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"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": [], + "parse_format": null, + "impute_strategy": "median", + "profile_stats": { + "missing_rate": 0.0, + "unique_count": 796, + "unique_ratio": 0.104243, + "example_values": [ + "346", + "796", + "453", + "87", + "325" + ] + } + }, + { + "name": "Type of Answer", + "role": "target", + "semantic_type": "boolean", + "nullable": false, + "missing_tokens": [], + "parse_format": null, + "impute_strategy": "mode", + 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a/SynthData0523/main/c6/ctgan/ctgan-c6-20260422_025941/staged/public/staged_features.json b/SynthData0523/main/c6/ctgan/ctgan-c6-20260422_025941/staged/public/staged_features.json new file mode 100644 index 0000000000000000000000000000000000000000..5523fb7a16718db5c4122f8381d3cff51e337c45 --- /dev/null +++ b/SynthData0523/main/c6/ctgan/ctgan-c6-20260422_025941/staged/public/staged_features.json @@ -0,0 +1,42 @@ +[ + { + "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": 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0000000000000000000000000000000000000000..a44f521b78e3581d24e9830d4bfb6d4e12ae7f26 --- /dev/null +++ b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_X_host.npy @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:42ce9dd53b247a3c19042aaa57617a99b3f630e320a65896ef869cb6f571a075 +size 32896 diff --git a/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_gen.py b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_gen.py new file mode 100644 index 0000000000000000000000000000000000000000..afa0dc5ed9cb114196ff701c43ef8160bd6b29d1 --- /dev/null +++ b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_gen.py @@ -0,0 +1,8 @@ + +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)) diff --git a/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_meta_host.json b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_meta_host.json new file mode 100644 index 0000000000000000000000000000000000000000..53dcd54eabd6b7fe3a696fcee499f383e430b0f8 --- /dev/null +++ b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_meta_host.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3146442992cf09791afa81e4f3fc08f4c0d4fc2d757ccb7e9a8a270e0ba1cc81 +size 167 diff --git a/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_train.py b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_train.py new file mode 100644 index 0000000000000000000000000000000000000000..2ef52bf6c9e5a8a0278d0db521539c53e29dc31c --- /dev/null +++ b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/_fd_train.py @@ -0,0 +1,36 @@ + +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') diff --git a/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/forest-c6-7636-20260510_205311.csv b/SynthData0523/main/c6/forestdiffusion/forest-c6-20260510_205308/forest-c6-7636-20260510_205311.csv new file mode 100644 index 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"6___CATEGORICAL___Subtopic___Complex Numbers", "104": "6___CATEGORICAL___Subtopic___Definite Integrals", "105": "6___CATEGORICAL___Subtopic___Derivatives", "106": "6___CATEGORICAL___Subtopic___Differential Equations", "107": "6___CATEGORICAL___Subtopic___Domain, Image and Graphics", "108": "6___CATEGORICAL___Subtopic___Double Integration", "109": "6___CATEGORICAL___Subtopic___Eigenvalues and Eigenvectors", "110": "6___CATEGORICAL___Subtopic___Elementary Geometry", "111": "6___CATEGORICAL___Subtopic___Graph Theory", "112": "6___CATEGORICAL___Subtopic___Integration Techniques", "113": "6___CATEGORICAL___Subtopic___Limits and Continuity", "114": "6___CATEGORICAL___Subtopic___Linear Optimization", "115": "6___CATEGORICAL___Subtopic___Linear Systems", "116": "6___CATEGORICAL___Subtopic___Linear Transformations", "117": "6___CATEGORICAL___Subtopic___Matrices and Determinants", "118": "6___CATEGORICAL___Subtopic___Nonlinear Optimization", "119": "6___CATEGORICAL___Subtopic___Numerical Methods", "120": "6___CATEGORICAL___Subtopic___Partial Differentiation", "121": "6___CATEGORICAL___Subtopic___Probability", "122": "6___CATEGORICAL___Subtopic___Set