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Exponent

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Exponent[expr, form] gives the maximum power with which form appears in the
expanded form of expr.
Exponent[expr, form, h] applies h to the set of exponents (default Max).
form may be a symbol, a kernel, or a product of terms; expr need not be
expanded.  Exponent is purely syntactic (no zero-coefficient recognition).
Exponent[0, x] is -Infinity.  Exponent[expr, {f1, f2, ...}] gives the list of
exponents for each fi.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Exponent[1 + x^2 + a x^3, x]
Out[1]= 3

In[2]:= Exponent[0, x]
Out[2]= -Infinity

In[3]:= Exponent[x^(n+1) + 2 Sqrt[x] + 1, x]
Out[3]= Max[1/2, 1 + n]

In[4]:= Exponent[(x^2+1)^3 - 1, x, Min]
Out[4]= 2

In[5]:= Exponent[1 + x^2 + a x^3, x, List]
Out[5]= {0, 2, 3}

Implementation notes

  • Listable, Protected.
  • The default aggregator is h = Max. Exponent[expr, form, Min] gives the lowest power; Exponent[expr, form, List] gives the sorted, de-duplicated set of exponents.
  • form may be a symbol, a kernel (e.g. Sin[x]), or a product of terms.
  • Works whether or not expr is explicitly given in expanded form (it expands internally).
  • Purely syntactic: it does not attempt to recognise zero coefficients.
  • Exponents may be rational numbers or symbolic expressions.
  • Exponent[0, x] is -Infinity (empty exponent set, h = Max).
  • The Listable attribute makes Exponent[expr, {form1, form2, ...}] give the list of exponents for each formi.

Attributes: Listable, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References