# 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, b, c
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Mult, Real, zero

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(Exp(a, b), Exp(a, c)), Exp(a, Add(b, c))), And(InSet(a, Complex), InSet(b, Real), InSet(c, Real), NotEquals(a, zero)))

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\{\left(a^{b} \cdot a^{c}\right) = a^{b + c} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  a \neq 0\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, 11, 12
7Operationoperator: 13
operands: 14
8Operationoperator: 29
operands: 15
9Operationoperator: 18
operands: 16
10Operationoperator: 18
operands: 17
11Operationoperator: 18
operands: 19
12Operationoperator: 20
operands: 21
13Literal
14ExprTuple22, 23
15ExprTuple33, 24
16ExprTuple33, 25
17ExprTuple34, 26
18Literal
19ExprTuple35, 26
20Literal
21ExprTuple33, 27
22Operationoperator: 29
operands: 28
23Operationoperator: 29
operands: 30
24Operationoperator: 31
operands: 32
25Literal
26Literal
27Literal
28ExprTuple33, 34
29Literal
30ExprTuple33, 35
31Literal
32ExprTuple34, 35
33Variable
34Variable
35Variable