Theory", "123": "6___CATEGORICAL___Subtopic___Statistics", "124": "6___CATEGORICAL___Subtopic___Vector Spaces", "125": "7___CATEGORICAL___Keywords___Addition, multiplication, and total probability rules", "126": "7___CATEGORICAL___Keywords___Addition, multiplication, and total probability rules,Independence,Event", "127": "7___CATEGORICAL___Keywords___Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability", "128": "7___CATEGORICAL___Keywords___Adjacency matrix", "129": "7___CATEGORICAL___Keywords___Adjacency matrix,Simple graph", "130": "7___CATEGORICAL___Keywords___Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form", "131": "7___CATEGORICAL___Keywords___Algebraic form,Principal 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"7___CATEGORICAL___Keywords___Bayes' Theorem,Conditional probability", "142": "7___CATEGORICAL___Keywords___Bernoulli equation,Linear differential equation", "143": "7___CATEGORICAL___Keywords___Cartesian coordinates,x-simple region (type II),Changing order of integration", "144": "7___CATEGORICAL___Keywords___Cartesian equations of a line,Orthogonality,Collinearity", "145": "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Cartesian equations of a line", "146": "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Cartesian equations of a line,Collinearity", "147": "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Intersection,Cartesian equations of a line", "148": "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line", "149": "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Orthogonality", "150": "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Orthogonality,Locus,Distance", 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"7___CATEGORICAL___Keywords___Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial", "205": "7___CATEGORICAL___Keywords___Eigenvector,Eigenvalue", "206": "7___CATEGORICAL___Keywords___Eigenvector,Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue", "207": "7___CATEGORICAL___Keywords___Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue", "208": "7___CATEGORICAL___Keywords___Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue,Diagonalization", "209": "7___CATEGORICAL___Keywords___Equations involving complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Real part", "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 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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 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Equations": 106, "6___CATEGORICAL___Subtopic___Domain, Image and Graphics": 107, "6___CATEGORICAL___Subtopic___Double Integration": 108, "6___CATEGORICAL___Subtopic___Eigenvalues and Eigenvectors": 109, "6___CATEGORICAL___Subtopic___Elementary Geometry": 110, "6___CATEGORICAL___Subtopic___Graph Theory": 111, "6___CATEGORICAL___Subtopic___Integration Techniques": 112, "6___CATEGORICAL___Subtopic___Limits and Continuity": 113, "6___CATEGORICAL___Subtopic___Linear Optimization": 114, "6___CATEGORICAL___Subtopic___Linear Systems": 115, "6___CATEGORICAL___Subtopic___Linear Transformations": 116, "6___CATEGORICAL___Subtopic___Matrices and Determinants": 117, "6___CATEGORICAL___Subtopic___Nonlinear Optimization": 118, "6___CATEGORICAL___Subtopic___Numerical Methods": 119, "6___CATEGORICAL___Subtopic___Partial Differentiation": 120, "6___CATEGORICAL___Subtopic___Probability": 121, "6___CATEGORICAL___Subtopic___Set Theory": 122, "6___CATEGORICAL___Subtopic___Statistics": 123, "6___CATEGORICAL___Subtopic___Vector Spaces": 124, "7___CATEGORICAL___Keywords___Addition, multiplication, and total probability rules": 125, "7___CATEGORICAL___Keywords___Addition, multiplication, and total probability rules,Independence,Event": 126, "7___CATEGORICAL___Keywords___Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability": 127, "7___CATEGORICAL___Keywords___Adjacency matrix": 128, "7___CATEGORICAL___Keywords___Adjacency matrix,Simple graph": 129, "7___CATEGORICAL___Keywords___Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form": 130, "7___CATEGORICAL___Keywords___Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number": 