# 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 ExprTuple, Lambda, l
from proveit.logic import Bijections
from proveit.numbers import Add, Mod
from proveit.physics.quantum.QPE import _b_floor, _full_domain, _m_domain, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(l, Mod(Add(_b_floor, l), _two_pow_t)), Bijections(_full_domain, _m_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(l \mapsto \left(\left(b_{\textit{f}} + l\right) ~\textup{mod}~ 2^{t}\right), \left[\{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~2^{t} - 1\}\right]\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Lambdaparameter: 20
body: 4
2Operationoperator: 5
operands: 6
3ExprTuple20
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 24
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11Operationoperator: 32
operands: 15
12ExprTuple16, 27
13Literal
14ExprTuple17, 18
15ExprTuple19, 20
16Operationoperator: 32
operands: 21
17Literal
18Operationoperator: 32
operands: 22
19Literal
20Variable
21ExprTuple23, 38
22ExprTuple24, 35
23Operationoperator: 36
operand: 27
24Operationoperator: 28
operands: 26
25ExprTuple27
26ExprTuple30, 34
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Literal
31Operationoperator: 32
operands: 33
32Literal
33ExprTuple34, 35
34Literal
35Operationoperator: 36
operand: 38
36Literal
37ExprTuple38
38Literal