logo

Expression of type ExprTuple

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, ExprTuple, Lambda, a, b, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, n], Conditional(Equals(Exp(Mult(a, b), n), Mult(Exp(a, n), Exp(b, n))), And(InSet(a, Complex), InSet(b, Complex), 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(\left(a, b, n\right) \mapsto \left\{\left(a \cdot b\right)^{n} = \left(a^{n} \cdot b^{n}\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  n \in \mathbb{N}^+\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
2ExprTuple31, 32, 33
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14
10Operationoperator: 29
operands: 15
11Operationoperator: 26
operands: 16
12Operationoperator: 19
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15ExprTuple21, 33
16ExprTuple22, 23
17ExprTuple31, 24
18ExprTuple32, 24
19Literal
20ExprTuple33, 25
21Operationoperator: 26
operands: 27
22Operationoperator: 29
operands: 28
23Operationoperator: 29
operands: 30
24Literal
25Literal
26Literal
27ExprTuple31, 32
28ExprTuple31, 33
29Literal
30ExprTuple32, 33
31Variable
32Variable
33Variable