Liste des dĂ©veloppements possibles 

 

> dev_possibles := {"LGN", "TCL", "TIL", "An_simple", "Lemme_Borel", "Lemme_Morse", "Loi_Gamma", "Action_SOn_Sn-1", "Borne_Bezout", "Cardinal_SO2q", "Ellipse_Steiner", "Ensembles_Julia", "Etude_astroide", "Extrema_lies", "Formule_Poisson", "Galton_Watson", "Geodesique_IH", "Loi_even_rares", "Lp_inclus_Lq", "Methode_Newton", "Nombres_Bell", "Nombres_normaux", "Pendule_amorti", "Sev_fermes_Cab", "Simplicite_SO3", "Simplicite_SOn", "Theoreme_Fejer", "Theoreme_Molien", "Theoreme_Muntz", "Algorithme_Faddeev", "Automorphismes_KX", "Formule_complements", "Prolongement_gamma", "Reduction_sym_cpct", "Serie_harmonique", "Sev_C01_normsup_2", "Table_caracteres_S4", "Theoreme_Bernstein", "Theoreme_Brouwer", "Theoreme_Burnside", "Theoreme_Chudnovsky", "Theoreme_Jordan_C1", "Theoreme_Kronecker", "Theoreme_Plancherel", "Algorithme_Wiedemann", "Courbe_brachistochrone", "Couronnes_biholomorphes", "Decomposition_Dunford", "Equation_Hill_Mathieu", "Existence_corps_finis", "Inversion_Fourier_L1", "Operateur_hypercyclique", "Operateurs_et_adjoint", "Points_extremaux_BLE", "Polynomes_orthogonaux", "Reciprocite_quadratique", "Reduction_endo_normaux", "Sous_algebre_reduite", "Sous_groupes_finis_SO3", "Theoreme_Abel_angulaire", "Theoreme_Browder_Goehde", "Theoreme_Grothendieck", "Theoreme_Lie_Kolchin", "Theoreme_Riesz_Fischer", "Theoreme_Sophie_Germain", "Theoreme_boule_chevelue", "Theoreme_deux_carres", "expu_diago_ssi_u_diago", "Algo_facteurs_invariants", "Calcul_integrale_Fresnel", "Inegalite_isoperimetrique", "Inversion_Fourier_distrib", "Irreductibilite_pol_cyclo", "Isometries_cube_tetraedre", "Methode_gradient_conjugue", "Nombre_matrices_diago_Fq", "Operateur_algebrique_Banach", "Primalite_nombres_Mersenne", "Prolongement_appl_lipsch", "Prolongement_dzeta_Re_pos", "Sev_dim_finie_C01_CVS_CVU", "Suite_polygones_converge", "Theoreme_Cartan_vonNeumann", "Theoreme_Cauchy_Lipschitz", "Theoreme_Chevalley_Warning", "Theoreme_Frechet_Kolmogorov", "Theoreme_Rothstein_Trager", "Theoreme_lacunes_Hadamard", "Classification_groupes_ordre_8", "Definition_bifocale_coniques", "Generateurs_groupe_orthogonal", "Partition_entier_parts_fixees", "Theoreme_Frobenius_Zolotarev", "Transformee_Fourier_gaussienne", "Composantes_connexes_fq_non_degen", "Comptage_racines_forme_quadratique", "Endomorphismes_MnC_stabilisent_GLnC", "Etude_asymptotique_suite_polynomes", "Exponentielle_MnC_GLnC_surjective", "Groupes_distingues_table_caracteres", "Semi_normes_invariantes_similitude", "Theoreme_Hahn_Banach_geometrique", "Densite_C01_fonctions_continues_nullepart_der"}:
 

 