131, "7___CATEGORICAL___Keywords___Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number,Modulus of a complex number": 132, "7___CATEGORICAL___Keywords___Area of a planar region ,Fundamental theorem of Calculus": 133, "7___CATEGORICAL___Keywords___Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space": 134, "7___CATEGORICAL___Keywords___Axioms of probability,Event,Independence,Addition, multiplication, and total probability rules,Sample space": 135, "7___CATEGORICAL___Keywords___Basis": 136, "7___CATEGORICAL___Keywords___Basis,Dimension": 137, "7___CATEGORICAL___Keywords___Basis,Span": 138, "7___CATEGORICAL___Keywords___Basis,Span,Change-of-basis matrix": 139, "7___CATEGORICAL___Keywords___Basis,Span,Subspace,Linear combination,Dimension": 140, "7___CATEGORICAL___Keywords___Bayes' Theorem,Conditional probability": 141, "7___CATEGORICAL___Keywords___Bernoulli equation,Linear differential equation": 142, "7___CATEGORICAL___Keywords___Cartesian coordinates,x-simple region (type II),Changing order of integration": 143, "7___CATEGORICAL___Keywords___Cartesian equations of a line,Orthogonality,Collinearity": 144, "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Cartesian equations of a line": 145, "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Cartesian equations of a line,Collinearity": 146, "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Intersection,Cartesian equations of a line": 147, "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line": 148, "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Orthogonality": 149, "7___CATEGORICAL___Keywords___Cartesian equations of a plane,Orthogonality,Locus,Distance": 150, "7___CATEGORICAL___Keywords___Cauchy problem,Exact differential form": 151, "7___CATEGORICAL___Keywords___Chain rule": 152, "7___CATEGORICAL___Keywords___Change-of-basis matrix,Span,Basis,Dimension": 153, "7___CATEGORICAL___Keywords___Changing order of integration,Cartesian coordinates": 154, "7___CATEGORICAL___Keywords___Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum": 155, "7___CATEGORICAL___Keywords___Chi square distribution,Student distribution,Quantile,Hypothesis testing": 156, "7___CATEGORICAL___Keywords___Chromatic number": 157, "7___CATEGORICAL___Keywords___Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product": 158, "7___CATEGORICAL___Keywords___Collinearity,Locus,Orthogonality,Orthogonal projection,Scalar product,Distance": 159, "7___CATEGORICAL___Keywords___Collinearity,Orthogonality,Distance,Scalar product": 160, "7___CATEGORICAL___Keywords___Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations": 161, "7___CATEGORICAL___Keywords___Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations": 162, "7___CATEGORICAL___Keywords___Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations": 163, "7___CATEGORICAL___Keywords___Complex plane": 164, "7___CATEGORICAL___Keywords___Conditional probability": 165, "7___CATEGORICAL___Keywords___Conditional probability,Bayes' Theorem": 166, "7___CATEGORICAL___Keywords___Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part": 167, "7___CATEGORICAL___Keywords___Conjugate number,Operations with complex numbers": 168, "7___CATEGORICAL___Keywords___Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part": 169, "7___CATEGORICAL___Keywords___Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number": 170, "7___CATEGORICAL___Keywords___Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part": 171, "7___CATEGORICAL___Keywords___Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system": 172, "7___CATEGORICAL___Keywords___Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system": 173, "7___CATEGORICAL___Keywords___Continuity,Limits": 174, "7___CATEGORICAL___Keywords___Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line": 175, "7___CATEGORICAL___Keywords___Cross product,Orthogonality": 176, "7___CATEGORICAL___Keywords___Cross product,Orthogonality,Scalar product": 177, "7___CATEGORICAL___Keywords___Cycle and circuit,Shortest path,Path,Planar graph,Tree,Adjacency matrix,Chromatic number,Simple graph,Spanning tree,Incidence