Is_Totally_Polynomial - Texas Instruments TI-89 Developer's Manual

258

is_totally_polynomial

Declaration: Boolean is_totally_polynomial (EStackIndex i )
Category(ies): Algebra Utilities
Description: Determines whether the expression indexed by i is polynomial in all of its
variables, generalized to permit non-negative fractional powers of
variables.
i
Inputs:
Outputs: Returns TRUE if the expression indexed by i is polynomial in all of its
variables, generalized to permit non-negative fractional powers of
variables. Otherwise returns FALSE.
Assumptions: None
Side Effects: None
Availability: All versions of the TI-89 / TI-92 Plus.
TI-89 / TI-92 Plus
None
Differences:
See Also: is_polynomial_in_var_or_kern
Example: Returns TRUE if i indexes (x^(1/2) + y) † x.
Returns TRUE if i indexes p + ln(2).
Returns FALSE if i indexes x^-1 + 2.
Returns FALSE if i indexes ln(x).
Boolean is_totally_polynomial (EStackIndex i)
{ Quantum q;
for (;;)
{ if (is_variable (i) || is_constant (i)) return TRUE;
if (EXPONENTIATION_TAG == (q = ESTACK (i)))
{ q = ESTACK (next_expression_index (--i));
if (is_variable (i))
return NONNEGATIVE_INTEGER_TAG == q ||
if (NONNEGATIVE_INTEGER_TAG != q) return FALSE;
}
else if ((ADD_TAG == q || MULTIPLY_TAG == q) &&
is_totally_polynomial (--i) )
i = next_expression_index (i);
else return FALSE;
}
}
TI-89 / TI-92 Plus Developer Guide
Appendix A: System Routines — Algebra Utilities
— Index of the top tag of an internally-simplified algebraic expression.
POSITIVE_FRACTION_TAG == q;
Not for Distribution Beta Version January 26, 2001