# 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.
# import Expression classes needed to build the expression
from proveit import b
from proveit.logic import Forall, InSet, Set
from proveit.numbers import IntervalOC, Neg, frac, one, two
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b

In [2]:
# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
expr = Forall(instance_param_or_params = [b], instance_expr = InSet(_delta_b, IntervalOC(Neg(sub_expr1), sub_expr1)), domain = Set(_b_floor, _b_round))

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())

\forall_{b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\}}~\left(\delta_{b} \in \left(-\frac{1}{2},\frac{1}{2}\right]\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 19
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple19, 12
10Operationoperator: 13
operand: 19
11Operationoperator: 15
operands: 16
12Operationoperator: 17
operands: 18
13Literal
14ExprTuple19
15Literal
16ExprTuple20, 25
17Literal
18ExprTuple21, 22
19Variable
20Operationoperator: 23
operand: 25
21Literal
22Literal
23Literal
24ExprTuple25
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Literal
29Literal