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, c
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Exp, Mult, RealPos
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, RealPos), InSet(c, RealPos)))))
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}^+\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
2ExprTuple32, 33, 34
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14
10Operationoperator: 15
operands: 16
11Operationoperator: 28
operands: 17
12Operationoperator: 20
operands: 18
13Operationoperator: 20
operands: 19
14Operationoperator: 20
operands: 21
15Literal
16ExprTuple22, 23
17ExprTuple32, 24
18ExprTuple32, 25
19ExprTuple33, 26
20Literal
21ExprTuple34, 26
22Operationoperator: 28
operands: 27
23Operationoperator: 28
operands: 29
24Operationoperator: 30
operands: 31
25Literal
26Literal
27ExprTuple32, 33
28Literal
29ExprTuple32, 34
30Literal
31ExprTuple33, 34
32Variable
33Variable
34Variable