Geodesic
Reduction for systems of nonlinear equations with symmetry
Matematičeskoe modelirovanie, Tome 3 (1991) no. 6, pp. 72-83.

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The method of reduction of symmetrical systems of equations is proposed. Solutions of reduced systems are solutions of the initial system invariant upon a given group of matrices. Constructed systems are of the same dimension as the initial one. The method of automatical group analysis and automatical reduction is introduced for a case of equivariancy upon transpositions. The method is used in the code “Ariadna”. 
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     author = {G. G. Yelenin and Yu. V. Troshchiev},
     title = {Reduction for systems of nonlinear equations with symmetry},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {72--83},
     publisher = {mathdoc},
     volume = {3},
     number = {6},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1991_3_6_a6/}
}
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G. G. Yelenin; Yu. V. Troshchiev. Reduction for systems of nonlinear equations with symmetry. Matematičeskoe modelirovanie, Tome 3 (1991) no. 6, pp. 72-83. http://geodesic.mathdoc.fr/item/MM_1991_3_6_a6/