matrix": 178, "7___CATEGORICAL___Keywords___Determinant computation,Determinant properties": 179, "7___CATEGORICAL___Keywords___Determinant computation,Determinant properties,Inverse matrix ,Matrix operations": 180, "7___CATEGORICAL___Keywords___Determinant computation,Determinant properties,Solve matrix equation": 181, "7___CATEGORICAL___Keywords___Determinant properties,Inverse matrix ,Solve matrix equation,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Commuting matrices,Determinant computation": 182, "7___CATEGORICAL___Keywords___Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication": 183, "7___CATEGORICAL___Keywords___Direct inspection": 184, "7___CATEGORICAL___Keywords___Direct inspection,Simple integration": 185, "7___CATEGORICAL___Keywords___Direct integrals ,Fundamental theorem of Calculus": 186, "7___CATEGORICAL___Keywords___Directional derivative,Gradient": 187, "7___CATEGORICAL___Keywords___Directional derivative,Gradient,First order,Second order": 188, "7___CATEGORICAL___Keywords___Distance,Cross product,Orthogonality": 189, "7___CATEGORICAL___Keywords___Distance,Orthogonal projection,Orthogonality": 190, "7___CATEGORICAL___Keywords___Distance,Orthogonality,Locus": 191, "7___CATEGORICAL___Keywords___Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus": 192, "7___CATEGORICAL___Keywords___Distance,Scalar product,Cross product,Orthogonality": 193, "7___CATEGORICAL___Keywords___Domain": 194, "7___CATEGORICAL___Keywords___Domain,Image of a function": 195, "7___CATEGORICAL___Keywords___Duality theory,Excel solver add-in,Simplex method,Linear programming,Sensitivity analysis,Postoptimality analysis": 196, "7___CATEGORICAL___Keywords___Duality theory,Linear programming": 197, "7___CATEGORICAL___Keywords___Eigenvalue,Diagonalization,Spectrum,Characteristic polynomial": 198, "7___CATEGORICAL___Keywords___Eigenvalue,Eigenvector": 199, "7___CATEGORICAL___Keywords___Eigenvalue,Eigenvector,Diagonalization": 200, "7___CATEGORICAL___Keywords___Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial": 201, "7___CATEGORICAL___Keywords___Eigenvalue,Spectrum,Characteristic polynomial": 202, "7___CATEGORICAL___Keywords___Eigenvalue,Spectrum,Diagonalization,Characteristic polynomial": 203, "7___CATEGORICAL___Keywords___Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial": 204, "7___CATEGORICAL___Keywords___Eigenvector,Eigenvalue": 205, "7___CATEGORICAL___Keywords___Eigenvector,Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue": 206, "7___CATEGORICAL___Keywords___Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue": 207, "7___CATEGORICAL___Keywords___Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue,Diagonalization": 208, "7___CATEGORICAL___Keywords___Equations involving complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Real part": 209, "7___CATEGORICAL___Keywords___Euclidean spaces,Orthogonal basis": 210, "7___CATEGORICAL___Keywords___Euclidean spaces,Orthogonal basis,Basis": 211, "7___CATEGORICAL___Keywords___Event,Addition, multiplication, and total probability rules,Independence": 212, "7___CATEGORICAL___Keywords___Event,Addition, multiplication, and total probability rules,Sample space": 213, "7___CATEGORICAL___Keywords___Event,Axioms of probability": 214, "7___CATEGORICAL___Keywords___Event,Axioms of probability,Addition, multiplication, and total probability rules,Sample space": 215, "7___CATEGORICAL___Keywords___Event,Axioms of probability,Sample space": 216, "7___CATEGORICAL___Keywords___Event,Independence,Addition, multiplication, and total probability rules": 217, "7___CATEGORICAL___Keywords___Event,Sample space": 218, "7___CATEGORICAL___Keywords___Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability": 219, "7___CATEGORICAL___Keywords___Exact differential form,Cauchy problem": 220, "7___CATEGORICAL___Keywords___Excel solver add-in,Simplex method,Linear programming": 221, "7___CATEGORICAL___Keywords___Excel solver add-in,Simplex method,Linear programming,Transportation problem": 222, "7___CATEGORICAL___Keywords___Exponential function,Simplify expressions": 223, "7___CATEGORICAL___Keywords___Exponential