuit", "357": "7___CATEGORICAL___Keywords___Path,Simple graph,Cycle and circuit", "358": "7___CATEGORICAL___Keywords___Planar graph", "359": "7___CATEGORICAL___Keywords___Platonic solids", "360": "7___CATEGORICAL___Keywords___Platonic solids,Regular polygon", "361": "7___CATEGORICAL___Keywords___Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas", "362": "7___CATEGORICAL___Keywords___Polygons", "363": "7___CATEGORICAL___Keywords___Polygons,Geometric transformations,Geometrical figures", "364": "7___CATEGORICAL___Keywords___Polygons,Geometrical figures", "365": "7___CATEGORICAL___Keywords___Polygons,Regular polygon", "366": "7___CATEGORICAL___Keywords___Polygons,Triangles", "367": "7___CATEGORICAL___Keywords___Polyhedrons,Geometric solids,Classification of geometric solids", "368": "7___CATEGORICAL___Keywords___Polyhedrons,Platonic solids,Geometric solids", "369": "7___CATEGORICAL___Keywords___Polynomial interpolation,Lagrange's interpolation", "370": "7___CATEGORICAL___Keywords___Polynomial interpolation,Newton\u2019s interpolation", "371": "7___CATEGORICAL___Keywords___Population,Sample", "372": "7___CATEGORICAL___Keywords___Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean", "373": "7___CATEGORICAL___Keywords___Postoptimality analysis,Duality theory,Excel solver add-in,Simplex method,Linear programming,Sensitivity analysis", "374": "7___CATEGORICAL___Keywords___Power of trigonometric functions", "375": "7___CATEGORICAL___Keywords___Power rule,Product rule", "376": "7___CATEGORICAL___Keywords___Power rule,Quotient rule,Product rule,Trigonometric rules", "377": "7___CATEGORICAL___Keywords___Power rule,Trigonometric rules,Logarithmic rule", "378": "7___CATEGORICAL___Keywords___Power rule,Trigonometric rules,Logarithmic rule,First order", "379": "7___CATEGORICAL___Keywords___Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form", "380": "7___CATEGORICAL___Keywords___Product rule,Logarithmic rule,Trigonometric rules", "381": "7___CATEGORICAL___Keywords___Product rule,Trigonometric rules", "382": "7___CATEGORICAL___Keywords___Product rule,Trigonometric rules,Exponential rule", "383": "7___CATEGORICAL___Keywords___Product rule,Trigonometric rules,Logarithmic rule", "384": "7___CATEGORICAL___Keywords___Product rule,Trigonometric rules,Quotient rule", "385": "7___CATEGORICAL___Keywords___Quadratic equations,Simplify expressions,Linear equations", "386": "7___CATEGORICAL___Keywords___Quadrilaterals,Geometrical figures", "387": "7___CATEGORICAL___Keywords___Quadrilaterals,Geometrical figures,Classification of geometrical figures", "388": "7___CATEGORICAL___Keywords___Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures", "389": "7___CATEGORICAL___Keywords___Quadrilaterals,Rhombus", "390": "7___CATEGORICAL___Keywords___Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode", "391": "7___CATEGORICAL___Keywords___Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode", "392": "7___CATEGORICAL___Keywords___Quotient rule", "393": "7___CATEGORICAL___Keywords___Quotient rule,Product rule,Power rule,Trigonometric rules", "394": "7___CATEGORICAL___Keywords___Quotient rule,Product rule,Trigonometric rules", "395": "7___CATEGORICAL___Keywords___Quotient rule,Trigonometric rules", "396": "7___CATEGORICAL___Keywords___Quotient rule,Trigonometric rules,Logarithmic rule,Product rule", "397": "7___CATEGORICAL___Keywords___Range,Kernel", "398": "7___CATEGORICAL___Keywords___Range,Kernel,Isomorphism", "399": "7___CATEGORICAL___Keywords___Range,Kernel,Isomorphism,Injective linear application", "400": "7___CATEGORICAL___Keywords___Range,Kernel,Matrix of a linear transformation", "401": "7___CATEGORICAL___Keywords___Rational