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Expression of type Conditional

from the theory of proveit.physics.quantum.QPE

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, e
from proveit.logic import InSet
from proveit.numbers import Real
from proveit.physics.quantum.QPE import Pfail, _e_domain
In [2]:
# build up the expression from sub-expressions
expr = Conditional(InSet(Pfail(e), Real), InSet(e, _e_domain))
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[P_{\rm fail}\right]\left(e\right) \in \mathbb{R} \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\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: 4
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple13, 8
6Operationoperator: 9
operand: 13
7Literal
8Operationoperator: 11
operands: 12
9Literal
10ExprTuple13
11Literal
12ExprTuple29, 14
13Variable
14Operationoperator: 23
operands: 15
15ExprTuple16, 17
16Operationoperator: 18
operands: 19
17Operationoperator: 27
operand: 22
18Literal
19ExprTuple22, 21
20ExprTuple22
21Operationoperator: 23
operands: 24
22Literal
23Literal
24ExprTuple25, 26
25Literal
26Operationoperator: 27
operand: 29
27Literal
28ExprTuple29
29Literal