> dev_lecons_couplees := {[101, {"Action_SOn_Sn-1", "Nombre_matrices_diago_Fq"}], [102, {"Irreductibilite_pol_cyclo", "Suite_polygones_converge"}], [103, {"Theoreme_Lie_Kolchin", "Simplicite_SO3"}], [104, {"Theoreme_Molien", "Nombre_matrices_diago_Fq"}], [105, {"Table_caracteres_S4", "Theoreme_Frobenius_Zolotarev"}], [106, {"Action_SOn_Sn-1", "Simplicite_SO3"}], [107, {"Theoreme_Molien", "Table_caracteres_S4"}], [108, {"Simplicite_SO3", "Sous_algebre_reduite"}], [109, {"Theoreme_Molien", "Table_caracteres_S4"}], [120, {"Reciprocite_quadratique", "Irreductibilite_pol_cyclo"}], [121, {"Reciprocite_quadratique", "Irreductibilite_pol_cyclo"}], [122, {"Algo_facteurs_invariants", "Theoreme_Rothstein_Trager"}], [123, {"Existence_corps_finis", "Reciprocite_quadratique"}], [124, {"Theoreme_Molien", "Partition_entier_parts_fixees"}], [125, {"Automorphismes_KX", "Existence_corps_finis"}], [126, {"Reciprocite_quadratique", "Partition_entier_parts_fixees"}], [140, {"Automorphismes_KX", "Partition_entier_parts_fixees"}], [141, {"Existence_corps_finis", "Irreductibilite_pol_cyclo"}], [142, {"Borne_Bezout", "Theoreme_Molien"}], [143, {"Borne_Bezout", "Theoreme_Rothstein_Trager"}], [144, {"Theoreme_Kronecker", "Irreductibilite_pol_cyclo"}], [150, {"Simplicite_SO3", "Nombre_matrices_diago_Fq"}], [151, {"Theoreme_Molien", "Automorphismes_KX"}], [152, {"Borne_Bezout", "Suite_polygones_converge"}], [153, {"Decomposition_Dunford", "Sous_algebre_reduite"}], [154, {"Reduction_endo_normaux", "Theoreme_Lie_Kolchin"}], [155, {"Equation_Hill_Mathieu", "Reduction_endo_normaux"}], [156, {"Theoreme_Cartan_vonNeumann", "Exponentielle_MnC_GLnC_surjective"}], [157, {"Decomposition_Dunford", "Sous_algebre_reduite"}], [158, {"Lemme_Morse", "Composantes_connexes_fq_non_degen"}], [159, {"Extrema_lies", "Reciprocite_quadratique"}], [160, {"Simplicite_SO3", "Reduction_endo_normaux"}], [161, {"Simplicite_SO3", "Reduction_endo_normaux"}], [162, {"Methode_gradient_conjugue", "Algo_facteurs_invariants"}], [170, {"Lemme_Morse", "Reciprocite_quadratique"}], [171, {"Lemme_Morse", "Composantes_connexes_fq_non_degen"}], [180, {"Ellipse_Steiner", "Definition_bifocale_coniques"}], [181, {"Ellipse_Steiner", "Suite_polygones_converge"}], [182, {"Ellipse_Steiner", "Suite_polygones_converge"}], [183, {"Action_SOn_Sn-1", "Ellipse_Steiner"}], [190, {"Reciprocite_quadratique", "Nombre_matrices_diago_Fq"}], [201, {"Polynomes_orthogonaux", "Theoreme_Riesz_Fischer"}], [202, {"Theoreme_Fejer", "Densite_C01_fonctions_continues_nullepart_der"}], [203, {"Reduction_sym_cpct", "Theoreme_Jordan_C1"}], [204, {"Simplicite_SO3", "Theoreme_Jordan_C1"}], [205, {"Reduction_sym_cpct", "Theoreme_Cauchy_Lipschitz"}], [206, {"TIL", "Theoreme_Cauchy_Lipschitz"}], [207, {"Polynomes_orthogonaux", "Couronnes_biholomorphes"}], [208, {"Reduction_sym_cpct", "Theoreme_Riesz_Fischer"}], [209, {"Theoreme_Fejer", "Theoreme_Bernstein"}], [213, {"Reduction_sym_cpct", "Polynomes_orthogonaux"}], [214, {"Lemme_Morse", "TIL"}], [215, {"Theoreme_Cartan_vonNeumann", "Extrema_lies"}], [216, {"Courbe_brachistochrone", "Inegalite_isoperimetrique"}], [217, {"Extrema_lies", "Theoreme_Cartan_vonNeumann"}], [218, {"Methode_Newton", "Decomposition_Dunford"}], [219, {"Extrema_lies", "Courbe_brachistochrone"}], [220, {"Courbe_brachistochrone", "Equation_Hill_Mathieu"}], [221, {"Equation_Hill_Mathieu", "Etude_asymptotique_suite_polynomes"}], [223, {"Methode_Newton", "Couronnes_biholomorphes"}], [224, {"Serie_harmonique", "Etude_asymptotique_suite_polynomes"}], [226, {"Methode_Newton", "Decomposition_Dunford"}], [228, {"Theoreme_Bernstein", "Densite_C01_fonctions_continues_nullepart_der"}], [229, {"Galton_Watson", "Courbe_brachistochrone"}], [230, {"Serie_harmonique", "Theoreme_Abel_angulaire"}], [232, {"Methode_Newton", "Methode_gradient_conjugue"}], [234, {"Polynomes_orthogonaux", "Theoreme_Riesz_Fischer"}], [235, {"Theoreme_Fejer", "Theoreme_Riesz_Fischer"}], [236, {"Inegalite_isoperimetrique", "Transformee_Fourier_gaussienne"}], [239, {"Theoreme_Jordan_C1", "Transformee_Fourier_gaussienne"}], [240, {"Transformee_Fourier_gaussienne", "Inversion_Fourier_distrib"}], [241, {"Theoreme_Fejer", "Theoreme_Riesz_Fischer"}], [243, {"Nombres_Bell", "Theoreme_Abel_angulaire"}], [244, {"Nombres_Bell", "Theoreme_Abel_angulaire"}], [245, {"Couronnes_biholomorphes", "Transformee_Fourier_gaussienne"}], [246, {"Theoreme_Fejer", "Inegalite_isoperimetrique"}], [247, {"Theoreme_Abel_angulaire", "Serie_harmonique"}], [249, {"Nombres_normaux", "Theoreme_Bernstein"}], [253, {"Methode_gradient_conjugue", "Courbe_brachistochrone"}], [254, {"Formule_Poisson", "Inversion_Fourier_distrib"}], [255, {"Formule_Poisson", "Inversion_Fourier_distrib"}], [260, {"Galton_Watson", "Theoreme_Bernstein"}], [261, {"Transformee_Fourier_gaussienne", "Galton_Watson"}], [262, {"TCL", "Theoreme_Riesz_Fischer"}], [263, {"TCL", "Transformee_Fourier_gaussienne"}], [264, {"Nombres_normaux", "Theoreme_Bernstein"}]}:
 

> select(y -> evalb(y[2] < 2), map(x -> [x[1], nops(x[2])], %));
 

(1)
 

> dev := `union`(op(map(x -> x[2], dev_lecons_couplees)));dev subset dev_possibles; nops(dev);
 

 

 

{
{
{
{
{
{
{
{
{
{
{
{
{
{
true
52 (2)
 

> #analyse : 24 algèbre : 22 deux : 7
 

> dev_lecons_utile := sort([seq([dev_courant, map(y -> y[1], select(x -> evalb(dev_courant in x[2]), dev_lecons_couplees))], dev_courant in dev)], (x, y) -> nops(x[2]) > nops(y[2]));
 

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(3)
 

> dev_nb_lecons_utile := map(x -> [x[1], nops(x[2])], dev_lecons_utile);
 

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(4)
 

> Statistics[Mean](map(x -> x[2], dev_nb_lecons_utile));
 

3.307692308 (5)
 

> Statistics[Median](map(x -> x[2], dev_nb_lecons_utile));
 

3. (6)
 

> Statistics[StandardDeviation](map(x -> x[2], dev_nb_lecons_utile));
 

HFloat(1.4624510923742817) (7)
 

>