rule": 224, "7___CATEGORICAL___Keywords___First order": 225, "7___CATEGORICAL___Keywords___First order,Directional derivative": 226, "7___CATEGORICAL___Keywords___First order,Directional derivative,Gradient": 227, "7___CATEGORICAL___Keywords___First order,Gradient": 228, "7___CATEGORICAL___Keywords___First order,Second order": 229, "7___CATEGORICAL___Keywords___Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median": 230, "7___CATEGORICAL___Keywords___Frequency,Quantile,Mean,Variance,Median,Mode": 231, "7___CATEGORICAL___Keywords___Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency": 232, "7___CATEGORICAL___Keywords___Fundamental theorem of Calculus,Volume of revolution": 233, "7___CATEGORICAL___Keywords___Geometric solids": 234, "7___CATEGORICAL___Keywords___Geometric solids,Geometrical figures,Classification of geometric solids": 235, "7___CATEGORICAL___Keywords___Geometrical figures": 236, "7___CATEGORICAL___Keywords___Geometrical figures,Polygons": 237, "7___CATEGORICAL___Keywords___Geometrical figures,Quadrilaterals,Rhombus": 238, "7___CATEGORICAL___Keywords___Geometrical figures,Triangles,Classification of geometrical figures": 239, "7___CATEGORICAL___Keywords___Gradient,Directional derivative": 240, "7___CATEGORICAL___Keywords___Gradient,First order": 241, "7___CATEGORICAL___Keywords___Gradient,First order,Directional derivative": 242, "7___CATEGORICAL___Keywords___Graphical method,Linear programming": 243, "7___CATEGORICAL___Keywords___Homogeneous equation": 244, "7___CATEGORICAL___Keywords___Homogeneous equation,Cauchy problem": 245, "7___CATEGORICAL___Keywords___Imaginary part,Complex plane ,Real part": 246, "7___CATEGORICAL___Keywords___Imaginary part,Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers": 247, "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers": 248, "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Operations with complex numbers,Real part,Equations involving complex numbers": 249, "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part": 250, "7___CATEGORICAL___Keywords___Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part": 251, "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system": 252, "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system": 253, "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Homogeneous system,Consistent system": 254, "7___CATEGORICAL___Keywords___Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system": 255, "7___CATEGORICAL___Keywords___Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system": 256, "7___CATEGORICAL___Keywords___Indeterminate forms,Limits": 257, "7___CATEGORICAL___Keywords___Injective linear application,Invertible linear operator,Isomorphism": 258, "7___CATEGORICAL___Keywords___Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism": 259, "7___CATEGORICAL___Keywords___Injective linear application,Isomorphism": 260, "7___CATEGORICAL___Keywords___Injective linear application,Range,Kernel,Isomorphism": 261, "7___CATEGORICAL___Keywords___Integration by parts": 262, "7___CATEGORICAL___Keywords___Integration by parts,Fundamental theorem of Calculus": 263, "7___CATEGORICAL___Keywords___Integration by parts,Substitution,Simple integration,Direct inspection": 264, "7___CATEGORICAL___Keywords___Intersection,Cartesian equations of a plane": 265, "7___CATEGORICAL___Keywords___Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix": 266, "7___CATEGORICAL___Keywords___Inverse matrix ,Determinant computation,Determinant properties,Matrix operations": 267, "7___CATEGORICAL___Keywords___Invertible linear operator,Isomorphism,Injective linear application": 268, "7___CATEGORICAL___Keywords___Iterate integrals": 269, "7___CATEGORICAL___Keywords___Iterate integrals,Area ,y-simple region (type I),Cartesian coordinates": 270, "7___CATEGORICAL___Keywords___Iterate integrals,Cartesian coordinates,y-simple region (type I)": 271, "7___CATEGORICAL___Keywords___Kernel,Isomorphism,Injective linear application,Range": 272, "7___CATEGORICAL___Keywords___Lagrange multipliers,Maximum,Minimum": 273, "7___CATEGORICAL___Keywords___Lagrange multipliers,Minimum,Maximum,Stationary