functions", "402": "7___CATEGORICAL___Keywords___Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number", "403": "7___CATEGORICAL___Keywords___Rotation,Linear application", "404": "7___CATEGORICAL___Keywords___Saddle point,Optimal solution,Minimum,Maximum,Stationary point", "405": "7___CATEGORICAL___Keywords___Sample space,Addition, multiplication, and total probability rules,Axioms of probability,Event", "406": "7___CATEGORICAL___Keywords___Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability", "407": "7___CATEGORICAL___Keywords___Sample space,Event", "408": "7___CATEGORICAL___Keywords___Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile", "409": "7___CATEGORICAL___Keywords___Scalar product,Orthogonality,Orthogonal projection,Distance", "410": "7___CATEGORICAL___Keywords___Second order", "411": "7___CATEGORICAL___Keywords___Second order,First order", "412": "7___CATEGORICAL___Keywords___Sensitivity analysis,Postoptimality analysis,Duality theory,Excel solver add-in,Simplex method,Linear programming", "413": "7___CATEGORICAL___Keywords___Separable variables equation", "414": "7___CATEGORICAL___Keywords___Shortest path,Tree,Spanning tree,Path", "415": "7___CATEGORICAL___Keywords___Simple graph", "416": "7___CATEGORICAL___Keywords___Simple graph,Adjacency matrix", "417": "7___CATEGORICAL___Keywords___Simple integration,Direct inspection", "418": "7___CATEGORICAL___Keywords___Simplex method,Duality theory", "419": "7___CATEGORICAL___Keywords___Simplex method,Linear programming,Assignment problem,Excel solver add-in", "420": "7___CATEGORICAL___Keywords___Simplify expressions", "421": "7___CATEGORICAL___Keywords___Simplify expressions,Exponential function", "422": "7___CATEGORICAL___Keywords___Simplify expressions,Linear equations,Quadratic equations", "423": "7___CATEGORICAL___Keywords___Simplify expressions,Logarithmic function", "424": "7___CATEGORICAL___Keywords___Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system", "425": "7___CATEGORICAL___Keywords___Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system,Inconsistent system", "426": "7___CATEGORICAL___Keywords___Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Determinant properties,Matrix rank,Hermitian matrix,Matrix operations,Symmetric matrix,Matrix multiplication,Linearly independent rows,Commuting matrices", "427": "7___CATEGORICAL___Keywords___Span,Linear combination,Subspace", "428": "7___CATEGORICAL___Keywords___Span,Subspace,Linear combination", "429": "7___CATEGORICAL___Keywords___Spanning tree,Shortest path,Path,Tree", "430": "7___CATEGORICAL___Keywords___Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue", "431": "7___CATEGORICAL___Keywords___Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system", "432": "7___CATEGORICAL___Keywords___Square roots,Simplify expressions", "433": "7___CATEGORICAL___Keywords___Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean", "434": "7___CATEGORICAL___Keywords___Stationary point,Maximum,Saddle point,Optimal solution,Minimum", "435": "7___CATEGORICAL___Keywords___Stationary point,Maximum,Saddle point,Second derivative test,Optimal solution,Minimum", "436": "7___CATEGORICAL___Keywords___Stationary point,Minimum,Optimal solution,Lagrange multipliers", "437": "7___CATEGORICAL___Keywords___Stem and Leaf diagram,Relative frequency,Sample,Frequency", "438": "7___CATEGORICAL___Keywords___Student distribution,Confidence interval,Point estimate,Hypothesis testing", "439": "7___CATEGORICAL___Keywords___Student distribution,Hypothesis testing", "440": "7___CATEGORICAL___Keywords___Subset", "441": "7___CATEGORICAL___Keywords___Subspace", "442": "7___CATEGORICAL___Keywords___Subspace,Basis,Dimension", "443": "7___CATEGORICAL___Keywords___Subspace,Change-of-basis matrix,Linear 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