# 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, Lambda, l
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, ModAbs
from proveit.physics.quantum.QPE import _full_domain, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = Lambda(l, Conditional(Equals(ModAbs(l, _two_pow_t), Abs(l)), InSet(l, _full_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())

l \mapsto \left\{\left|l\right|_{\textup{mod}\thinspace 2^{t}} = \left|l\right| \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameter: 18
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple18, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operand: 18
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple18, 17
13Literal
14ExprTuple18
15Literal
16ExprTuple19, 24
17Operationoperator: 25
operands: 20
18Variable
19Operationoperator: 29
operands: 21
20ExprTuple27, 31
21ExprTuple22, 35
22Operationoperator: 33
operand: 24
23ExprTuple24
24Operationoperator: 25
operands: 26
25Literal
26ExprTuple27, 28
27Literal
28Operationoperator: 29
operands: 30
29Literal
30ExprTuple31, 32
31Literal
32Operationoperator: 33
operand: 35
33Literal
34ExprTuple35
35Literal