# 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 Conditional, l
from proveit.logic import And, Equals, InSet, TRUE
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Exp(Abs(_rel_indexed_alpha), two)
sub_expr2 = InSet(l, _neg_domain)
expr = Equals(Conditional(sub_expr1, And(sub_expr2, TRUE)), Conditional(sub_expr1, sub_expr2)).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} ,  \top\right.. \\  = \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right.. \end{array} \end{array}

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()(1)('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Conditionalvalue: 6
condition: 5
4Conditionalvalue: 6
condition: 10
5Operationoperator: 7
operands: 8
6Operationoperator: 38
operands: 9
7Literal
8ExprTuple10, 11
9ExprTuple12, 40
10Operationoperator: 13
operands: 14
11Literal
12Operationoperator: 15
operand: 18
13Literal
14ExprTuple33, 17
15Literal
16ExprTuple18
17Operationoperator: 19
operands: 20
18Operationoperator: 21
operand: 25
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25
23Operationoperator: 42
operands: 26
24Operationoperator: 46
operand: 31
25Operationoperator: 28
operands: 29
26ExprTuple30, 48
27ExprTuple31
28Literal
29ExprTuple32, 33
30Operationoperator: 46
operand: 36
31Operationoperator: 42
operands: 35
32Literal
33Variable
34ExprTuple36
35ExprTuple37, 48
36Operationoperator: 38
operands: 39
37Variable
38Literal
39ExprTuple40, 41
40Literal
41Operationoperator: 42
operands: 43
42Literal
43ExprTuple44, 45
44Literal
45Operationoperator: 46
operand: 48
46Literal
47ExprTuple48
48Literal