FUNCTION derive_definite_integral_domain

(* SCHEMA mathematical_functions_schema; *)

FUNCTION derive_definite_integral_domain(igrl : definite_integral_function)
                                        : tuple_space;

  -- Internal utility function:
  FUNCTION process_product_space(spc         : product_space;
                                 idx, prefix : INTEGER;
                                 vdomn       : maths_space) : product_space;
    LOCAL
      uspc : uniform_product_space;
      expnt : INTEGER;
      factors : LIST OF maths_space;
    END_LOCAL;
    IF (schema_prefix + 'UNIFORM_PRODUCT_SPACE') IN TYPEOF (spc) THEN
      uspc := spc;
      expnt := uspc.exponent + prefix;
      IF idx <= uspc.exponent THEN  expnt := expnt - 1;  END_IF;
      IF expnt = 0 THEN
        RETURN (make_listed_product_space([]));
      ELSE
        RETURN (make_uniform_product_space(uspc.base,expnt));
      END_IF;
    ELSE
      factors := spc\listed_product_space.factors;
      IF idx <= SIZEOF (factors) THEN  REMOVE (factors, idx);  END_IF;
      IF prefix > 0 THEN
        INSERT (factors, vdomn, 0);
        IF prefix > 1 THEN  INSERT (factors, vdomn, 0);  END_IF;
      END_IF;
      RETURN (make_listed_product_space(factors));
    END_IF;
  END_FUNCTION;  -- process_product_space

  -- Resume body of derive_definite_integral_domain function
  LOCAL
    idomn : tuple_space := igrl.integrand.domain;
    types : SET OF STRING := TYPEOF (idomn);
    idx : INTEGER := igrl.variable_of_integration;
    tupled : BOOLEAN := bool(((space_dimension(idomn) = 1) AND
                             ((schema_prefix + 'TUPLE_SPACE') IN types)));
    prefix : INTEGER := 0;
    espc : extended_tuple_space;
    vdomn : maths_space;
  END_LOCAL;
  IF tupled THEN
    idomn := factor1(idomn);
    types := TYPEOF (idomn);
  END_IF;
  IF igrl.lower_limit_neg_infinity THEN  prefix := prefix + 1;  END_IF;
  IF igrl.upper_limit_pos_infinity THEN  prefix := prefix + 1;  END_IF;
  vdomn := factor_space(idomn,idx);
  IF (schema_prefix + 'EXTENDED_TUPLE_SPACE') IN types THEN
    espc := idomn;
    idomn := make_extended_tuple_space(process_product_space(espc.base,idx,
      prefix,vdomn),espc.extender);
  ELSE
    idomn := process_product_space(idomn,idx,prefix,vdomn);
  END_IF;
  IF tupled THEN  RETURN (one_tuples_of(idomn));
  ELSE            RETURN (idomn);                 END_IF;
END_FUNCTION;  -- derive_definite_integral_domain

Referenced By

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2012-03-27T17:13:59-04:00