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Expression of type Conditional

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(Exp(a, Neg(b)), n), Exp(a, Neg(Mult(b, n)))), And(InSet(a, Complex), InSet(b, Complex), 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\{(a^{-b})^{n} = a^{-\left(b \cdot n\right)} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  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
7Operationoperator: 23
operands: 12
8Operationoperator: 23
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operands: 18
12ExprTuple19, 34
13ExprTuple26, 20
14ExprTuple26, 21
15Literal
16ExprTuple33, 21
17Literal
18ExprTuple26, 22
19Operationoperator: 23
operands: 24
20Operationoperator: 29
operand: 28
21Literal
22Literal
23Literal
24ExprTuple26, 27
25ExprTuple28
26Variable
27Operationoperator: 29
operand: 33
28Operationoperator: 31
operands: 32
29Literal
30ExprTuple33
31Literal
32ExprTuple33, 34
33Variable
34Variable