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Expression of type InSet

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 l
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Real, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
expr = InSet(Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain)), Real)
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(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right) \in \mathbb{R}
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.()()('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: 23
operands: 1
1ExprTuple2, 3
2Operationoperator: 56
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 8
operand: 10
6Operationoperator: 8
operand: 11
7ExprTuple10
8Literal
9ExprTuple11
10Lambdaparameter: 42
body: 12
11Lambdaparameter: 42
body: 14
12Conditionalvalue: 15
condition: 16
13ExprTuple42
14Conditionalvalue: 17
condition: 18
15Operationoperator: 21
operands: 19
16Operationoperator: 23
operands: 20
17Operationoperator: 21
operands: 22
18Operationoperator: 23
operands: 24
19ExprTuple68, 25
20ExprTuple42, 26
21Literal
22ExprTuple68, 27
23Literal
24ExprTuple42, 28
25Operationoperator: 58
operands: 29
26Operationoperator: 32
operands: 30
27Operationoperator: 58
operands: 31
28Operationoperator: 32
operands: 33
29ExprTuple42, 63
30ExprTuple34, 35
31ExprTuple36, 63
32Literal
33ExprTuple41, 47
34Operationoperator: 56
operands: 37
35Operationoperator: 66
operand: 41
36Operationoperator: 56
operands: 39
37ExprTuple40, 68
38ExprTuple41
39ExprTuple42, 43
40Operationoperator: 66
operand: 47
41Operationoperator: 56
operands: 45
42Variable
43Operationoperator: 66
operand: 49
44ExprTuple47
45ExprTuple48, 68
46ExprTuple49
47Operationoperator: 58
operands: 50
48Variable
49Operationoperator: 51
operands: 52
50ExprTuple63, 53
51Literal
52ExprTuple54, 55
53Operationoperator: 56
operands: 57
54Operationoperator: 58
operands: 59
55Operationoperator: 60
operand: 65
56Literal
57ExprTuple64, 62
58Literal
59ExprTuple63, 64
60Literal
61ExprTuple65
62Operationoperator: 66
operand: 68
63Literal
64Literal
65Literal
66Literal
67ExprTuple68
68Literal