# from the theory of proveit.numbers.exponentiation¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, a, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Exp, NaturalPos, Neg, frac, one

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(a, Neg(n)), frac(one, Exp(a, n))), And(InSet(a, ComplexNonZero), InSet(n, NaturalPos)))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{a^{-n} = \frac{1}{a^{n}} \textrm{ if } a \in \mathbb{C}^{\neq 0} ,  n \in \mathbb{N}^+\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10
7Operationoperator: 24
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11ExprTuple26, 17
12Literal
13ExprTuple18, 19
14ExprTuple26, 20
15Literal
16ExprTuple27, 21
17Operationoperator: 22
operand: 27
18Literal
19Operationoperator: 24
operands: 25
20Literal
21Literal
22Literal
23ExprTuple27
24Literal
25ExprTuple26, 27
26Variable
27Variable