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algebraic program algebraic variable ALGOL 60 program arccos ARCTAN AUGMENT INDEX B(Cefr begin integer begin real BINOMIAL COEFF(2 Boolean BOUND ON ARGUMENT CALC OF UNKNOWNS calculate the Taylor Cauchy problem coeff commutative law complex numbers computational program CONV PRODUCT declared DEF ALGOL ST DEFINE TAYLOR COEFFICIENTS diff eq[3 diff eq[new differential equations dimension element(T elementary functions end else begin end else if_ end end end formula program free arr free indexes free set goto highest degree index from free index vector index[i input tape integer array integer procedure JUMP TO CALC multivalued functions numb of free number of Taylor order do begin output PR array PR ass st PR conv PR string PR zeroth array procedure Taylor index real procedure set of free st for arr step subformulae take index tauO Taylor arrays Taylor series theorem TRANSFORM Z-aT zeroth array element