point": 274, "7___CATEGORICAL___Keywords___Lagrange multipliers,Optimal solution,Minimum,Maximum": 275, "7___CATEGORICAL___Keywords___Lagrange's interpolation,Polynomial interpolation": 276, "7___CATEGORICAL___Keywords___Limits": 277, "7___CATEGORICAL___Keywords___Limits,Indeterminate forms": 278, "7___CATEGORICAL___Keywords___Linear application,Composition of linear applications": 279, "7___CATEGORICAL___Keywords___Linear application,Linearity": 280, "7___CATEGORICAL___Keywords___Linear combination,Span": 281, "7___CATEGORICAL___Keywords___Linear combination,Subspace,Span": 282, "7___CATEGORICAL___Keywords___Linear differential equation": 283, "7___CATEGORICAL___Keywords___Linear differential equation,Homogeneous equation": 284, "7___CATEGORICAL___Keywords___Linear differential equation,Integral curve,Cauchy problem": 285, "7___CATEGORICAL___Keywords___Linear equations,Quadratic equations,Simplify expressions": 286, "7___CATEGORICAL___Keywords___Linear independence,Span,Linear dependence": 287, "7___CATEGORICAL___Keywords___Linear independence,Subspace,Linear combination,Linear dependence,Span": 288, "7___CATEGORICAL___Keywords___Linear programming": 289, "7___CATEGORICAL___Keywords___Linear programming,Assignment problem,Excel solver add-in,Simplex method": 290, "7___CATEGORICAL___Keywords___Linear programming,Excel solver add-in,Simplex method": 291, "7___CATEGORICAL___Keywords___Linear regression": 292, "7___CATEGORICAL___Keywords___Linearity,Invertible linear operator,Composition of linear applications,Linear application": 293, "7___CATEGORICAL___Keywords___Linearity,Linear application": 294, "7___CATEGORICAL___Keywords___Linearity,Matrix of a linear transformation,Linear application": 295, "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": 296, "7___CATEGORICAL___Keywords___Linearly independent rows,Matrix rank": 297, "7___CATEGORICAL___Keywords___Locus,Distance": 298, "7___CATEGORICAL___Keywords___Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity": 299, "7___CATEGORICAL___Keywords___Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality": 300, "7___CATEGORICAL___Keywords___Logarithmic function,Exponential function,Simplify expressions": 301, "7___CATEGORICAL___Keywords___Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule": 302, "7___CATEGORICAL___Keywords___Logarithmic rule,Power rule,Trigonometric rules": 303, "7___CATEGORICAL___Keywords___Logarithmic rule,Product rule,Trigonometric rules": 304, "7___CATEGORICAL___Keywords___Logarithmic rule,Trigonometric rules": 305, "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": 306, "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": 307, "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": 308, "7___CATEGORICAL___Keywords___Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank": 309, "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": 310, "7___CATEGORICAL___Keywords___Matrix multiplication,Symmetric matrix,Matrix operations": 311, "7___CATEGORICAL___Keywords___Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties": 312, "7___CATEGORICAL___Keywords___Matrix of a linear transformation": 313, "7___CATEGORICAL___Keywords___Matrix of a linear transformation,Linear application,Linearity": 314, "7___CATEGORICAL___Keywords___Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix": 315, "7___CATEGORICAL___Keywords___Matrix operations,Determinant computation,Determinant properties,Inverse matrix": 316, "7___CATEGORICAL___Keywords___Matrix operations,Inverse matrix": 317, "7___CATEGORICAL___Keywords___Matrix operations,Matrix multiplication": 318, "7___CATEGORICAL___Keywords___Matrix operations,Matrix multiplication,Determinant computation,Determinant properties": 319, "7___CATEGORICAL___Keywords___Matrix rank,Linearly independent rows": 320, "7___CATEGORICAL___Keywords___Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation": 321, "7___CATEGORICAL___Keywords___Mean,Median,Mode": 322, "7___CATEGORICAL___Keywords___Mean,Median,Outliers,Interquartile range": 323, "7___CATEGORICAL___Keywords___Mean,Variance,Standard deviation,Median,Mode": 