# 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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([a, b, c], 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, c\right) \mapsto \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..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple36, 37, 38
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14, 15
10Operationoperator: 16
operands: 17
11Operationoperator: 32
operands: 18
12Operationoperator: 21
operands: 19
13Operationoperator: 21
operands: 20
14Operationoperator: 21
operands: 22
15Operationoperator: 23
operands: 24
16Literal
17ExprTuple25, 26
18ExprTuple36, 27
19ExprTuple36, 28
20ExprTuple37, 29
21Literal
22ExprTuple38, 29
23Literal
24ExprTuple36, 30
25Operationoperator: 32
operands: 31
26Operationoperator: 32
operands: 33
27Operationoperator: 34
operands: 35
28Literal
29Literal
30Literal
31ExprTuple36, 37
32Literal
33ExprTuple36, 38
34Literal
35ExprTuple37, 38
36Variable
37Variable
38Variable