324, "7___CATEGORICAL___Keywords___Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance": 325, "7___CATEGORICAL___Keywords___Minimum,Maximum,Lagrange multipliers,Saddle point,Unconstrained optimization,Second derivative test": 326, "7___CATEGORICAL___Keywords___Minimum,Maximum,Stationary point,Second derivative test,Unconstrained optimization,Saddle point,Optimal solution": 327, "7___CATEGORICAL___Keywords___Minimum,Stationary point,Maximum,Saddle point,Optimal solution": 328, "7___CATEGORICAL___Keywords___Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median": 329, "7___CATEGORICAL___Keywords___Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number": 330, "7___CATEGORICAL___Keywords___Newton\u2019s interpolation,Polynomial interpolation": 331, "7___CATEGORICAL___Keywords___Newton\u2019s method,Nonlinear equation": 332, "7___CATEGORICAL___Keywords___Nonlinear equation,Newton\u2019s method": 333, "7___CATEGORICAL___Keywords___Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas": 334, "7___CATEGORICAL___Keywords___Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas": 335, "7___CATEGORICAL___Keywords___Operations with complex numbers": 336, "7___CATEGORICAL___Keywords___Operations with complex numbers,Conjugate number": 337, "7___CATEGORICAL___Keywords___Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part": 338, "7___CATEGORICAL___Keywords___Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form": 339, "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Maximum": 340, "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point": 341, "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Maximum,Stationary point,Saddle point": 342, "7___CATEGORICAL___Keywords___Optimal solution,Minimum,Stationary point,Maximum,Saddle point": 343, "7___CATEGORICAL___Keywords___Optimal solution,Second derivative test,Minimum,Maximum,Stationary point,Saddle point": 344, "7___CATEGORICAL___Keywords___Optimal solution,Stationary point,Minimum,Maximum,Saddle point": 345, "7___CATEGORICAL___Keywords___Orthogonal projection,Distance,Cross product,Orthogonality": 346, "7___CATEGORICAL___Keywords___Orthogonality": 347, "7___CATEGORICAL___Keywords___Orthogonality,Cross product": 348, "7___CATEGORICAL___Keywords___Orthogonality,Cross product,Distance": 349, "7___CATEGORICAL___Keywords___Orthogonality,Distance,Cross product": 350, "7___CATEGORICAL___Keywords___Orthogonality,Distance,Scalar product": 351, "7___CATEGORICAL___Keywords___Orthogonality,Locus,Scalar product,Cross product,Collinearity": 352, "7___CATEGORICAL___Keywords___Orthogonality,Orthogonal projection,Cross product,Scalar product": 353, "7___CATEGORICAL___Keywords___Orthogonality,Orthogonal projection,Distance": 354, "7___CATEGORICAL___Keywords___Orthogonality,Scalar product": 355, "7___CATEGORICAL___Keywords___Path,Cycle and circuit": 356, "7___CATEGORICAL___Keywords___Path,Simple graph,Cycle and circuit": 357, "7___CATEGORICAL___Keywords___Planar graph": 358, "7___CATEGORICAL___Keywords___Platonic solids": 359, "7___CATEGORICAL___Keywords___Platonic solids,Regular polygon": 360, "7___CATEGORICAL___Keywords___Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas": 361, "7___CATEGORICAL___Keywords___Polygons": 362, "7___CATEGORICAL___Keywords___Polygons,Geometric transformations,Geometrical figures": 363, "7___CATEGORICAL___Keywords___Polygons,Geometrical figures": 364, "7___CATEGORICAL___Keywords___Polygons,Regular polygon": 365, "7___CATEGORICAL___Keywords___Polygons,Triangles": 366, "7___CATEGORICAL___Keywords___Polyhedrons,Geometric solids,Classification of geometric solids": 367, "7___CATEGORICAL___Keywords___Polyhedrons,Platonic solids,Geometric solids": 368, "7___CATEGORICAL___Keywords___Polynomial interpolation,Lagrange's interpolation": 369, "7___CATEGORICAL___Keywords___Polynomial interpolation,Newton\u2019s interpolation": 370, "7___CATEGORICAL___Keywords___Population,Sample": 371, "7___CATEGORICAL___Keywords___Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean": 372, "7___CATEGORICAL___Keywords___Postoptimality analysis,Duality theory,Excel solver 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